Light and Video Microscopy
Light and Video Microscopy
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Light and Video Microscopy
Randy Wayne
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This book is dedicated to my brother Scott.
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
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Contents
Preface
1. The Relation between the Object
and the Image
Luminous and Nonluminous Objects
Object and Image
Theories of Vision
Light Travels in Straight Lines
Images Formed in a Camera Obscura: Geometric
Considerations
Where Does Light Come From?
How Can the Amount of Light Be Measured?
2. The Geometric Relationship between
Object and Image
Reflection by a Plane Mirror
Reflection by a Curved Mirror
Reflection from Various Sources
Images Formed by Refraction at a Plane Surface
Images Formed by Refraction at a Curved Surface
Fermat’s Principle
Optical Path Length
Lens Aberrations
Geometric Optics and Biology
Geometric Optics of the Human Eye
Web Resources
3. The Dependence of Image Formation
on the Nature Of Light
Christiaan Huygens and the Invention of the
Wave Theory of Light
Thomas Young and the Development of the Wave
Theory of Light
James Clerk Maxwell and the Wave Theory of Light
Ernst Abbe and the Relationship of Diffraction to
Image Formation
Resolving Power and the Limit of Resolution
Contrast
Web Resources
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4. Bright-Field Microscopy
Components of the Microscope
The Optical Paths of the Light Microscope
Using the Bright-Field Microscope
Depth of Field
Out-of-Focus Contrast
Uses of Bright-Field Microscopy
Care and Cleaning of the Light Microscope
Web Resources
5. Photomicrography
Setting up the Microscope for Photomicrography
Scientific History of Photography
General Nature of the Photographic Process
The Resolution of the Film
Exposure and Composition
The Similarities between Film and the Retina
Web Resources
6. Methods of Generating Contrast
Dark-Field Microscopy
Rheinberg Illumination
Oblique Illumination
Phase-Contrast Microscopy
Oblique Illumination Reconsidered
Annular Illumination
7. Polarization Microscopy
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What Is Polarized Light?
Use an Analyzer to Test for Polarized Light
Production of Polarized Light
Influencing Light
Design of a Polarizing Microscope
What Is the Molecular Basis of Birefringence?
Interference of Polarized Light
The Origin of Colors in Birefringent Specimens
Use of Compensators to Determine the
Magnitude and Sign of Birefringence
Crystalline versus Form Birefringence
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Contents
Orthoscopic versus Conoscopic Observations
Reflected Light Polarization Microscopy
Uses of Polarization Microscopy
Optical Rotatory (or Rotary) Polarization and
Optical Rotatory (or Rotary) Dispersion
Web Resources
8. Interference Microscopy
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Generation of Interference Colors
The Relationship of Interference Microscopy
to Phase-Contrast Microscopy
Quantitative Interference Microscopy:
Determination of the Refractive Index, Mass,
Concentration of Dry Matter, Concentration of
Water, and Density
Source of Errors When Using an Interference
Microscope
Making a Coherent Reference Beam
Double-Beam versus Multiple-Beam
Interference
Interference Microscopes Based on a MachZehnder Type Interferometer
Interference Microscopes Based on Polarized
Light
The Use of Transmission Interference
Microscopy in Biology
Reflection-Interference Microscopy
Uses of Reflection-Interference Microscopy
in Biology
9. Differential Interference Contrast
(DIC) Microscopy
Design of a Transmitted Light Differential
Interference Contrast Microscope
Interpretation of a Transmitted Light
Differential Interference Contrast Image
Design of a Reflected Light Differential
Interference Contrast Microscope
Interpretation of a Reflected Light Differential
Interference Contrast Image
10. Amplitude Modulation Contrast
Microscopy
Hoffman Modulation Contrast Microscopy
Reflected Light Hoffman Modulation Contrast
Microscopy
The Single-Sideband Edge Enhancement
Microscope
11. Fluorescence Microscopy
Discovery of Fluorescence
Physics of Fluorescence
Design of a Fluorescence Microscope
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Fluorescence Probes
Pitfalls and Cures in Fluorescence Microscopy
Web Resources
12. Various Types of Microscopes and
Accessories
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Confocal Microscopes
Laser Microbeam Microscope
Optical Tweezers
Laser Capture Microdissection
Laser Doppler Microscope
Centrifuge Microscope
X-Ray Microscope
Infrared Microscope
Nuclear Magnetic Resonance Imaging
Microscope
Stereo Microscopes
Scanning Probe Microscopes
Acoustic Microscope
Horizontal and Traveling Microscopes
Microscopes for Children
Microscope Accessories
Web Resources
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13. Video and Digital Microscopy
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The Value of Video and Digital Microscopy
Video and Digital Cameras: The Optical to
Electrical Signal Converters
Monitors: Conversion of an Electronic Signal
into an Optical Signal
Storage of Video and Digital Images
Connecting a Video System
Web Resources
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14. Image Processing and Analysis
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Analog Image Processing
Digital Image Processing
Enhancement Functions of Digital Image
Processors
Analysis Functions of Digital Image Processors
The Ethics of Digital Image Processing
Web Resources
15. Laboratory Exercises
Laboratory 1: The Nature of Light and
Geometric Optics
Laboratory 2: Physical Optics
Laboratory 3: The Bright-Field Microscope
and Image Formation
Laboratory 4: Phase-Contrast Microscopy,
Dark-Field Microscopy, Rheinberg
Illumination, and Oblique Illumination
Laboratory 5: Fluorescence Microscopy
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ix
Contents
Laboratory 6: Polarized Light
240
Laboratory 7: Polarizing Light Microscopy
241
Laboratory 8: Interference Microscopy
241
Laboratory 9: Differential Interference
Contrast Microscopy and Hoffman Modulation
Contrast Microscopy
242
Laboratory 10: Video and Digital Microscopy
and Analog and Digital Image Processing
243
Commercial Sources for Laboratory Equipment
and Specimens
245
References
247
Appendix I. A Final Exam
273
Appendix II. A Microscopist’s Model of
the Photon
277
Index
285
Visit our companion website for additional book content, including answers to the final exam in the book, all of the images
from the book, and additional color images HYPERLINK “http://www.elsevierdirect.com/companions/9780123742346”
www.elsevierdirect.com/companions/9780123742346
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Preface
I am very lucky. I am sitting in the rare book room of the
library waiting for Robert Hooke’s (1665) Micrographia,
Matthias Schleiden’s (1849) Principles of Scientific
Botany, and Hermann Schacht’s (1853) The Microscope.
I am thankful for the microscopists and librarians at Cornell
University, both living and dead, who have nurtured a continuous link between the past and the present. By doing so,
they have built a strong foundation for the future.
Robert Hooke (1665) begins the Micrographia by stating that “… the science of nature has already too long
made only a work of the brain and the fancy: It is now high
time that it should return to the plainness and soundness of
observations on material and obvious things.” Today, too
many casual microscope users do not think about the relationship between the image and reality and are content to
push a button, capture an image, enhance the image with
Adobe Photoshop, and submit it for publication. However,
the sentence that followed the one just quoted indicates that
the microscope was not to be used in place of the brain,
but in addition to the brain. Hooke (1665) wrote, “It is said
of great empires, that the best way to preserve them from
decay, is to bring them back to the first principles, and arts,
on which they did begin.” To understand how a microscope
forms an image of a specimen still requires the brain, and
today I am privileged to be able to present the work of
so many people who have struggled and are struggling to
understand the relationship between the image and reality,
and to develop instruments that, when used thoughtfully,
can make a picture that is worth a thousand words.
Matthias Schleiden (1849), the botanist who inspired
Carl Zeiss to build microscopes, wrote about the importance of the mind of the observer:
It is supposed that nothing more is requisite for microscopical
investigation than a good instrument and an object, and that it
is only necessary to keep the eye over the eye-piece, in order to
be au fait. Link expresses this opinion in the preface to his phytotomical plates: ‘I have generally left altogether the observation
to my artist, Herr Schmidt, and the unprejudiced mind of this
observer, who is totally unacquainted with any of the theories of
botany, guarantees the correctness of the drawings.’ The result of
such absurdity is, that Link’s phytotomical plates are perfectly
useless; and, in spite of his celebrated name, we are compelled
to warn every beginner from using them…. Link might just as
well have asked a child about the apparent distance of the moon,
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
expecting a correct opinion on account of the child’s unprejudiced views. Just as we only gradually learn to see with the naked
eye in our infancy, and often experience unavoidable illusions,
such as that connected with the rising moon, so we must first
gradually learn to see through the medium of the microscope…..
We can only succeed gradually in bringing a clear conception
before our mind….
Hermann Schacht (1853) emphasized that we should
“see with intelligence” when he wrote,
But the possession of a microscope, and the perfection of such
an instrument, are not sufficient. It is necessary to have an intimate acquaintance, not only with the management of the microscope, but also with the objects to be examined; above all things
it is necessary to see with intelligence, and to learn to see with
judgment. Seeing, as Schleiden very justly observes, is a difficult art; seeing with the microscope is yet more difficult….Long
and thorough practice with the microscope secures the observer
from deceptions which arise, not from any fault in the instrument, but from a want of acquaintance with the microscope, and
from a forgetfulness of the wide difference between common
vision and vision through a microscope. Deceptions also arise
from a neglect to distinguish between the natural appearance of
the object under observation, and that which it assumes under the
microscope.
Throughout the many editions of his book, The
Microscope, Simon Henry Gage (1941) reminded his readers
of the importance of the microscopist as well as the microscope (Kingsbury, 1944): “To most minds, and certainly to
those having any grade of originality, there is a great satisfaction in understanding principles; and it is only when the
principles are firmly grasped that there is complete mastery of instruments, and full certainty and facility in using
them …. for the highest creative work from which arises real
progress both in theory and in practice, a knowledge of principles is indispensable.” He went on to say that an “image,
whether it is made with or without the aid of the microscope,
must always depend upon the character and training of the
seeing and appreciating brain behind the eye.”
This book is a written version of the microscopy course
I teach at Cornell University. I introduce my students to
the principles of light and microscopy through lecturedemonstrations and laboratories where they can put themselves in the shoes of the masters and be virtual witnesses
to their original observations. In this way, they learn the
strengths and limitations of the work, how first principles
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were uncovered, and, in some respects, feel the magic of
discovery. I urge my students to learn through personal
experience and to be skeptical of everything I say. I urge
the reader to use this book as a guide to gain personal
experience with the microscope. Please read it with a skeptical and critical mind and forgive my limitations.
Biologists often are disempowered when it comes to
buying a microscope, and the more scared they are, the
more likely it is that they will buy an expensive microscope, in essence, believing that having a prestigious brand
name will make up for their lack of knowledge. So buying
an expensive microscope when a less expensive one may
be equally good or better may be more a sign of ignorance
than a sign of wisdom and greatness. I wrote this book,
describing microscopy from the very beginning, not only to
teach people how to use a microscope and understand the
relationship between the specimen and the image, but to
empower people to buy a microscope based on its virtues,
not on its name. You can see whether or not a microscope
manufacturer is looking for a knowledgeable customer by
searching the web sites to see if the manufacturer offers
information necessary to make a wise choice or whether
the manufacturer primarily is selling prestige. Of course,
sometimes the prestigious microscope is the right one for
your needs.
If you are ready to buy a microscope after reading
this book, arrange for all the manufacturers to bring their
microscopes to your laboratory and then observe your samples on each microscope. See for yourself: Which microscopes have the features you want? Which microscope
gives you the best image? What is the cost/benefit relationship? I thank M. V. Parthasarathy for teaching me this way
of buying a microscope.
Epistemology is the study of how we know what we
know—that is, how reality is perceived, measured, and
understood. Ontology is the study of the nature of what we
know that we consider to be real. This book is about how
a light microscope can be used to help you delve into the
Preface
invisible world and obtain information about the microscopic world that is grounded in reality. The second book
in this series, entitled, Plant Cell Biology, is about what we
have learned about the nature of life from microscopical
studies of the cell.
The interpretation of microscopic images depends on
our understanding of the nature of light and its interactions with the specimen. Consequently, an understanding
of the nature of light is the foundation of our knowledge of
microscopic images. Appendix II provides my best guess
about the nature of light from studying its interactions with
matter with a microscope.
I thank David Bierhorst, Peter Webster, and especially Peter Hepler for introducing me to my life-long
love of microscopy. The essence of my course comes
from the microscopy course that Peter Hepler taught at the
University of Massachusetts. Peter also stressed the importance of character in doing science. Right now, I am looking through the notes from that course. I was very lucky
to have had Peter as a teacher. I also thank Dominick
Paolillo, M. V. Parthasarathy, and George Conneman for
making it possible for me to teach a microscopy course
at Cornell and for being supportive every step of the way.
I also thank the students and teaching assistants who shared
in the mutual and never-ending journey to understand light,
microscopy, and microscopic specimens. I have used the
pictures that my student’s have taken in class to illustrate
this book. Unfortunately, I no longer know who took which
picture, so I can only give my thanks without giving them
the credit they deserve. Lastly, I thank my family: mom
and dad, Scott and Michelle, for making it possible for me
to write this book.
As Hermann Schacht wrote in 1853, “Like my predecessors, I shall have overlooked many things, and perhaps
have entered into many superfluous particulars: but, as
far as regards matters of importance, there will be found
in this work everything which, after mature consideration,
I have thought necessary.”
Randy Wayne
Chapter 1
The Relation between the Object
and the Image
And God said, “Let there be light,” and there was light. God
saw that the light was good, and he separated the light from the
darkness.
Gen. 1:3-4
We get much of our information about the real world
through our eyes, and we depend on the constancy of the
interaction of light and matter to determine the physical and
chemical characteristics of an object. Due to the constancy
of the interaction of light with matter, we can determine
the size, shape, color, transparency, chemical composition,
and texture of objects with our eyes. After we understand
the nature of the interaction of light with matter, we can
use light as a tool to probe the properties of matter under
the microscope. We can use a dark-field microscope or a
phase-contrast microscope to see invisible (e.g., transparent) cells. We can use a polarizing microscope to determine
the orientation of molecules in a cell and even determine
the entropy and enthalpy of the polymerization reaction
of the microtubules in the mitotic spindle. We can use an
interference microscope to ascertain the mass of the cell’s
nucleus. We can use a fluorescence microscope to localize
proteins in the cytoplasm or genes on a chromosome. We
can also use a fluorescence microscope to determine the
membrane potential of the endoplasmic reticulum or the
free Ca2 concentration and pH of the cytoplasm. We can
use a laser microscope or a centrifuge microscope to measure the forces involved in cellular motility or to determine
the elasticity and viscosity of the cytoplasm.
We can do all these things with a light microscope
because the light microscope is a device that permits us
to study the interaction of light with matter at a resolution
much greater than that of the unaided eye. The light microscope is one of the most elegant tools available, and I wrote
this book so that you can make the most of the potential
of the light microscope and even extend its uses. To this
end, the goals of this book are to:
● Describe the relationship between an object and its
image.
● Describe how light interacts with matter to yield
information about the structure, composition, and local
environment of biological and other specimens.
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
● Describe how optical systems work. This will permit
us to interpret the images obtained at high resolution and
magnification.
● Give you the necessary procedures and tricks so that
you can gain practical experience with the light microscope
and become an excellent microscopist.
LUMINOUS AND NONLUMINOUS OBJECTS
All objects, which are perceived by our sense of sight, can
be divided into two classes. One class of objects, known
as luminous bodies, includes the sun, the stars, torches,
oil lamps, candles, and light bulbs. These objects are visible to our eyes. The second class of objects is nonluminous. However they can be made visible to our eyes when
they are in the presence of a luminous body. Thus the sun
makes the moon, Earth, and other planets visible to us, and
a light bulb makes all the objects in a room or on a microscope slide visible to us. The nonluminous bodies become
visible by reemitting the light they absorb from the luminous bodies. A luminous or nonluminous body is visible
to us only if there are sufficient differences in brightness
or color between it and its surroundings. The difference in
brightness or color between points in the image formed of
an object on our retina is known as contrast.
OBJECT AND IMAGE
Each object is composed of many infinitesimally small
points composed of atoms or molecules. Ultimately, the
image of each object is a point-by-point representation of
that object upon our retina. Each point in the image should
be a faithful representation of the brightness and color of
the conjugate point in the object. Two points on different
planes are conjugate if they represent identical spatial locations on the two planes. The object we see may itself be
an intermediate image of a real object. The intermediate
image of a real object observed with a microscope, telescope, or by looking at a photograph, movie, or television
screen should also be a faithful point-by-point representation of the brightness and color of each conjugate point
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of the real object. While we only see brightness and color,
the mind interprets the relative brightness and colors of the
points of light on the retina and makes a judgment as to the
size, shape, location, and position of the real object.
What we see, however, is not a perfect representation
of the physical world. First, our eyes are not perfect, and
our vision is limited by physical factors (Inoué, 1986;
Helmholtz, 2005). For example, we cannot see clearly
things that are too far or too close, too dark or too bright,
or things that emit radiation outside the visible range of
wavelengths. Second, our vision is affected by psychological factors, and we can be easily fooled by our sense of
sight (Russ, 2004). Goethe (1840) stressed the psychological component of color vision after noticing that when an
opaque object is irradiated with colored light, the shadow
appears to be the complementary color of the illuminating light even though no light exists in the shadow of the
object.
Another famous example of the psychological component of vision is the “Moon Illusion”. For example, the
moon rising on the horizon looks bigger than the moon
on the meridian, yet we can easily see that they are the
same size by holding a quarter at arms length and observing that in both cases the quarter just obscures the moon
(Molyneux, 1687; Wallis, 1687; Berkeley, 1709; Schleiden,
1849; Kaufman and Rock, 1962). When walking through
a museum, it appears as if the eyes in the portraits seem
to follow the viewer, yet the eyes do not move (Wollaston,
1824; Brewster, 1835). When a friend walks toward you,
he or she appears to get taller, but does he or she actually
get taller?
In order to demonstrate the effect of perspective on
the appearance of size, hold one meter stick and look at
another meter stick, parallel to the first and one meter further from your eyes. How long does ten centimeters on the
distant stick appear to be when measured with the nearer
stick? If we were to run two pieces of string from our eye
to the two points 10 centimeters apart on the further meter
stick, we would see that the string would touch the exact
two points on the nearer stick that we used to measure how
long 10 centimeters of the further stick appeared. It is as
if light from the points on the two meter sticks traveled to
our eyes along the straight lines defined by the strings. The
relationship between distance and apparent size is known
as perspective, and is used in painting as a way of capturing the world as we see it on a piece of canvas (da Vinci,
1970; Gill, 1974). Alternatively, anamorphosis is a technique devised by Leonardo da Vinci to hide images so that
we can view them only if we know the laws of perspective
(Leeman, 1977). Look at the following optical illusions
and ask yourself, is seeing really believing? On the other
hand, is believing seeing (Figure 1-1)?
Optical illusions are a fun way to remind ourselves that
there can be a tenuous relationship between what we see
and what we think we see. To further test the relationship
Light and Video Microscopy
between seeing and believing, look at the following
books on optical illusions: Luckiesh, 1965; Joyce, 1995;
Fineman, 1981; Seckel, 2000, 2001, 2002, 2004a, 2004b.
Do you believe that all the people in da Vinci’s Last Supper
were men? Is that what you see? What do you think vision
would be like if a blind person were suddenly able to see
(Zajonc, 1993)?
THEORIES OF VISION
In order to appreciate the relationship between an object
and its image, the ancient Greeks developed several theories of vision, which can be reduced into two classes
(Priestley, 1772; Lindberg, 1976; Ronchi, 1991; Park,
1997):
● Theories that state that vision results from the
emission of visual rays from the eye to the object being
viewed (extramission theory).
● Theories that state that vision results from light that
is emitted from the object and enters the eye (intromission
theory).
The extramission theory was based, in part, on a comparison of the sense of vision with the sense of touch. It
provided an explanation for the facts that we can see
images when we sleep in the dark, we see light when we
rub our eyes, and we can see only the surface of objects.
The intromission theory was based on the idea that the
image was formed from a thin skin of atoms that flew off
the object and into the eye. Evidence supporting the intromission theory comes from the facts that we cannot see
in the dark, we cannot see objects that are too close to the
eye, and we can see the stars, and in doing so our eyes do
not collapse from sending out an infinite number of visual
rays such a vast distance (Sabra, 1989).
Historically, most theories of vision were synthetic theories that combined the two theses, suggesting that light emitted from the object combines with the visual rays in order for
vision to occur (Plato, 1965). Many writers, from Euclid to
Leonardo da Vinci, wavered back and forth between the two
extreme theories. In 1088, Al-Haytham, a supporter of the
intromission theory, suggested that images may be formed by
eyes, in a manner similar to the way that they are formed by
pinholes (Sabra, 1989). The similarity between the eye and
a pinhole camera also was expressed by Giambattista della
Porta, Leonardo da Vinci (1970), and Francesco Maurolico
(1611). However they never were able to reasonably explain
the logical consequence that, if an eye formed images just
like a pinhole camera, then the world should appear upside
down (Arago, 1857).
By 1604, Johannes Kepler developed, what is in
essence, our current theory of vision. Kepler inserted an
eyeball, whose back had been scraped away to expose the
retina, in the pinhole of a camera obscura. Upon doing
3
Chapter | 1 The Relation between the Object and the Image
Which center circle is larger?
Which man is the tallest?
Can you make these figures three dimensional?
(a)
Which rectangle is larger?
(b)
FIGURE 1-1 (a) Optical illusions. Is seeing believing? (b) “All is vanity” by Charles Allan Gilbert (1892). When we look at this ambiguous optical
illusion, our mind forms two alternative interpretations, each of which is a part of the single reality printed on the page. Instead of seeing what is actually on the page, our mind produces two independent images, each of which makes sense to us and each of which has meaning. When we look at a
specimen through a microscope, we must make sure that we are seeing what is there and find meaning in what is there, as opposed to seeing only that
which is already meaningful to us.
this, he discovered that the eye contains a series of hard
and soft elements that act together as a convex lens, which
projects an inverted image of the object on the concave
retina. The image formed on the retina is an inverted pointby-point replica that represents the brightness and color of
the object. Kepler dismissed the problem of the “upside
up world” encountered by Porta, da Vinci, and Maurolico,
by suggesting that the brain subsequently deals with the
inverted image. The importance of the brain in vision was
expanded by George Berkeley (1709).
Before I discuss the physical relationship between
an object and an image, I will take a step backward and
discuss the larger philosophical problem of recognizing
which is the object and which is the image. Plato illustrates
4
Light and Video Microscopy
light in this world, and of truth and understanding in the other.
He who attains to the beatific vision is always going upwards….
Although this parable can be discussed at many
levels, I will use it just to emphasize that we see images of
the world, and not the world itself. Plato went on to suggest that the relationship between the image and its reality could be understood through study, particularly the
progressive and habitual study of mathematics. In Novum
Organum, Francis Bacon (in Commins and Linscott, 1947)
described four classes of idols that plague one’s mind in
the scientific search for knowledge. One of these he called
“the idols of the cave.” He wrote,
FIGURE 1-2 The troglodytes in a cave.
this point in the Republic (Jowett, 1908; also see Cornford,
1945) where he tells the following parable known as The
Allegory of the Cave (Figure 1-2). Plato writes,
And now I will describe in a figure the enlightenment or unenlightenment of our nature: Imagine human beings living in an
underground den which is open towards the light; they have
been there from childhood, having their necks and legs chained,
and can only see into the den. At a distance there is a fire, and
between the fire and the prisoners a raised way, and a low wall is
built along the way, like the screen over which marionette players
show their puppets. Behind the wall appear moving figures, who
hold in their hands various works of art, and among them images
of men and animals, wood and stone, and some of the passersby are talking and others silent .… They are ourselves … and they
see only the shadows of the images which the fire throws on the
wall of the den; to these they give names, and if we add an echo
which returns from the wall, the voices of the passengers will
seem to proceed from the shadows. Suppose now that you suddenly turn them round and make them look with pain and grief
to themselves at the real images; will they believe them to be
real? Will not their eyes be dazzled, and will they not try to get
away from the light to something which they are able to behold
without blinking? And suppose further, that they are dragged up
a steep and rugged ascent into the presence of the sun himself,
will not their sight be darkened with the excess of light? Some
time will pass before they get the habit of perceiving at all; and
at first they will be able to perceive only shadows and reflections
in the water; then they will recognize the moon and the stars, and
will at length behold the sun in his own proper place as he is.
Last of all they will conclude: This is he who gives us the year
and the seasons, and is the author of all that we see. How will
they rejoice in passing from darkness to light! How worthless
to them will seem the honours and glories of the den! But now
imagine further, that they descend into their old habitations; in
that underground dwelling they will not see as well as their fellows, and will not be able to compete with them in the measurement of the shadows on the wall; there will be many jokes about
the man who went on a visit to the sun and lost his eyes, and if
they find anybody trying to set free and enlighten one of their
number, they will put him to death, if they can catch him. Now
the cave or den is the world of sight, the fire is the sun, the way
upwards is the way to knowledge, and in the world of knowledge
the idea of good is last seen and with difficulty, but when seen is
inferred to be the author of good and right–parent of the lord of
The Idols of the Cave are the idols of the individual man. For
everyone (besides the errors common to human nature in general)
has a cave or den of his own, which refracts and discolors the light
of nature; owing either to his own proper and peculiar nature or to
his education and conversation with others; or to the reading of
books, and the authority of those whom he esteems and admires;
or to the differences of impressions, accordingly as they take place
in a mind preoccupied and predisposed or in a mind indifferent
and settled; or the like. So that the spirit of man (according as it
is meted out to different individuals) is in fact a thing variable and
full of perturbation, and governed as it were by chance. Whence it
was well observed by Heraclitus that men look for science in their
own lesser worlds, and not in the greater or common world.
Charles Babbage (1830) wrote, in Reflections on the
Decline of Science, about the importance of understanding
the “irregularity of refraction” and the “imperfections of
instruments” used to observe nature. In his book, entitled,
The Image, Daniel Boorstin (1961) contends that many of
the advances in optical technologies have contributed to a
large degree in separating the real world from our image
of it. Indeed, the physical reality of our body and our own
image of it does not have a one-to-one correspondence.
In A Leg to Stand On, Oliver Sacks (1984) describes the
neurological relationship between our body and our own
image of our body.
Thus it is incumbent on us to understand that when we
look at something, we are not directly sensing the object,
but an image of the object projected on our retinas, and
processed by our brains. The image, then, depends not
only on the intrinsic properties of the object, but on the
properties of the light that illuminates it, as well as the
physical, physiological, and psychological basis of vision.
Thus before we even prepare our specimen for viewing
in the microscope, we must prepare our mind. While looking
through the microscope, I would like you to keep the
following general questions in mind:
1. How do we receive information about the external
world?
2. What is the nature and validity of the information?
3. What is the relationship of the perceiving organism
to the world perceived?
4. What is the nature and validity of the information
obtained by using an instrument to extend the senses; and
5
Chapter | 1 The Relation between the Object and the Image
what is the relationship of the information obtained by the
perceiving organism with the aid of an instrument to the
world perceived?
LIGHT TRAVELS IN STRAIGHT LINES
It has been known for a long time that light travels in
straight lines. Mo Tzu (470–391 BC) inferred that the light
rays from luminous sources travel in straight lines because:
A shadow cast by an object is sharp, and it faithfully
reproduces the shape of the object.
● A shadow never moves by itself, but only if the light
source or the object moves.
● The size of the shadow depends on the distance
between the object and the screen upon which it is projected.
● The number of shadows depends on the number of
light sources: if there are two light sources, there are two
shadows (Needham, 1962).
●
The ancient Greeks also came to the conclusion that
light travels in straight lines. Aristotle (384–322 BC,
Physics Book 5, in Barnes, 1984) concluded that light travels in straight lines as part of his philosophical outlook that
nature works in the briefest possible manner. Evidence,
however, for the rectilinear propagation of light came in
part from observing shadows. Euclid observed that there
is a geometric relationship between the height of an object
illuminated by the sun and the length of the shadow cast
(Figure 1-3). Theon of Alexandria (335–395) amplified
Euclid’s conclusion that light travels in straight lines by
showing that the size of a shadow depended on whether an
object was illuminated by parallel rays, converging rays, or
diverging rays (Lindberg and Cantor, 1985).
Mirrors and lenses have been used for thousands of
years as looking glasses and for starting fires. Aristophanes
(423 BC) describes their use in The Clouds. Euclid, Diocles,
and Ptolemy used the assumption that a light ray (or visual
ray) travels in a straight line in order to build a theory of
geometrical optics that was powerful enough to predict the
position of images formed by mirrors and refracting surfaces (Smith, 1996). According to geometrical optics, an
image is formed where all the rays emanating from a single point on the object combine to make a single point of
the image. The brighter the point in the object, the greater
the number of rays it emits. Bright points emit many rays
and darker points emit fewer rays. The image is formed on
the surface where the rays from each point meet the other
rays emitted from the same point. The success that the
geometrical theory of optics had in predicting the position
of images provided support that the assumption that light
travels in straight lines, upon which this theory is based,
must be true.
Building on the atomistic theories of Leucippus,
Democritus, Epicurus, and Lucretius—and contrary to the
Sun
Height
of opaque
object
Length of shadow
FIGURE 1-3 There is a geometrical relationship between the height of an
object illuminated by the sun and the length of the shadow cast. Heightobject 1/
Length of shadowobject 1 Heightobject 2/Length of shadowobject 2 constant.
continuous theories championed by Aristotle, Simplicus,
and Descartes—Isaac Newton proposed that light traveled
along straight lines as corpuscles.
Interestingly, the fact that light travels in straight lines
allows us to “see what we want to see.” The mathematician, William Rowan Hamilton (1833) began his paper on
the principle of least action in the following way:
The law of seeing in straight lines was known from the infancy of
optics, being in a manner forced upon men’s notice by the most
familiar and constant experience. It could not fail to be observed that
when a man looked at any object, he had it in his power to interrupt his vision of the object, and hide it at pleasure from his view,
by interposing his hand between his eyes and it; and that then, by
withdrawing his hand, he could see the object as before: and thus the
notion of straight lines or rays of communication, between a visible
object and a seeing eye, must very easily and early have arisen.
IMAGES FORMED IN A CAMERA OBSCURA:
GEOMETRIC CONSIDERATIONS
Mo Tzu provided further evidence that rays emitted by each
point of a visible object travel in a straight line by observing the formation of images (Needham, 1962; Hammond,
1981; Knowles, 1994). He noticed that although the light
emitted by an object is capable of forming an image in our
eyes, it is not able to form an image on a piece of paper
or screen. However, Mo Tzu found that the object could
form an image on a screen if he eliminated most of the rays
issuing from each point by placing a pinhole between the
object and the screen (Figure 1-4). The image that appears,
however, is inverted. Mo Tzu (in Needham, 1962) wrote,
An illuminated person shines as if he was shooting forth rays.
The bottom part of the man becomes the top part of the image
and the top part of the man becomes the bottom part of the
image. The foot of the man sends out, as it were light rays, some
of which are hidden below (i.e. strike below the pinhole) but
others of which form an image at the top. The head of the man
sends out, as it were light rays, some of which are hidden above
(i.e. strike above the pinhole) but others of which form its image
at the bottom. At a position farther or nearer from the source
6
Light and Video Microscopy
FIGURE 1-4 A pinhole forms an inverted image because light travels
in straight lines. The pinhole blocks out the majority of rays that radiate from a single point on the object. The rays that do pass through the
pinhole form the image. The smaller the pinhole, the smaller the circle of
confusion that makes up each “point” of the image.
of light, reflecting body, or image there is a point (the pinhole)
which collects the rays of light, so that the image is formed only
from what is permitted to come through the collecting-place.
The fact that the image can be reconstructed by drawing a straight line from every point of the outline of the
object, through the pinhole, and to the screen, confirms
that light does travel in straight lines According to John
Tyndall (1887), “This could not be the case if the straight
lines and the light rays were not coincident.” Shen Kua
(1086) extended Mo Tzu’s work by showing the analogy
between pinhole images and reflected images. However,
Shen Kua’s work could not go too far since it lacked a geometric foundation (Needham, 1962).
The Greeks also had discovered that images could be
formed by a pinhole. Aristotle noticed that the light of the
sun during an eclipse coming through a small hole made
between leaves casts an inverted image of the eclipse on
the ground (Aristotle; Problems XV:11 in Barnes, 1984).
The description of image formation based on geometric
optics by Euclid and Ptolemy was extended by scholars in
the Arab World. Al-Kindi (ninth century) in De aspectibus
showed that light entering a dark room through windows
travels in straight lines. Likewise the light of a candle is
transmitted through a pinhole in straight lines (Lindberg
and Cantor, 1985). Al-Kindi’s work was extended by
Al-Haytham, or Alhazen as he is often known (in Lindberg,
1968), who wrote in his Perspectiva,
The evidence that lights and colors are not intermingled in air
or in transparent bodies is that when a number of candles are in
one place, [although] in various and distinct positions, and all are
opposite an aperture that passes through to a dark place and in
the dark place opposite the aperture is a wall or an opaque body,
the lights of those candles appear on the [opaque] body or the
wall distinctly according to the number of candles; and each of
them appears opposite one candle along a [straight] line passing through the aperture. If one candle is covered, only the light
opposite [that] one candle is extinguished; and if the cover is
removed, the light returns…. Therefore, lights are not intermingled in air, but each of them is extended along straight lines.
The quality of the image formed by a pinhole depends
on the size of the pinhole (Figure 1-4). When the pinhole
is too small, not enough light rays can pass through it and
the image is dark. However, if the pinhole is too large,
too many light rays pass through and the image is blurry.
Seeing this, Al-Haytham and his commentator Al-Farisi
(fourteenth century) realized that the image formed by
the pinhole was actually a composite of numerous overlapping images of the pinhole, each one originating from
an individual luminous point on the object (Omar, 1977;
Lindberg, 1983; Sabra, 1989).
Each and every point on a luminous object forms a
cone of light that passes through the pinhole. The pinhole
marks the tip of the cone and the light at the base of the
cone forms the image. The fact that light originating from
a point on an object forms a circle of light on the image
leads to some blurring of the image known as the “circle of
confusion” (Time-Life, 1970). The image will be distinct
(or resolved) if the bases of the cones that originate
from the two extreme points of the object do not overlap. Likewise the image will be clearer when the bases of
cones originating from adjacent points on the object do
not overlap. Given this hypothesis, the sharpness of the
image would increase as the size of the aperture decreases.
However, the brightness of the images also decreases as
the size of the aperture decreases. Using geometry, AlHaytham found the optimal diameter of an aperture when
viewing an object of a given diameter (yo) and distance
(so) from the aperture. Al-Haytham showed, that when the
object is circular, and the object, aperture, and plane of the
screen are parallel, two light patches originating from two
points on the object will touch when the ratio of the diameter of the aperture (ao) to that of the object (yo) is equal to
the ratio of the distance between the image and the aperture (si), and the distance between the image and the object
(si so). That is:
a o / y o si (si so )
The position of the optimal image plane (si) and the optimal size of the aperture (ao) are given by the following
analysis (Figure 1-5).
Since tan θ (½ ao)/si (½ yo)/(si so), then ao/yo si/(si so) and yo/ao 1 so/si. For large distances
between the object and the pinhole, yo/aoso/si, and for
a given so, the greater the aperture size, the greater is the
distance from the aperture to a clear image.
Leonardo da Vinci (1970) also concluded that light
travels through a pinhole in straight lines to form an image.
He wrote, “All bodies together, and each by itself, give off
to the surrounding air an infinite number of images which
are all-pervading and each complete, each conveying the
nature, colour and form of the body which produces it.” da
Vinci proved this hypothesis by observing that when one
makes “a small round hole, all the illuminated objects will
project their images through that hole and be visible inside
7
Chapter | 1 The Relation between the Object and the Image
ao
θ
yo
ao
so
si
FIGURE 1-5 The position of the optimal image plane (si ) and the optimal size of the aperture (ao) for an object of height (yo) placed at the object
plane (so).
FIGURE 1-6 A converging lens can collect more of the rays that
emanate from a point on an object than a pinhole can, thus producing a
brighter image.
the dwelling on the opposite wall which may be made
white; and there in fact, they will be upside down, and if
you make similar openings in several places on the same
wall you will have the same result from each. Hence the
images of the illuminated objects are all everywhere on this
wall and all in each minutest part of it.” da Vinci (1970)
also realized that the images formed by the pinhole were
analogous to the images formed by the eye. He wrote,
An experiment, showing how objects transmit their images or
pictures, intersecting within the eye in the crystalline humour,
is seen when by some small round hole penetrate the images of
illuminated objects into a very dark chamber. Then, receive these
images on a white paper placed within this dark room and rather
near to the whole and you will see all the objects on the paper in
their proper forms and colours, but much smaller; and they will
be upside down by reason of that very intersection. These images
being transmitted from a place illuminated by the sun will seem
actually painted on this paper which must be extremely thin and
looked at from behind.
Light rays that emanate from a point in an object separate from each other and form a cone. The pinhole sets a
limit on the size of the cone that is used to form an image
of any given point. When the aperture is large, the cone of
light emanating from each point is large. Under this condition, light from every point on the object illuminates every
part of the screen and there is no image. As the aperture
decreases, however, the cone of light from each point illuminates a limited region of the screen, and an image is
formed. The screen must be far enough behind the pinhole so that the cones of light emanating from two nearby
points do not overlap. The greater the distance between the
screen and the pinhole, the larger the image will be, but it
will also become dimmer. This dimness problem can be
overcome by putting a converging lens over the pinhole
(Wright, 1907; Figure 1-6).
Girolamo Cardano suggested in his book, De subtilitate, written in 1550, that a biconvex lens placed in
front of the aperture would increase the brightness of the
image (Gernsheim, 1982). In 1568, Daniel Barbaro, in his
book on perspective, also mentioned that a biconvex lens
increases the brightness of the image. The lens focuses
all the rays emanating from each point of an object that it
can capture and focuses them to form the corresponding
conjugate point on the image. Thus a lens is able to capture a larger cone of light emitted from each point than an
aperture can. In contrast to an image formed by a pinhole,
an image formed by a lens is restricted to only one plane,
known as the image plane. In front of or behind the image
plane, the rays are converging to a spot or diverging from a
spot, respectively. Consequently, the “out-of-focus” image
of a bright spot is dim, and in the “out-of-focus” image
there is no clear relationship between the brightness of the
image and the brightness of the object. The distance of the
image plane from the lens, as well as the magnification of
the image depends on the focal length of the lens. For an
object at a set distance in front of the lens, the image distance and magnification increases with an increase in the
focal length of the lens (Figure 1-7).
With lenses of the same focal length, the brightness of
the image increases as the diameter of the lens increases.
This is because the larger a lens, the more rays it can collect from each point on the object. The sharpness of the
image produced by a lens is related to the number of rays
emanating from each point that is collected by that lens.
The camera obscura was popularized by Giambattista
della Porta in his book Natural Magic (1589), and by
the seventeenth century, portable versions of the camera
obscura were fabricated and/or used by Johann Kepler
(who coined the term camera obscura, which literally
means dark room) for drawing the land he was surveying and for observing the sun. Kepler also suggested that
8
Light and Video Microscopy
Hydrogen emission spectrum
f1
f2
f3
f3
I3
f2
f1
I2
Hydrogen absorption spectrum
I1
FIGURE 1-7 As the focal length of a lens increases (f1 f2 f3), the
image plane moves farther from the lens and the image becomes more
magnified.
the camera obscura could be improved by adding a second biconvex lens to correct the inverted image. Moreover,
he suggested that the focal length of the lens could be
reduced by combining a concave lens with the convex lens.
Johann Zahn, Athanasius Kircher, and others used camera
obscuras in order to facilitate drawing scenes far away
from the studio, and Johann Hevelius connected a camera obscura to a microscope to facilitate drawing enlarged
images of microscopic specimens (Hammond, 1981).
Some Renaissance painters, including Vermeer, used
the camera obscura as a drawing aid. Indeed, it is thought
that “A View of Delft” was painted with the aid of the
camera obscura since the edges of the painting are out of
focus. In 1681, Robert Hooke suggested that the screen of
the camera obscura should be concave, since the image
formed by either a pinhole or a simple lens does not form
a flat field at sharp focus, but has a curved field of sharp
focus. When a camera obscura was open to the public, the
crowded dark room was used both as a venue to present
shows of natural magic and as a convenient place to pick
the pockets of the unsuspecting audience.
WHERE DOES LIGHT COME FROM?
Light comes from matter, the atoms of which are in an
excited state, which has more energy than the most stable
or ground state (Clayton, 1970). An atom becomes excited
when one of its electrons makes a transition from an orbital
close to the nucleus to an orbital further from the nucleus
(Bohr, 1913; Kramers and Holst, 1923). Atoms can become
excited by various forms of energy, including heat, pressure, an electric discharge, and by light itself (Wedgewood,
1792; Nichols and Wilber, 1921a, 1921b). Heating limestone (CaCO3) for example gives off a bright light. Thomas
Drummond (1826) took advantage of this property to
design a spotlight that was used in theatrical productions in
the nineteenth century. This is how we got the expression,
“being in the limelight.”
Although the ancient Chinese invented fireworks, the
stunning colors were not added until the discovery and characterization in the nineteenth century of the optical properties of the elements. Various elements burned in a flame
emit a spectacular spectrum of rich colors and each element
400 nm
700 nm
FIGURE 1-8 A diffraction grating resolves the light emitted from an
incandescent gas into bright lines. When a sample of the same gas is
placed between a white light source and a diffraction grating, black lines
appear at the same places as the emission lines occurred, indicating that
gases absorb the same wavelengths as they emit.
gives off a characteristic color. For example, the chlorides
of copper, barium, sodium, calcium, and strontium give off
blue, green, yellow, orange, and red light, respectively. This
indicates that there is a relationship between the atomic
structure of the elements and the color of light emitted.
Interestingly, the structure of atoms has been determined to
a large degree by analyzing the characteristic colors that are
emitted from them (Brode, 1943; Serway et al., 2005).
In 1802, William Wollaston and, in 1816, Joseph von
Fraunhöfer independently identified dark lines in the spectrum of the sun. Fraunhöfer identified the major lines with
uppercase letters (A, B, C, D, E, F …) and the minor lines
with lowercase letters. John Herschel (1827) noticed that
a given salt gave off a characteristic colored light when
heated and suggested that chemicals might be identified
by their spectra. Fraunhöfer suggested that the colored
lines given off by heated elements might be related to the
dark lines observed in solar spectra, and subsequently he
developed diffraction gratings to resolve and quantify the
positions of the spectral lines (Figure 1-8). Independently,
William Henry Fox Talbot (1834c) discovered that lithium
and strontium gave off colored light when they were heated,
and since the color of the light was characteristic of the element, Talbot also suggested that optical analysis would be
an excellent method for identifying minute amounts of an
element. Following this suggestion, Robert Wilhelm Bunsen
and Gustav Kirchhoff used the gas burner Bunsen invented
to determine the spectrum of light given off by each element
(Kirchhoff and Bunsen, 1860; Gamow, 1988).
Fraunhöfer’s A (759.370 nm) and B (686.719 nm) lines
turned out to be due to oxygen absorption, the C (656.281)
line was due to hydrogen absorption, the D1 (589.592 nm)
and D2 (588.995 nm) lines were due to sodium absorption,
the D3 (587.5618 nm) line was due to hydrogen absorption,
the E (546.073 nm) line was due to mercury absorption, the
E2 (527.039 nm) line was due to iron absorption, and the F
(486.134 nm) line was due to hydrogen absorption. These
lines are used as standards by lens makers to characterize
9
700
650
600
550
Nanometers
500
450
400
h␯
n
n4
n3
Paschen
series
IR
n2
Balmer
series
visible
Absorption
Emission
Ionization
n1
⌬E
0 eV
1.51 eV
Ground state
Frequency
3.4 eV
HYDROGEN
Lyman
series
uv
Atom
Absorption
750
Molecule with
distinct substates
13.6 eV
FIGURE 1-9 The bright spectral lines represent light emitted by electrons jumping from a higher energy level to a lower energy level. The dark
absorption lines (shown in Figure 1-8) represent light absorbed by electrons
jumping from a lower energy level to a higher energy level. The energy levels are designated by principal quantum numbers (n) and by binding energies in electron volts (1 eV 1.6 1019 J). Transitions in the ultraviolet
range give rise to the Lyman series, transitions in the visible range give rise
to the Balmer series, and transitions in the infrared range give rise to the
Paschen series.
corrections for chromatic aberration in objective lenses
used in microscopes (see Chapter 4).
When the emitted light from incandescent atoms or
diatomic molecules is passed through a diffraction grating or
a prism, the light is split into a series of discrete bands known
as a line spectrum (Schellen, 1885; Schellen et al., 1872;
Pauling and Goudsmit, 1930; Herzberg, 1944). The spectral
lines represent the energy levels of the atom (Figure 1-9).
When an excited electron returns to the ground state, the
energy that originally was used to excite the atom is released
in the form of radiant energy or light. The wavelength of the
emitted light can be determined using Planck’s Law:
λ hc/ ΔE
where λ is the wavelength (in m), h is Planck’s Constant
(6.626 1034 J s), c is the speed of light (3108 m s1),
and ΔE is the transitional energy difference between
electrons in the excited and the ground states (in J). Niels
Bohr (1913) introduced the total quantum number (n) to
describe the distance between the electron and its nucleus.
When gaseous atoms are combined into complex
gaseous molecules, there is an increase in the number of
spectral lines because of the formation of molecular orbitals, which exist in many vibrational and rotational states.
Consequently, a gaseous molecule gives a banded spectrum
Absorption
Chapter | 1 The Relation between the Object and the Image
Frequency
FIGURE 1-10 The absorption (and emission) spectra broaden and the
peaks become less resolved, as a chemical gets more and more complex.
This occurs because a complex molecule can utilize absorbed energy in
more ways that a simple molecule by vibrating, rotating, and distributing the energy to other parts of the molecule. Likewise, the various vibrational, rotational, or conformational states of a molecule give rise to more
complex spectra. The absorption and emission spectra of molecules are
used to determine their chemical structure.
instead of a line spectrum (Figure 1-10). The spectra of
liquids or solids are broadened further because a range of
transition energies become possible as a consequence of the
interactions between molecules. The various lines and bands
become overlapping and the spectrum appears as a continuous spectrum. In the visible region, the spectrum appears as
a continuous band of light, with colors that change smoothly
from blue to red. The intensity of the various colors in a continuous spectrum depends on the temperature (Planck, 1949)
and the relative velocity of the light source and the observer
(Doppler, 1842). The sun and other stars can be considered to be black body radiators. Isaac Newton (1730) used
a prism to resolve the sun’s whitish-yellow glow, which is
known as black body radiation, into its component parts.
Each point of an object emits light when an electron
in an atom or molecule at that point undergoes a transition from a high energy level to a lower energy level. If
any energy source besides light were used to excite the
electron, then the object is known as a luminous source.
If light itself is used to excite the electron, the object is
known as a nonluminous source. The light emitted by the
excited electron travels along rays emanating from that
point. If the rays converge, an image is formed. In order to
gain as much information as possible about the molecules
that make up each point of the object, we have to understand the interaction of light with the atoms and molecules
that make up that point; how the environment surrounding a molecule (e.g., pH, pressure, electrical potential,
and viscosity) affects the emission of light from that molecule, how neighboring molecules influence each other,
10
and finally how the light travels from the object in order to
form an image.
HOW CAN THE AMOUNT OF LIGHT
BE MEASURED?
The measurement of light, which is known as photometry, calorimetry, and radiometry, involves the absorption
of light by a detector and the subsequent conversion of
the radiant energy to another form of energy (Thompson,
1794; Talbot, 1834a; Johnston, 2001). A thermal detector
converts light energy into thermal energy. A thermal detector is a type of thermometer whose detecting surface has
been blackened so that it absorbs light from all regions of
the spectrum.
A thermocouple is a thermal detector that consists of a
junction of two metals coated with a black surface. When
light strikes the blackened junction, a voltage is generated,
a process discovered by Thomas Seebeck (1821). Often
Light and Video Microscopy
several (20–120) thermocouples are arranged in series to
increase the response of the system. This arrangement is
called a thermopile.
The bolometer is a thermal detector in which the detector is a thin strip of blackened platinum foil whose resistance increases with temperature. The bolometer was
developed by Samuel Pierpont Langley (1881), the founder
of the National Zoological Park in Washington, DC.
Modern bolometers use thermistors made out of ceramic
mixtures of manganese, nickel, cobalt, copper, and uranium oxides whose resistance decreases with temperature.
The amount of light can be measured by using chemical
reactions whose rate is proportional to the amount of light
that strikes the chemical substrates. This technique, known
as chemical actinometry, can be done by using photographic paper, and then relating the amount of incident light
to the darkening of the silver bromide impregnated paper.
I will discuss the use of electrical detectors, including
photodiodes, photomultiplier tubes, video cameras, and
charge coupled devices in Chapter 13.
Chapter 2
The Geometric Relationship
between Object and Image
REFLECTION BY A PLANE MIRROR
In the last chapter I presented evidence that light travels
in straight lines, and I used this assumption to describe
image formation in a camera obscura. This hypothesis is
limited, however, to light traveling through a homogeneous
medium, and it is not true when light strikes an opaque
body. After striking an opaque body, the light bounces
back in a process known as reflection. Consider a flat
surface that is capable of reflecting light. A line perpendicular to this surface is called the normal, from the Latin
name of the carpenter’s square used to draw perpendiculars. Experience shows that a ray of light that moves along
the normal and then strikes the reflective surface head on
will double back on its tracks. In general, if a ray of light
strikes the reflective surface at an angle relative to the normal it will move away from the reflective surface at the
other side of the normal at an angle equal to the angle the
incident light beam made with the normal. The light beam
moving toward the reflective surface is called the incident
ray and its angle relative to the normal is called the angle
of incidence. The light beam moving away from the reflective surface is called the reflected ray and its angle relative
to the normal is called the angle of reflection. For all light
rays striking the surface at any angle, the angle of incidence equals the angle of reflection (Figure 2-1). That is,
i r, where i is the angle of incidence (in degrees)
and r is the angle of reflection (in degrees). Although
Euclid (third century BC) first described the law of reflection in his Elements, perhaps the most famous version of
the law is found in literature. Dante Alighieri (1265–1321)
described the law of reflection in The Divine Comedy
(Longfellow’s translation):
As when from off the water, or a mirror,
The sunbeam leaps unto the opposite side,
Ascending upwards in the self-same measure
That it descends, and deviates as far
From falling of a stone in line direct,
(As demonstrate experiment and art)….
To determine the position, orientation, and size of an
image formed by a plane mirror, we can draw rays from
at least two different points on the object to the mirror.
Once the rays strike the mirror, we assume that they are
reflected in such a way that the angle of reflection equals
the angle of incidence. Practically, we can find an image
point by drawing two characteristic rays from a point on
the object using the following rules (Figures 2-2 and 2-3):
Image
Mirror
θi
Normal
θr
Eye
FIGURE 2-1 The law of reflection: The angle of reflection (θr) equals
the angle of incidence (θi).
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
0
Point object
Eye
FIGURE 2-2 The image of a point formed by a plane mirror can be
determined by using the law of reflection. Draw several rays that obey
the law of reflection. The rays diverge when they enter the eye. The brain
imagines that the diverging rays originated from a single point behind the
mirror. The place where the rays appear to originate is known as the virtual image.
11
12
FIGURE 2-3 A virtual image produced by the eye and the brain of a
person looking at a reflection of an object in a plane mirror.
1. Draw a line from each point in the object perpendicular to the mirror. Since i 0, then r 0. Extend
the reflected ray behind the mirror.
2. Draw another line from each point in the object to
any point on the mirror. Draw the normal to the mirror at
this point and then draw the reflected rays using the rule
i r. Extend the reflected rays behind the mirror, to
the other reflected extension ray originating from the same
point in the object. The point of intersection of the extension rays originating from the same object point is the
position of the image of that object point.
If the reflected rays converged in front of the mirror,
which they do not do when they strike a plane mirror, a real
image would have been formed. A real image is an image
that can be projected on a ground glass screen or a piece of
paper, or captured by a camera; the light intensities of the
points that make up a real image can be measured with a
light meter. However, since the reflected rays diverge from
the mirror, we extend the rays back from where they appear
to be diverging. This is where the image appears to be, and
thus is called a virtual image. A virtual image appears in a
given place, but if we put a ground glass screen, a piece of
paper, or a photographic film in that spot, nothing would
appear.
Our eyes cannot distinguish whether light has been
reflected or not. Many times, while watching a movie,
we see an actor or actress and as the camera moves away
we see that we have been fooled, and we saw only the
reflection of that person in a mirror. When we look at ourselves in a mirror we see an image of ourselves behind the
mirror—as if the image was actually behind the mirror
and the light rays traveled in a straight line from it to our
eyes. Because the image does not exist where we see it, the
image is called a virtual image. That is, it has the virtues of
an image without the image actually being there. Actually
the image is reversed and the right of the object is on the
left of the image and the left of the object is the right of
the image. Perhaps this is the reason we usually do not like
photographs of ourselves. We usually see a mirror image
of ourselves where right and left are reversed. An image in
Light and Video Microscopy
FIGURE 2-4 Diffuse reflection from a rough surface. The angle of
reflection still equals the angle of incidence, but there are many angles
of reflection. You can tell if a reflective surface is rough or smooth by
observing if the reflection is diffuse or specular.
FIGURE 2-5 When light strikes a partially silvered mirror, some of the
light is reflected and some of the light is transmitted. In this way, a partially silvered mirror functions as a beam splitter.
a photograph is in the correct orientation and thus seems
strange to us. In older microscopes, plane mirrors were
used to transmit sunlight to the specimen and for a drawing attachment known as a camera lucida.
I have been discussing front surface mirrors where the
reflecting surface is deposited on the front of the glass.
At home we use mirrors where the reflecting surface is
deposited on the back of the glass. Therefore, there are two
reflecting surfaces, the glass and the silvered surface. In
this case, two images are formed, one from the reflection
of each surface. Consequently, the image is a little blurred
and much more complimentary. These are examples of
specular reflection. By contrast, diffuse reflection is the
reflection from a surface with many imperfections where
parallel rays are broken up upon reflection. This occurs
because one ray may strike an area where the angle of incidence is 0° whereas a parallel ray may strike an area where
the angle of incidence is 10° (Figure 2-4).
Often two images need to be formed in a microscope:
one portion of the image-forming rays goes to the eyepieces and the other portion goes to the camera. Partially
silvered mirrors can be used to split the image-forming
rays into two portions. Since the mirror is not fully silvered, part of the light passes directly through the mirror
while the other part follows the normal law of reflection
(Figure 2-5). If the mirror were 20 percent silvered,
the image formed by the rays that go straight through
would be four times brighter than the reflected image.
Partially silvered mirrors are used in microscopes with
epi-illumination and in some interference microscopes
(Bradbury, 1988).
13
Chapter | 2 The Geometric Relationship between Object and Image
REFLECTION BY A CURVED MIRROR
Not all mirrors are planar and now I will describe images
formed by concave, spherical mirrors. The center of curvature of a mirror is defined as the center of the imaginary
sphere of which the curved mirror would be a part. The distance between the center of curvature of the spherical mirror and the mirror is equal to the radius of the sphere. The
line connecting the midpoint of the mirror with the center of
curvature is called the principal axis of the mirror. Consider
a beam of light that strikes the mirror parallel to the principal axis. When a ray of light in this beam moves down the
principal axis and strikes the mirror, it is reflected back on
itself. When a ray of light in this beam strikes the mirror
slightly above or below the principal axis, the ray makes a
small angle with the normal and consequently the reflected
ray is bent slightly toward the principal axis. If the incident
ray strikes the mirror farther away from the principal axis,
the reflected ray is bent toward the principal axis with a
greater angle. In all cases i r, and the reflected rays
from every part of the mirror converge toward the principal
axis at a point called the focus, which is midway between
the mirror and the center of curvature. The focal length is
equal to one-half the radius of curvature (Figure 2-6).
Figures 2-7 and 2-8 show examples of image formation
by spherical mirrors when the object is placed behind or in
front of the focus, respectively.
Using the law of reflection, we can determine the position, orientation, and size of the image formed by a concave spherical mirror. This can be done easily by drawing
two or three characteristic rays using the following rules:
1. A ray traveling parallel to the principal axis passes
through the focus after striking the mirror.
2. A ray that travels through the focus on the way to the
mirror or appears to come from the focus travels parallel to
the principal axis after striking the mirror.
3. A ray that strikes the point that is the intersection of
the spherical mirror and the principal axis is reflected so
that angle i r with respect to the principal axis.
4. A ray that passes through the center of curvature is
reflected back through the center of curvature.
5. A real image of an object point is formed at the
point where the rays converge. If the rays do not converge
at a point, trace back the reflected rays to a point from
where the extensions of each reflected ray seem to diverge
and that is where a virtual image will appear.
A concave spherical mirror typically was mounted on
the reverse side of the plane mirror on older microscopes
without sub-stage condensers. When the concave mirror
was rotated into the light path it focused the rays from the
sun or a lamp onto the specimen to provide bright, even
illumination (Carpenter, 1883; Hogg, 1898; Clark, 1925;
Barer, 1956). Concave mirrors are still used to increase the
intensity of the microscope illumination system; however,
nowadays they are placed behind the light source in order
to capture the backward traveling rays that would have
been lost. For this purpose, the light source is placed at the
center of curvature of the spherical mirror (Figure 2-9).
When the light source is placed at the center of curvature, the reflected rays converge on the light source
R
Object
f
Image
FIGURE 2-7 A virtual erect image is formed by the eye and brain of
a person looking at the reflection of an object placed between the focus
and a concave mirror. The virtual image of a point appears at the location
from which the rays of that point appear to have originated.
Focal
point
Principal axis
R
f
Object
R
f
Image
FIGURE 2-6 A beam of light, propagating parallel to the principal axis
of a concave mirror, is brought to a focus after it reflects off the mirror.
The focal point is equal to one-half the radius of curvature.
FIGURE 2-8 A real inverted image is produced by a concave mirror
when the object is placed in front of the focal point. The further the object
is from the focal point, the smaller the image, and the closer the image is
to the focal plane.
14
Light and Video Microscopy
so
so
yo
yo
R
yi
f
si
yi
f
R
si
FIGURE 2-9 When an object is placed at the radius of curvature of a
concave mirror, a real inverted image that is the same size as the object is
produced at the radius of curvature by a concave mirror. When the object
is the filament of a lamp, a concave mirror returns the rays going in the
wrong direction so that the lamp will appear twice as bright.
itself and form an inverted image. If the light source were
moved closer and closer to the focus of a concave mirror,
the reflected rays would converge farther and farther
away from the center of curvature. If the light source were
placed at the focus, the reflected rays would form a beam
parallel to the principal axis. This is the configuration used
in searchlights.
As an alternative to drawing characteristic rays, we
can determine where the reflected rays originating from
a luminous or nonluminous object will converge to form
an image with the aid of the following formula, which is
known as the Gaussian lens equation:
1/so 1/si 1/f
where so is the distance from the object to the mirror (in m),
si is the distance between the image and the mirror (in m),
and f is the focal length of the mirror (in m). The transverse magnification (mT), which is defined as yi/yo, is
given by the following formula:
m T y i /y o si /so
where yi and yo are linear dimensions (in m) of the image
and object, respectively. When using these formulae for
concave and convex mirrors, the following sign conventions
must be observed: so, si and f are positive when they are
on the left of V, where V is the intersection of the mirror
and the principal axis, and yi and yo are positive when they
are above the principal axis. When the mirror is concave,
the center of curvature is to the left of V and R is negative. When the mirror is convex, the center of curvature is
to the right of V and R is positive. The analytical formulae
used in geometric optics can be found in Menzel (1960)
and Woan (2000).
When si is positive, the image formed by a concave
mirror is real and when si is negative, the image formed
by a concave mirror is virtual. The image is erect when mT
is positive and inverted when mT is negative. The degree
of magnification or minification is given by the absolute
value of mT. Let’s have a little practice in using the preceding formulae:
● When an object is placed at infinity (so ), 1/so
equals zero, and thus 1/si 1/f and si f. In other words,
FIGURE 2-10 A virtual erect image is formed by a person looking at
the reflection of an object placed anywhere in front of a convex mirror.
The virtual image of a point appears at the location from which the rays
of that point appear to have originated.
when an object is placed at an infinite distance away from
the mirror, the image is formed at the focal point and the
magnification (–si/) is equal to zero.
● When an object is placed at the focus (so f),
1/so 1/f. Then 1/si must equal zero and si is equal to
infinity. In other words, when an object is placed at the
focus, the image is formed at infinity, and the magnification (–/so) is infinite.
● When an object is placed at the radius of curvature
(so 2f), then 1/so 1/(2f). Then 1/si 1/(2f), just as
½ – ¼ ¼. Thus si 2f, and the image is the same distance from the mirror as the object is. The magnification
(–2f /2f) is one, and the image is inverted.
● In any case where so f, the image will be real and
inverted.
What happens when the object is placed between
the focus and the mirror? In this case the reflected rays
diverge. These diverging rays appear to originate from
behind the mirror. Thus a virtual image is formed. The virtual image will be erect. We can determine the nature of
the image analytically:
●
When an object is placed at a distance ½f, then
2 /f 1/si 1/f
1/si 1/f 2 /f
1/si 1/f
si f
Since si is a negative number, the image is behind the
mirror. Since (–(–f))/(½f) equals 2, the image is erect,
virtual, and twice the height as the object.
Concave mirrors are spherical mirrors, which, by convention, have a negative radius of curvature. By contrast,
convex mirrors are spherical mirrors with a positive radius
of curvature (Figure 2-10). When a beam of light parallel to the principal axis strikes a convex mirror, the rays
are reflected away from the principal axis, and therefore
diverge. If we follow these rays backward, they appear to
originate from a point behind the mirror. This point is the
focus of the convex mirror. Since it is behind the mirror, it
is known as a virtual focus and f is negative.
15
Chapter | 2 The Geometric Relationship between Object and Image
strike the mirror, they are reflected back along the normal
and remain parallel. That is, they never converge and the
focal length of a plane mirror is equal to infinity. Therefore
1/f is equal to zero and the Gaussian lens equation for a
plane mirror becomes:
Using the law of reflection, we can determine the position, orientation, and size of the image formed by a convex
spherical mirror. This can be done easily by drawing two
or three characteristic rays using the following rules:
1. A ray traveling parallel to the principal axis
is reflected from the mirror as if it originated from the
focus.
2. A ray that travels toward the focus on the way to the
mirror is reflected back parallel to the principal axis after
striking the mirror.
3. A ray that strikes the point that is the intersection of
the spherical mirror and the principal axis is reflected so
that angle i r with respect to the principal axis.
4. A ray that strikes the mirror as it was heading
toward the center of curvature is reflected back along the
same path.
5. A real image of an object point is never formed. If
we trace back the reflected rays to a point from where the
extensions of each reflected ray seem to diverge, we will
find the virtual image of the object point that originated the
rays.
1/so 1/si 0
Since, for a plane mirror, si must equal –so, the image
formed by a plane mirror will always be virtual, erect, and
equal in size to the object. Table 2-1 summarizes the nature
of the images formed by spherical reflecting surfaces for
an object at a given location.
As long as we consider only the rays that emanate from
a given point of an object and strike close to the midpoint
of the mirror, we will find that these rays converge at a
point. However, when the incident rays hit the mirror far
from the midpoint, they will not be bent sharply enough
and will not converge at the same point as the rays that
strike close to the midpoint of the mirror. Thus even though
all rays obey the law of reflection where i r, with
a spherical mirror, a zone of confusion instead of a point
results. The inflation of a point into a sphere by a spherical mirror results in spherical aberration, from the Latin
word aberrans, which means wandering. Even though
spherical mirrors give rise to images with spherical aberration, they often are used because they are easy to make
and are thus inexpensive. Francesca Maurolico (1611)
and René Descartes (1637) found that spherical aberration could be eliminated by replacing a spherical mirror
with a parabolic mirror. In contrast to a sphere, where the
radius of curvature is constant, the radius of curvature at a
point on a parabola increases as the distance between the
point and the vertex increases. This relationship between
radius of curvature and position on a parabolic ensures
the elimination of spherical aberration. The rules used to
The focus of a convex mirror is negative and since an
object must be placed in front of a convex mirror, where
so is positive, to form an image, then it follows from the
Gaussian lens equation, that si will always be negative.
This means that the image formed by a convex mirror will
always be virtual. Since (–si/so) will always be positive, the
virtual image formed by a convex mirror will always be
erect. Moreover, since so is positive and (1/so 1/si) must
be negative, then the absolute value of si must be smaller
than the absolute value of so, and in all cases, the image
formed by a convex mirror will be minified.
The Gaussian lens equation can also be used to determine the characteristics of an image formed by a plane
mirror analytically. When light rays, parallel to the normal
TABLE 2-1 Nature of Images Formed by Spherical Mirrors
Object
Image in a concave mirror
Location
Type
Location
so 2f
Real
f si 2f
Inverted
Minified
so 2f
Real
si 2f
Inverted
Same size
f so 2f
Real
si 2f
Inverted
Magnified
so f
so f
Orientation
Virtual
si
so
Erect
Magnified
Object
Anywhere
Relative Size
Image in a convex mirror
Location
Type
Location
Virtual
si
f
Erect
Orientation
Relative Size
Minified
16
Light and Video Microscopy
f
R
FIGURE 2-11 Because of the law of reflection, where the angle of reflection equals the angle of incidence, a spherical mirror does not focus parallel
rays to a point, but instead produces a zone of confusion. This spherical aberration results because the rays that strike the distal regions of the mirror
are bent too strongly to go through the focus. Spherical aberration can be prevented by gradually and continuously decreasing the radius of curvature of
the distal regions of a concave mirror. Decreasing the radius of curvature gradually and continuously results in a parabolic mirror without any spherical
aberration.
characterize images formed by a spherical mirror can also
be used for characterizing the images formed by parabolic
mirrors (Figure 2-11).
REFLECTION FROM VARIOUS SOURCES
Catoptrics is the branch of optics dealing with the formation of images by mirrors. The name comes from the Greek
word Katoptrikos, which means “of or in a mirror.” There
are many chances to have fun studying image formation by
mirrors. Plato in his Timaeus, Aristotle in his Meteorologia,
and Euclid in his Catoptrica all describe various examples
of reflection in the natural world. Hero of Alexander,
who lived around 150 BC, wrote in his book, Catoptrics,
about the enjoyment people have in using mirrors “to see
ourselves inverted, standing on our heads, with three eyes
and two noses, and features distorted as if in intense grief”
just like in a fun house (Gamow, 1988). You can also have
fun understanding the use of mirrors in image formation
by studying kaleidoscopes (Brewster, 1818, 1858; Baker,
1985, 1987, 1990, 1993, 1999).
You can see your reflection in a plate glass window, in
pots and pans, in either side of a spoon, and in pools of
water. But don’t get too caught up in studying reflections.
Remember the story of Narcissus, the beautiful Greek boy,
who never missed a chance to admire his own reflection?
One day he saw his reflection in a cool mountain pool at
the bottom of a precipice. Seeing how beautiful he was,
he could not resist bending over and kissing his reflection.
However, he lost his balance, fell over the precipice, and
died. As a memoriam to the most beautiful human being
that had ever lived on Earth, the gods turned Narcissus into
a beautiful flower that, to this day, blossoms in the mountains in spring, and is still called Narcissus.
There is a close relationship between painting and geometrical optics (Hecht and Zajac, 1979; Summers, 2007).
Jan Van Eyck painted the reflection, in a convex mirror,
of John Arnolfini and His Wife in a painting by the same
name. In Venus and Cupid, Diego Rodriguez de Silva
y Veláquez painted Cupid holding a plane mirror so that
Venus could look at the viewer. Edouard Manet painted a
plane mirror that unintentionally did not follow the laws
of geometrical optics in The Bar at the Folies Bergères, to
give the viewer a more intimate feeling about the barmaid.
IMAGES FORMED BY REFRACTION
AT A PLANE SURFACE
In ancient times, it was known already that the position of
an image not only depended on the properties of opaque
surfaces, but also depended on the nature of the transparent medium that intercedes between the object and the
observer. In Catoptrica, Euclid explicitly stated as one of
his six assumptions: “If something is placed into a vessel
and a distance is so taken that it may no longer be seen,
with the distance held constant if water is poured, the thing
that has been placed will be seen again.”
Claudius Ptolemy (150 AD) described a simple party
trick, which would easily illustrate Euclid’s sixth assumption (Figure 2-12). Ptolemy wrote in his Theory of Vision
(Smith, 1996), that we could understand the
… breaking of rays… by means of a coin that is placed in a vessel called a baptistir. For, if the eye [A] remains fixed so that the
visual ray [C] passing over the lip of the vessel passes above the
coin, and if the water is then poured slowly into the vessel until
the ray that passes over the edge of the vessel is refracted toward
the interior to fall on the straight line extended from the eye to
a point [C] higher than the true point [B] at which the coin lies.
And it will be supposed not that the ray is refracted toward those
lower objects but, rather, that the objects themselves are floating
17
Chapter | 2 The Geometric Relationship between Object and Image
Apparent position of star
A
Actual position of star
C
B
FIGURE 2-12 An observer (A) is looking over the rim of a dish so he
or she can just not see a coin placed at B when the dish is full of air.
As water is gradually added to the dish the rays coming from the coin
are refracted at the water–air interface so that they will enter the eye.
Consequently, the coin will become visible to the observer. Thinking that
light travels in straight lines, the observer will think that the coin is at C.
and are raised up to meet the ray. For this reason, such objects
will be seen along the continuation of the incident visual ray, as
well as along the normal dropped from the visible object to the
water’s surface….
We see the coin suspended in the water and not at its true
position at the bottom of a bowl because our visual system,
which includes our eye and our brain, works on the assumption that light travels in straight lines. Consequently, we see
the apparent position and not the true position of the coin. This
brings up the question, what assumptions about light are made
by our visual system when we look through a microscope?
Ptolemy’s interest in the bending of light rays came
from his deep interest in astrology. He knew that light
had a big effect on plants for example, so it seemed reasonable to assume that the star light present at the time of
one’s birth would have a dramatic influence on a person’s
life (Ptolemy, 1936). Ptolemy knew, however, that since
light bends as it travels through different media of different
densities, he saw only the apparent positions of the stars,
and not their true positions. Thus if he wanted to know
the effect of star light on a person at the time of his or her
birth, he must know the real position of the stars and not
just the apparent positions he would observe after the rays
of starlight were bent as they traveled through the Earth’s
atmosphere (Figure 2-13). Again, we “see” the star in the
apparent position, instead of the real position because our
visual system made up of the eyes and brain “believes”
that light travels in a straight line, whether the intervening
medium is homogeneous or not.
Another common example, according to Cleomedes
(50 AD) where the assumption that light travels in straight
lines gives us a misleading view of the world is when the
mind “sees” a straight stick emerging from a water-air
interface as bent. In order to understand the relationship
between reality and the image, Ptolemy studied the relationship between the angle of incidence and the angle of
transmission.
Ptolemy noticed that when light travels from one transparent medium to another it travels forward in a straight
Earth
Atmosphere
FIGURE 2-13 Rays from stars are refracted as they enter the Earth’s
atmosphere. Since we think that light travels in straight lines, we see the
image of the star higher in the sky than it actually is.
θi
Glass
θt
FIGURE 2-14 When light travels from air to glass it is bent or refracted
toward the normal. By contrast, when light travels from glass to air,
it is bent away from the normal. This behavior is codified by the SnellDescartes law that states that the sine of the angle of incidence times the
refractive index of the incident medium equals the sine of the angle of
transmission times the refractive index of the transmission medium.
line, if and only if it enters the second medium perpendicular to the interface of the two media. However if the light
ray impinges on the second medium at an angle greater
than zero degrees relative to the normal, its direction of
travel, although still forward, will change. This phenomenon is known as refraction and the rays are said to be
refrangible.
When an incident light ray traveling through air strikes
a denser medium (e.g., water or glass) at an oblique angle
(θi) with respect to the normal, the ray is bent toward the
normal in the denser medium (Figure 2-14). The angle
that the light ray makes in the denser medium, relative
to the normal, is known as the angle of transmission (θt).
Ptolemy found that the angle of transmission is always
smaller than the angle of incidence. He made a chart of
the angles of incidence and transmission for an air-glass
interface, but even though he knew trigonometry, he never
figured out the relationship between the angle of incidence
and the angle of transmission. Likewise, Vitello, Kircher,
and Kepler also tried, but never discovered the relationship
between the angle of incidence and the angle of transmission (Priestley, 1772).
The mathematical relationship between the angle of
incidence and the angle of transmission was first worked
18
Light and Video Microscopy
out by Willebrord Snell in 1621 (Shedd, 1906). Snell, however, did not publish his work, and René Descartes, who
independently worked out the relationship, first published
the law of refraction in 1637. The Snell-Descartes Law
states that when light passes from air to a denser medium,
the ratio of the sine of the angle of incidence to the sine of
the angle of transmission is constant. The Snell-Descartes
Law can be expressed by the following equation:
sin θ i /sin θ t n
where n is a constant, known as the refractive index. It
is a characteristic of a given substance, and is correlated
with its density. Descartes (1637) assumed that light, like
sound, traveled faster in a more viscoelastic medium than
in a lesser one. He wrote that light
… was nothing else but a certain movement or an action,
received in a very subtle material that fills the pores of other bodies; and you should consider that, as a ball loses much more of
its agitation in falling against a soft body than, against one that
is hard, and as it rolls less easily on a carpet than on a totally
smooth table, so the action of this subtle material [light] can be
much more impeded by the particles of air…than by those of
water…. So that, the harder and firmer are the small particles
of a transparent body, the more easily do they allow the light to
pass; for this light does not have to drive any of them out of their
places, as a ball must expel those of water, in order to find passage among them.
Isaac Newton read Descartes’ work and after analyzing the refraction of light rays through media of differing
densities with his newly developed laws of motion, Isaac
Newton (1730) concluded that when light struck an interface between two media of different densities, the corpuscles of light were accelerated by the high density media
such that the component of the velocity perpendicular to
the interface, but not the component parallel to the interface, increased. Newton (Book II, Proposition X) assumed
that the relative velocity of light could be determined by
comparing the distance light traveled in the two media perpendicular to the interface at a given distance parallel to the
interface from the point of incidence. Once the velocities
were obtained, according to Newton, the attractive force
in each medium could be determined by taking the square
of the normal component of velocity in that medium. By
assuming that the refractive index was the ratio of the force
of attraction between the light corpuscles and the medium
of transmission relative to the force of attraction between
the light corpuscles and the medium of incidence and proportional to vincident2/vtransmission2, Newton could use his
theory to obtain the known refractive indices of transparent
media and to explain the cause of the refraction of light.
Newton’s analysis led him to the conclusion that
light travels faster in the denser medium than in the rarer
medium, a conclusion that no one thought to test for
approximately 150 years. Ultimately, Foucault showed that
the speed of light is faster in rarer media than it is in denser
media, a conclusion that was contrary to Newton’s hypothesis. However, Foucault’s data were consistent with the
wave nature of light (see Chapter 3) and now we define the
index of refraction according to the wave theory of light.
That is, the index of refraction is now defined as the ratio
of the velocity of light in a vacuum to the velocity of light
in the medium in question. That is,
n i c/v i
where ni is the index of refraction of medium i (dimensionless), c is the speed of light (2.99792458 × 108 m/s which
is almost equal to 3 × 108 m/s), and vi is the velocity of
light in medium i (in m/s). Table 2-2 lists the refractive
indices of various media. As you can see from the following table, the refractive index of a substance is correlated
with its density (in kg/m3) and indeed, the refractive index
depends on environmental variables like temperature and
pressure that affect the density. The temperature coefficient
of the refractive index is the amount the refractive index
changes for each degree of temperature. The temperature coefficients of refractive indices are approximately
0.000001–0.00001 for solids and 0.0003–0.0009 for liquids (McCrone et al., 1984).
The law of refraction or the Snell-Descartes Law can
be generalized to describe the bending of light by any two
media by including both of their refractive indices:
n i sin θ i n t sin θ t
where ni and nt are the refractive indices of the incident
and transmitting medium, respectively.
What is the physical meaning of the index of refraction? The index of refraction is a dimensionless measure
of the optical density of a material. The optical density is
essentially the concentration of electrons that can absorb
and reemit photons in the visible range. That is why the
refractive index is correlated with the density of the substance. However, there is more to the optical density than
the density of electrons since the optical density depends
on the color (e.g., wavelength) of the light. That is, each
TABLE 2-2 Refractive Indices of Various Media
(measured at 589.3 nm, which is the D line from a
sodium vapor lamp)
Medium
n
Approximate
density (kg/m3)
Vacuum
1.00000
0
Air
1.00027
1.25
Water
1.3330
1000
Glass
1.515
2600
Diamond
2.42
3500
19
Chapter | 2 The Geometric Relationship between Object and Image
medium has a cross-section, given in units of area, that
describes how much the atoms in it interfere with the forward motion of light of different colors. The greater the
cross-section of the atoms for light of a given color, the
greater the light is slowed down or bent by the atoms.
The absorption and subsequent reemission of photons
in the visible light range takes approximately 1015 s per
interaction. Therefore light of a given wavelength traveling through a medium with a high index of refraction travels slower than light traveling through a medium with a
lower index of refraction. The variation of refractive index
with wavelength is known as dispersion. Glass makers
go to great lengths varying the chemical composition of
glass to produce transparent lenses with minimal dispersion (Hovestadt, 1902). The wavelength-dependence of the
refractive index of glass and water is given in Table 2-3.
Dispersion by the glass that makes up a lens results in
unwanted chromatic aberration. On the other hand, dispersion is desirable and welcome in prisms where it results in
the separation of light by color (Figure 2-15).
Refraction causes an object that is immersed in a liquid to appear closer than it would if it were immersed in
air (Clark, 1925; McCrone et al., 1984). To see the effect
of refractive index on the apparent length, we can measure
the actual height of a cover slip and the apparent height
that it seems to have when light passes right through it.
To compare the actual height with the apparent height of
a cover slip, focus on a scratch on the top of a microscope
slide and read the value of the fine focus adjustment knob
(height a). Then place the cover slip over the scratch and
take another reading of the fine focus adjustment knob
(height b). Lastly, focus on a scratch on the top of the
cover slip and take a third reading of the fine focus adjustment knob (height c). The difference between (a) and (c)
gives the actual height of the cover slip, and the difference
between (b) and (c) gives the apparent height. This means
that the fine focus adjustment knob, which is calibrated in
micrometers/division for objects immersed in air, will not
directly give the actual thickness of a transparent specimen
if we focus on the top and bottom of it, but will give us
only the apparent thickness due to the “contraction effect”
of the refractive index.
This effect can be used to estimate the refractive index
of a substance. I say estimate, because this technique is
accurate only to within 5 to 10 percent of the refractive
index. In Chapter 8, I will discuss a more accurate method
to measure thickness using an interference microscope.
The refractive index can be estimated from the following
formula:
n actual thickness/apparent thickness
When a light ray travels from a medium with a higher
refractive index to a medium with a lower refractive index
it is possible for the angle of refraction to be greater than
90 degrees. This means that the incident ray will never
leave the first medium and enter the second medium
(Figure 2-16). This is known as total internal reflection
(Pluta, 1988). And since the rays undergoing reflection
travel in the same medium as the incident rays, the SnellDescartes Law reduces to the Law of Reflection, where
i r. The angle of incidence that will cause an angle
of refraction of 90 degrees is called the critical angle.
When θt is 90 degrees, the sine of θt equals one and the
critical angle is given by the following formulae:
n t /n i sin θ i
TABLE 2-3 Refractive Indices of Crown Glass, Flint
Glass, and Water for Different Wavelengths
486.1 nm
(blue)
589.3 nm
(yellow)
656.3 nm
(red)
Crown Glass
1.5240
1.5172
1.5145
Flint Glass
1.6391
1.6270
1.6221
Water
1.3372
1.3330
1.3312
or
θ i arcsin (n t /n i ) sin1 (n t /n i )
n2
θc
n1
n2
θi
n1
n1n2
n1
Red
θt
White
light
Violet
FIGURE 2-15 The refractive index of a medium is a function of the
wavelength of light. This is the reason that a prism can disperse or resolve
white light into its various color components.
FIGURE 2-16 When a light ray travels from a medium with a higher
refractive index to a medium with a lower refractive index, the angle of
refraction can be greater than 90°, resulting in internal reflection. The
critical angle θc is the incident angle that gives an angle of refraction
of 90°.
20
Light and Video Microscopy
TABLE 2-4 Critical Angles
Medium
Refractive
index
Critical angle
(degrees)
Water
1.3330
48.6066
Crown Glass
1.5172
41.2319
Flint Glass
1.6270
37.9249
Diamond
2.42
24.4075
Table 2-4 gives the critical angle for the air-medium interface for media with various refractive indices.
Diamonds are cut in such a way that the incoming light
undergoes total internal reflection within the diamond. The
increased optical path length allows the light to take maximal advantage of the dispersion of a diamond to break up
the spectrum and give more “fire.” Total internal reflection
also redirects the light so that it is emitted in the direction
of the observer. Prisms take advantage of total internal
reflection to reorient light by ninety degrees. Fiber optic
cables also take advantage of total internal reflection to
transmit light down a cable from one place to another without any loss in intensity. The optical fibers within a bundle can be configured in parallel to transmit an image or
arranged randomly to scramble and homogenize an image.
Total internal reflection is really a misnomer, since if
we move another refracting medium within a few hundred nanometers of the air-medium interface, the light will
jump from the first medium in which it was confined to the
second refracting medium. The ability to jump across the
forbidden zone is known as frustrated internal reflection
and the waves that jump across are known as evanescent
waves. The transfer of light trapped within a glass slide
to an object of interest can be visualized in a total internal
reflection microscope (TIRM; Temple, 1981). When combined with fluorescence microscopes (TIRFM), the evanescent wave can be used to visualize single molecules with
high contrast (Axelrod, 1990; Steyer and Almers, 1997;
Tokunaga and Yanagida, 1997; Gorman et al., 2007).
IMAGES FORMED BY REFRACTION
AT A CURVED SURFACE
Glass that is curved into the shape of a lentil seed is known
as a lens, the Latin word for lentil. Lenses typically are made
of glass, a silicate of sodium and calcium, but optical glass
may include oxides of lead, barium, antimony, and arsenic.
According to Pliny (Nat Hist XXXVI: 190, in Needham,
1962), glass was discovered accidentally by Phoenician
traders who needed something to prop up their cooking
pots while they were camping on a sandy spot where the
Belus River meets the sea. They used the bags of natron
(sodium carbonate) they were carrying; the heat fused the
sand (SiO2) and the natron along with some lime (calcium
carbonate) into small balls of glass. Glass manufacturing
began in Mesopotamia some time around 2900 BC.
In ancient Greece, lenses were used for starting fires.
Aristophanes (423 BC) wrote about the use of glass for
starting fires in The Clouds:
Strepsiades. “I say, haven’t you seen in druggists’ shops
That stone, that splendidly transparent stone,
By which they kindle fire?”
Socrates
“The burning glass?”
Strepsiades. “That’s it: well then, I’d get me one of these,
And as the clerk was entering down my case,
I’d stand, like this, some distance towards the sun,
And burn out every line.”
Not only have lenses been used to burn bills, but lenses
have long been used to improve our ability to see the
world. Using the laws of dioptrics, the study of refraction,
inventors have been able to develop spectacles, telescopes,
and microscopes. It is not clear who invented spectacles
and when people began to wear them. Perhaps Roger
Bacon made a pair in the thirteenth century. It is inscribed
on a tomb, that Salvinus Armatus, who died in 1317, was
the inventor of spectacles. In any case, by the mid sixteenth
century, Francesco Maurolico (1611) already understood
and wrote about how concave and convex lenses can be
used to correct nearsightedness and farsightedness, respectively, and the time was ripe for the invention of telescopes
and microscopes. It is thought that the children of spectacle makers playing with the lenses made by their fathers,
including James Metius, John Lippersheim, and Zacharias
Joannides (Jansen), may accidentally have looked
through two lenses at the same time and discovered that
objects appeared large and clear. Perhaps such playing led
to the invention of the telescope that Galileo (1653) used to
increase our field of clear vision to Jupiter and Saturn.
Soon after the invention of the telescope, the microscope, which Robert Hooke (1665) used to extend our
vision into the minute world of nature, was invented by
Zacharias Jansen and his son, Hans. The priority of discovery is not certain: Francis Fontana claims to have invented
the microscope in 1618, three years before the Jansens
(Priestley, 1772).
Thus the extent of our vision has been increased orders of
magnitude, thanks to a little grain of sand, the main component of glass lenses. William Blake (1757–1827) wrote:
To see a world in a grain of sand
And a heaven in a wild flower
Hold infinity in the palm of your hand
And eternity in an hour.
When a light ray passes from air through a piece of glass
with parallel edges and returns to the air, the refraction at
the far edge reverses the refraction at the near edge and the
ray emerges parallel to the incident ray, although slightly
displaced (Figure 2-17). The amount of displacement
21
Chapter | 2 The Geometric Relationship between Object and Image
θi
2
θi
Air
θt
θt
2
1
θt2
Glass
θi1
Air
FIGURE 2-17 Light traveling from air through a piece of glass with
parallel sides and back through air is slightly displaced compared with
where the light would have been had it passed through only air. The
degree of displacement depends on the thickness of the glass and its
refractive index. The light that leaves the glass is parallel to the light that
enters the glass because the refraction at the far side of the glass reverses
the refraction at the near side.
θt1
θi2
FIGURE 2-18 When the two surfaces of the glass are not parallel,
but form a prism, the refraction that takes place on the far side does not
reverse the effect of the refraction that takes place on the near side. The
second refraction amplifies the first refraction and the incident light is
bent toward the base of the prism.
θi1
θt1
θi2
θt2
FIGURE 2-19 Two prisms, with their bases cemented together, bend the incident light propagating parallel to the bases of the prisms toward the
bases. The prisms do not have the correct shape to focus parallel light to a point since the rays that strike the two corresponding prisms farther and
farther from the principal axis will converge at greater and greater distances from the double prism.
depends on two things: the refractive index of the glass and
the distance the beam travels in the glass. However, when
the edges are not parallel, the refraction at the far edge will
not reverse the effect of the refraction at the near edge. In
this case, the light ray will not emerge parallel to the incident light ray, but will be bent in a manner that depends on
the shape of the edges.
Consider a ray of light passing through a prism oriented
with its apex upward (Figure 2-18). If the ray of light hits
the normal at an angle from below, it crosses into the glass
above the normal but makes a smaller angle with respect
to the normal since the glass has a higher refractive index
than the air. When the ray of light reaches the glass–air
interface at the far side of the prism, it makes an angle
with a new normal. As it emerges into the air it bends away
from the normal since the refractive index of air is less than
the refractive index of glass. The result is the ray of light is
bent twice in the same direction.
What would happen to the incident light rays when
they strike two prisms whose bases are cemented together
(Figure 2-19)? Suppose that a parallel beam of light
impinges on both prisms with an orientation parallel to the
bases. The light that strikes the upper prism will be bent
downward toward its base and the light that strikes the
lower prism will be bent upward toward its base. The two
halves of the beam of light will converge and cross on the
other side.
The beam emerging from this double prism will not
come to a focus since the rays that strike the two corresponding prisms farther and farther from the principal axis
will converge at greater and greater distances from the
double prism. However, imagine that the front and back
surfaces of the prisms were smoothed out to form a “lentil-shaped” lens (Figure 2-20). Now suppose that a parallel beam of light impinges on the near edge of the glass.
The light ray that goes through the thickest, center portion
22
Light and Video Microscopy
of the glass will enter parallel to the normal at that point
and thus will go straight through the glass. Light rays that
impinge on the glass just above this point will make a
small angle with the normal and thus will be bent toward
the axis. Light rays that impinge on the glass even higher
up will make an even larger angle with the normal and thus
will be bent even more toward the normal. This behavior
continues as the parallel light rays impinge farther and farther from the axis. That is, as the parallel rays strike farther and farther from the axis, the rays are bent more and
more toward the axis. The same is true for the light rays
that strike the glass below the thickest point.
As the light rays reach the other side of the glass they
will be bent away from the normal since they will be traveling from a medium with a higher refractive index to a
medium with a lower refractive index. Thus, the light rays
that travel through the thickest part of the glass will travel
straight through since they make a zero degree angle with
the normal. The imaginary line coincident with this ray
is known as the principal axis. The rays that pass through
the thinner part of the glass arrive at the glass–air interface
at some angle to the normal. Thus, they will be refracted
toward the principal axis when they emerge from the lens.
The further from the principal axis the rays emerge, the
more they will be bent by the lens. Consequently, all the
rays converge at one point known as the focus.
The surface of a lens can be convex, flat, or concave.
Lenses can be biconvex, plano-convex, or concavo-convex
(also called a meniscus lens). All these lenses are thickest
at the center and thinnest at the edges, and thus, they typically act as converging lenses. Alternatively, lenses can be
biconcave, plano-concave, or convexo-concave. All these
lenses are thinnest at the center and thickest at the edges,
and consequently they typically act as diverging lenses
by causing the rays to diverge from the principal axis.
Converging lenses and diverging lenses can act as diverging lenses and converging lenses, respectively; but only if
their refractive index is smaller than the refractive index of
the medium in which they are used (Figure 2-21).
The ability of a lens to bend or refract light rays is characterized by its focal length; the shorter the focal length,
the greater the ability of the lens to bend light. The focal
length is related to the radius of curvature of the lens, the
refractive index of the lens (nl), and the refractive index of
the medium (nm). The focal length of a lens is given by the
lens maker’s equation:
1/f ((n1 /n m ) 1)(1/R1 1/R 2 )
θi1
θt1 θi
2
θt3 θi4
θt2
θt4
θi3
FIGURE 2-20 A lentil-shaped surface has the correct geometry to focus
parallel rays to a point.
fi
where R1 is the radius of curvature of the first surface and
R2 is the radius of curvature of the second surface. For a
biconvex lens, R1 is right of V, the intersection of the lens
with the principal axis, so R1 is positive and R2 is left of
V so it is negative. For a biconcave lens, R1 is negative
and R2 is positive. When one surface of the lens is planar,
R and 1/R 0. For a biconvex lens made of glass
(n 1.515) surrounded by air (n 1), 1/f 1.03/R. That
is, the focal length is approximately equal to the radius
of curvature. The focal length of a plano-convex lens is
approximately equal to half the radius of curvature.
fi
nl nm
nl nm
fi
fi
nl nm
nl nm
Converging lenses
Diverging lenses
FIGURE 2-21 A lentil-shaped biconvex piece of glass focuses parallel rays when the refractive index of the lens nl is greater than the refractive index
of the medium nm. When the refractive index of the medium is greater than the refractive index of the lens, the lens must be biconcave to focus parallel
rays. Whether a lens is converging or diverging is not a function of the lens alone but of the lens and its environment.
23
Chapter | 2 The Geometric Relationship between Object and Image
Every lens has a unique distance, called the object focal
length (fo). If an object is placed at this distance from a
converging lens, the image will appear an infinite distance
from the other side of the lens. In other words, if a point
source of light is placed on the principal axis at fo, a beam
of light parallel to the principal axis will emerge from the
other side of the lens.
Every lens has another unique distance called the image
focal length (fi). If an object is placed an infinite distance
in front of a converging lens, the image will appear at the
image focal length on the other side of the lens. In other
words, if a bundle of light impinges on the lens parallel to
the principal axis, it will converge on the principal axis,
at a distance fi from the lens. The focal planes are the two
planes, which are parallel to the lens, perpendicular to the
principal axis, and include a focal point.
Parallel rays emerging from a diverging lens appear to
come from a source placed at the object focal point. Parallel
rays impinging on a diverging lens appear to focus at the
image focal point. Light diverges from a real object and
converges toward a real image. By contrast, the light converges to a virtual object and diverges from a virtual image.
In order to determine where an image formed by a lens
will appear, we can use the method of ray tracing and draw
two or three characteristic rays. Remember:
● A ray that strikes a converging lens parallel to the
principal axis goes through the focus (fi).
● A ray that strikes a diverging lens parallel to the principal axis appears to have come from the focus (fi).
● A ray that strikes a converging lens after it passes
through the focus (fo) emerges parallel to the principal axis.
● A ray that strikes a diverging lens on its way to the
focus (fo) emerges parallel to the principal axis.
● A ray that passes through the center of a converging
or diverging lens (V) passes through undeviated.
Table 2-5 characterizes the type, location, orientation,
and relative size of images formed by converging and
diverging lenses. Note the similarity between the images
formed by concave mirrors and converging lenses and the
images formed by convex mirrors and diverging lenses.
Just as we could determine the characteristics of images
formed by mirrors analytically, we can use the Gaussian
lens equation and the magnification formula to determine
the characteristics of images formed by lenses analytically.
1/f 1/si 1/so
m T y i /y o si /so
We must, however, know the sign conventions for lenses:
so and fo are positive when they are to the left of V (the
intersection of the lens and the principal axis); si and fi are
positive when they are to the right of V; yi and yo are positive when they are above the principal axis; xo is positive
when it is to the left of fo; xi is positive when it is to the
right of fi; and R is positive when the center of curvature is
to the right of V and negative when the center of curvature
is to the left of V, above the principal axis.
When si is positive, the image formed by a spherical
lens is real and when si is negative, the image formed by
a spherical lens is virtual. The image is erect when mT is
positive and inverted when mT is negative. The degree of
magnification or minification is given by the absolute value
of mT. Notice the similarities between mirrors and lenses in
the sign conventions.
Not only can we use the Gaussian lens equation to predict and describe the images formed by lenses, but if we
know the relationship between the object and the image,
we can use the Gaussian lens equation to determine the
focal lengths of lenses. Next, I will derive the Gaussian
lens equation from geometrical optics. Consider the following optical situation (Figure 2-22):
TABLE 2-5 Nature of Images Formed by Spherical Lenses
Object
Image formed by a converging lens
Location
Type
Location
Orientation
Relative Size
so 2f
Real
f si 2f
Inverted
Minified
so 2f
Real
si 2f
Inverted
Same size
f so 2f
Real
si 2f
Inverted
Magnified
Erect
Magnified
so f
so f
Virtual
Object
si
so
Image formed by a diverging lens
Location
Type
Location
Orientation
Relative Size
Anywhere
Virtual
si
f
Erect
Minified
24
Light and Video Microscopy
yo
β
fo
γ
α
γ
β
xo
f
fi
f
so
α
yi
xi
si
FIGURE 2-22 Image formation by a converging lens with focal length f. The object with height yo and the image with height yi are distances so and si
from the lens, respectively. xo so – f and xi si – f .
yo
yo
α
fi
α
xi
Cancel like terms.
fo
β
β
xo
yi
yi
1/f (so si )/so si
1/f so /so si si /so si
Cancel like terms again and we get:
yo
γ
so
γ
1/f 1/si 1/so
si
yi
FIGURE 2-23 Three pairs of similar triangles made by the rays shown
in Figure 2-22.
which is the Gaussian lens equation.
Since tan γ yo/so yi/si, then yi/yo si/so. The
transverse magnification (yi/yo) is given by the following
equation:
m T si /so
Look at the pairs of similar triangles (Figure 2-23).
Remember that the tangent is the ratio of the length of the
opposite side to the length of the adjacent side. Since tan
α yo/fi yi/xi, and tan β yo/xo yi/fo, then
y i /y o x i /fi fo /x o
From Figure 2-22, we see that:
so fo x o
si fi x i
Rearranging we get:
x o so fo
x i si fi
Since xi/fi fo/xo, then
(si fi )/fi fo /(so fo )
For a biconvex or biconcave lens fo fi f, therefore
(si f)/f f/(so f)
f2 (so f)(si f)
f2 so si so f si f f2
f2 f2 so si so f si f 0
so si so f si f f(so si )
Multiply both sides by (1/f) (1/sosi)
(so si )(1/f)(1/so si ) f(so si )(1/f)(1/so si )
The minus sign comes from including the vectorial nature
of the distances and applying the sign conventions for
lenses. A positive magnification means the image is erect,
a negative magnification means the image is inverted.
The Gaussian lens equation is an approximation that
applies only to “thin lenses.” The equations used to determine the characteristics of an image made by a real or
“thick lens” can be found in Hecht and Zajac (1974).
Most lenses used in microscopy are compound lenses;
that is, they are composed of more than one refracting element (Figure 2-24). Microscope lenses include the eyepiece or ocular, the objective lens, the sub-stage condenser
lens, and the collecting lens. We can use the ray tracing
method to predict the type, location, orientation, and size
of the image formed by compound lenses. When using the
ray tracing method for compound lens, we follow the same
rules as for a single, thin lens. When the two lenses are
separated by a distance greater than the sum of their focal
lengths we can assume that the real image formed by the
first lens serves as a real object for the second lens.
In Figure 2-25, the compound lens system forms a real,
erect, magnified image. Here I would like to introduce four
new terms that characterize an optical system composed
of more than one lens. The distance from the object focus
to the first surface of the first optical element is called the
front focal length. The front focal plane occurs at this distance, perpendicular to the principal axis. The back (or
rear) focal length is the distance between the last optical
25
Eyepiece
Objective
Stage
Sub-stage Condenser
Collector
Aperture
Diaphragm
Field
Diaphragm
Mirror
Chapter | 2 The Geometric Relationship between Object and Image
FIGURE 2-24 The lenses found in a microscope are composed of more than one element.
L1
fo1
L2
fi1
fo2
fi 2
2
si1
FIGURE 2-25 Two converging lenses that are separated by a distance greater than the sum of their focal lengths form a real erect image.
L1
fo1
L2
fo2
fi1
fi 2
d
FIGURE 2-26
Image formation by two converging lenses separated by a distance smaller than either of their focal lengths.
surface and the second focal point (Fi2). The plane perpendicular to the principal axis that includes Fi2, is known as
the back (or rear) focal plane.
Now let us consider the case of two thin lenses that are
separated by a distance smaller than either of their focal
lengths (Figure 2-26). How do we know where the image
will be in this case? First consider ray 2; it goes through
the focus (fo1) of lens 1 and thus emerges parallel to the
principal axis. Since it enters lens 2 parallel to the principal axis, it will pass through the focus of lens 2 (fi2).
Now consider ray 1. It travels through the center of
lens 2 and thus does not deviate—it is as if lens 2 were not
there. However we do not know the angle that ray 1 makes
as it goes through lens 1 or lens 2. So, imagine that lens 2
is not there and construct two characteristic rays: one that
strikes the lens after it passes through the focus (fo1), and
one that passes through the center of lens 1 (Figure 2-27).
These two characteristic rays converge at P2.
Now we can easily construct ray 1 by tracing it backward from P2 through O2 through L1 to S2. We can also
draw ray 1 on the original figure where we easily drew ray 2
and see where ray 1 and ray 2 converge. This is where the
image is. It is real, inverted, and minified.
Just like we can determine the characteristics of images
formed by mirrors and single lenses analytically, we can
determine the position of images formed by compound
lenses analytically with the aid of the following equation:
si f2 d [f1f2 so /(so f1 )]
d f2 [f1so /(so f1 )]
26
Light and Video Microscopy
L1
L2
O2
fo1
S2
P′2
FIGURE 2-27 Finding the image produced by the first lens of the pair shown in Figure 2-26, if the second lens were not there and deducing the ray
that would go through the center of the second lens if it were there.
where so is the usual object distance (in m), si is the usual
image distance (in m), f1 is the focal length of lens 1 (in m),
f2 is the focal length of lens 2 (in m), and d is the distance
between the two lens (in m).
The total transverse magnification (mT) of the optical
system is given by the product of the magnification due to
lens 1 and the magnification due to lens 2.
m Total (m T1 )(m T 2 )
Thus, the first lens produces an intermediate image of magnification mT1, which is magnified by the second lens by
mT2. The total transverse magnification can be determined
analytically by the following equation:
m Total
f1si
d(so f1 ) so f1
The image is erect when mTotal is positive and inverted
when mTotal is negative. The front and back focal lengths of
the compound lens is given by the following formulae:
front focal length f1 (d f2 )
d (f1 f2 )
back focal length f2 (d f1 )
d (f1 f2 )
When d 0, the front and back focal lengths are equal,
and the focal length (f) of the optical system is given by
the following formula:
1/f 1/f1 1/f2
where f1 is the focal length of lens 1, and f2 is the focal
length of lens 2.
The dioptric power of a lens system (in m1 or diopters)
is defined as the reciprocal of the focal length (in m) and is
given by the following formula:
D 1/f
Therefore the total dioptric power of the optical system
(DTotal) is given by the following formula:
D Total D1 D2
where D1 is the dioptric power of lens 1, and D2 is the
dioptric power of lens 2. The greater the dioptric power of
a lens, the shorter its focal length and the more it bends
light. The strength of spectacles often is given in diopters.
A compound lens can also be described by its f number,
or f/#, where f/# is the ratio of the focal length to the diameter of the compound lens. The strengths of camera lenses
often are given in f numbers. A compound lens, 50 mm in
diameter, with a focal length of 200 mm, has an f/# of f/4.
The f-stops on a camera or on a photographic enlarger are
selected specifically so that every time you close down the
lens by one stop, you decrease the light by one-half.
FERMAT’S PRINCIPLE
By now we know how to use the Snell-Descartes Law to
predict the behavior of light rays through thin, thick, and
compound lenses. Now we will ask why light follows
the Snell-Descartes Law. According to Richard Feynman
(Feynman et al., 1963), the development of science proceeds in the following manner: First we make observations;
then we gather numbers and quantify the observations.
Third, we find a law that summarizes all observations, and
then comes the real glory of science: we find a new way of
thinking that makes the law self-evident. The new way of
thinking that made the Snell-Descartes Law evident came
from Pierre de Fermat in 1657. It is known as the principle of least time, or Fermat’s Principle. Fermat’s Principle
states that of all the possible paths that the light may take
to get from one point to another, light takes the path that
requires the shortest time.
First I will demonstrate that Fermat’s Principle is true
in the case of reflection in a plane mirror. Consider the following situation (Figure 2-28).
Which is the way to get from point A to point B in the
shortest time if we say that the light must strike the mirror
(MM)? Remember, the speed of light (c) in a vacuum is a
constant, so the distance light travels is related to the duration of travel by the following equation:
duration distance/c
The light could go to the mirror as quickly as possible
and strike at point D, but then it has a long way to go to
get to point B. Alternatively, the light can strike the mirror at point E and then continue to point B. The time it
takes to take this path is less than the time it takes to take
27
Chapter | 2 The Geometric Relationship between Object and Image
A
N
qi qr
B
A
B
F
M
M
D
E
C
F
M
M⬘
FIGURE 2-28 Why does the reflected light go from A to B by striking
point C on the mirror instead of rushing to the mirror and striking it at D
or rushing from the mirror after it strikes it at F?
A
C
B
B
FIGURE 2-30 The shortest distance between two points is a straight
line. Since AB is a straight line and AB AB, the shortest distance
between A and B is when ACN BCN, or the angle of incidence
equals the angle of reflection.
A
a
h
M
E
C
F
M
θi
LAND
SEA
x
h
ax
C
θt
b
B
FIGURE 2-29 B and B are equidistant to the mirror. BC BC and
EB EB.
the first path; however, this still isn’t the shortest path.
Remembering that light travels at a constant velocity in a
given medium, we can find the point where the light will
strike the mirror in order to get to point B in the shortest
possible time by using the following trick (Figure 2-29).
Consider an artificial point B, which is on the other side
of the mirror, and is the same distance below MM as point
B is above it. Draw the line EB. Because BFE is a right
angle and since BF FB and EF EF, then EB is equal
to EB (using the Pythagorean Theorem). Therefore the
distance AE EB is equal to AE EB. This distance is
proportional to the time it will take the light to travel. Since
the smallest distance between two points is a straight line,
the distance AC CB is the shortest line. How do we find
where point C is? Point C is the point where the light will
strike the mirror if it heads toward the artificial point B.
Now we will use geometry to find point C (Figure 2-30).
Since BF BF, CF CF, and CB CB, FCB and FCB
are similar triangles. Therefore FCB FCB. Also
FCB is equal to ACM since they are vertical angles.
Thus FCB ACM. Since both MCA and ACN,
and FCB and BCN are pairs of complementary angles,
ACN 90° – ACM and BCN 90°– FCB. Since
FCB ACM, it follows that ACN is equal to BCN.
Thus, the light ray that will take the shortest time to get
from point A to point B by striking the mirror will make
an angle where the angle of incidence equals the angle of
reflection. Therefore, according to Fermat, the reason the
angle of incidence equals the angle of reflection is because
light takes the path that requires the shortest time.
Hero of Alexandria proposed in his book, Catoptrics,
that light takes the path that is the shortest distance between
AC 1
(h2x2) 2
tAC b
1
(h2x2) 2
/ Vi
B
ax
FIGURE 2-31 Using Fermat’s Principle as the basis of the SnellDescartes law, a x (a–x).
1
CB (b2(ax)2) 2
1
tCB (b2(ax)2) 2 / Vt
two points when it is reflected from a mirror. This explanation would also be valid for the example with the mirror given earlier; however, Hero’s explanation could not be
applied to refraction since the shortest distance between two
points is a straight line and light bends upon refraction. This
was the impetus for Fermat to come up with a principle that
could be generalized for both reflection and refraction. Let
us use Fermat’s Principle to derive the Snell-Descartes Law
(Figure 2-31). We must assume that the speed of light in
water is slower than the speed of light in air by a factor, n.
According to Fermat’s Principle we must get from point
A to point B in the shortest possible time. According to
Hero of Alexandria we must get from point A to point B by
the shortest possible distance. The Snell-Descartes Law tells
us that Hero cannot be right. Let’s use an analogy to illustrate that Fermat’s Principle will lead to the Snell-Descartes
Law. Assume that your boyfriend or girlfriend fell out of
a boat and he or she is screaming for help at point B. You
are standing at point A. What do you do? You have to run
and swim to the poor victim. Do you follow a straight line?
(Yes, unless you use a little intelligence and apply Fermat’s
Principle first). If you think about it, you realize that you
can run faster than you can swim, so it would be advantageous to travel a greater distance on land than in the sea.
Where is point C, where you should enter the water?
The time that it will take to go from point A to point B
through point C will be equal to:
t t AC t CB (h 2 x 2 )1/ 2
(b2 (a x)2 )1/ 2
vi
vt
28
Light and Video Microscopy
where vi is the speed of travel on land (in m/s), and vt is
the speed of travel in the sea (in m/s).
If ACB is the quickest path, then any other path will be longer. So if we graph the time required to take each path and plot
these values against various points on the land/sea interface,
then point C will appear as the minimum. Near point C the
curve is almost flat. In calculus this is called a stationary value.
In order to minimize t with respect to variations in x we must
set dt/dx 0. The minimum (and maximum) time is where
dt/dx 0. (A full derivation requires taking the second derivative, which will determine whether C is a minimum or a maximum. If the second derivative is positive, C is a minimum.)
dt/dx and
x
(x a)
v i (h 2 x 2 )1/2
v t (b2 (a x)2 )1/2
x
(a x)
2
2
1
2
/
2
v i (h x )
v t (b (a x)2 )1/2
x
Since sin θ i 2
and
(h x 2 )1/2
(a x)
sin θ t 2
(b (a x)2 )1/2
then
sin θ t
sin θ i
vi
vt
d (h 2 x 2 )1/2
(b2 (a x)2 )1/2
0
dx
vi
vt
To solve this equation, use the chain rule. First differentiate
the first term:
d (h 2 x 2 )1/2
(h 2 x 2 )1/2
(1/2)
(2 x)
dx
vi
vi
(h 2 x 2 )1/2
(x)
vi
Use the chain rule for the second term:
d (b2 (a x)2 )1/2
d (b2 a 2 2ax x 2 )1/2
dx
vt
dx
vt
d (b2 a 2 2ax x 2 )1/2
dx
vt
(1/2)(b2 (a x 2 )1/2
( 2 x 2a )
vt
Since 2x 2a 2a 2x 2(x a), then
d (b2 a 2 2ax x 2 )1/2
dx
vt
(1/2)
(b2 a 2 2ax x 2 )1/2
(2)(x a)
vt
(x a)
(b2 (a x)2 )1/2
vt
Thus
dt/dx (x)
(h 2 x 2 )1/2
vi
(x a)
(b2 (a x)2 )1/2
0
vt
x
dt/dx 2
v i (h x 2 )1/2
(x a)
0
v i (b2 (a x)2 )1/2
Multiply both sides by c.
sin θ t
sin θ i
c
vi
vt
c
Since n i c
c
and n t vi
vt
then
n i sin θ i n t sin θ t
which is the Snell-Descartes Law.
I have just derived the Snell-Descartes Law using the
assumption that, when light travels from point A to point
B, it takes the path that gives the minimum transit time.
It is clear that the whole beautiful structure of geometric optics can be reduced to a single principle: Fermat’s
Principle of Least Time.
OPTICAL PATH LENGTH
The optical path length (OPL) through a homogeneous
medium is defined as the product of the thickness (s) of the
medium and the refractive index (n) of that medium:
OPL ns
If the medium is not homogeneous, but composed of many
layers, each having a different thickness and refractive
index (Figure 2-32), then the time it takes light to pass
from the beginning of the first layer through the mth layer
is given by the following formula:
m
t (1/c)∑ n js j (1/c) OPL
j1
and after rearranging,
OPL m
∑ n js j
j1
29
Chapter | 2 The Geometric Relationship between Object and Image
A
n1
Cool air
s1
Hot air
s2
n2
s3
n3
si
ni
sn1
nn1
sn
nn
B
FIGURE 2-32 A ray propagating through a specimen composed of
layers with various refractive indices and thicknesses has an optical path
length. The optical path length differs from the length itself. The optical
path length is obtained by finding the product of the refractive index and
thickness of each layer and then summing the products for all the layers.
The optical path length (OPL, in m) is defined as the sum
of the products of the refractive index of a given medium
and the distance traveled in that medium. In a perfect lens,
the optical path lengths of each and every ray emanating
from a given point on the object and going to the conjugate
point on the image are identical. That is, in a perfect lens,
the optical path difference (OPD) between all rays vanishes. We can also restate Fermat’s Principle by saying that
light, in going from point A to point B, traverses the route
having the shortest optical path length.
We can observe Fermat’s Principle in the world around
us. For example, when the sun begins to set, it looks like it
is above the horizon. However, it is actually already below
it. This is because the earth’s atmosphere is rare at the top
and dense at the bottom and the light travels faster through
the rarer medium than through the denser medium. Thus
the light can get to us more quickly if it does not travel in a
straight line, but travels a short distance through the denser
atmosphere and a longer distance through the rarer atmosphere. Since our visual system is hardwired to believe that
light travels in straight lines, the rays from the setting sun
appear to come from a position higher in the sky than the
sun actually is.
Another everyday example of Fermat’s Principle
is the mirage we see when we are driving on hot roads
(Figure 2-33). From a distance we see water on the road
FIGURE 2-33 On a hot day, when we look down at the road ahead of
us, we see the image of a tree or clouds on the road because light obeys
Fermat’s Principle and travels to our eyes in an arc. However, we think
that light travels through a medium with a continuously varying refractive
index in straight lines.
but when we get there it is as dry as a desert. What we
are really seeing is the skylight reflected on the road.
How does the skylight reflected from the road end up in
our eyes? The air is very hot and rarer just above the road
and cooler and denser higher up. The light comes to our
downward-looking eyes in the least amount of time by
traveling the longest distance in the rarer air and the shortest distance in the denser air. Since our visual system is
hardwired to believe that light travels in straight lines, the
image of the sky appears on the road ahead of us.
For other examples of natural phenomena that can be
explained by Fermat’s Principle, see Minnaert (1954) and
Williamson and Cummins (1983). And of course we see
Fermat’s principle every time we look through a camera
lens, spectacles, a microscope, a telescope, or any instrument that has a lens.
LENS ABERRATIONS
In order to get a perfect image of a specimen, all the rays
that diverge from each point of the object must converge at
the conjugate point in the image. However a lens may have
aberrations that cause some of the rays to wander (Gage
and Gage, 1914). The rays will wander if the focal length
varies for the different rays that come from each point on
the object. Just as is the case for mirrors, spherical aberration occurs when using spherical lenses. Spherical aberration occurs because the rays from any given object point
that hit the lens far from the principal axis are refracted
too strongly (Figure 2-34). This results in a zone of confusion around each point in the image plane and a point is
inflated into a sphere. Spherical aberration can be reduced
by replacing a biconvex lens with two plano-convex lenses,
or by using an aspherical lens. Lenses that have been corrected for spherical aberration are known as aspheric,
aplanactic, achromatic, fluorite, and apochromatic, in order
of increasing correction.
30
Light and Video Microscopy
Crown
Flint
Average
focal
plane
FIGURE 2-34 Spherical aberration occurs because the rays from any
given object point that hit a lens with spherical surfaces far from the principal axis are refracted too strongly. This results in a circle of confusion.
Spherical aberration can be reduced by grinding the lens so that it has
aspherical surfaces.
Violet
Average
focal plane
Achromatic doublet
FIGURE 2-36 Chromatic aberration can be reduced by combining a
diverging lens made of flint glass with a converging lens made of crown
glass. Because the flint glass has a greater dispersion than the crown
glass, the chromatic aberration produced by the crown glass is reduced
more than the magnification produced by the crown glass is reduced.
Red
Average
focal
Violet
plane
Red
O
FIGURE 2-35 Chromatic aberration occurs because the refractive index
of glass is color-dependent. This results in the violet-blue rays being more
strongly refracted by glass than the orange-red rays.
Rays of every wavelength are focused to the same point
by mirrors. However, since the refractive index of a transparent medium depends on wavelength, the lenses show
chromatic aberration. That is, rays of different colors coming from the same point on the object disperse and do not
focus at the same place in the object plane. Consequently,
instead of a single image, multiple monochromatic images
with varying degrees of magnification are produced by a
lens with chromatic aberration (Figure 2-35). Newton
believed that all transparent materials had an equal ability to disperse white light into colored light and therefore
chromatic aberrations could not be corrected. However,
Newton did not have sufficient observational data and John
Dollond (1758) showed that by combining two materials
with different dispersive powers, for example crown glass
and flint glass, color-corrected lenses in fact could be made
(Figure 2-36).
Lenses corrected for chromatic aberration are labeled
achromatic, fluorite, and apochromatic, in order of increasing correction. These compound lenses are made by putting together a plano-concave lens made out of flint glass
with a biconvex lens made out of crown glass, such that
each lens cancels the chromatic aberration of the other one
while still focusing the rays. Perhaps two types of plastic
with complementary dispersion properties could be put
together to make color-corrected lenses. Semiconductor
technology has been used to lightly coat lenses with silicon
FIGURE 2-37 The image plane of a converging lens is not flat.
Additional lens elements must be added to the converging lens to decrease
the focal length of the image close to the axis.
to correct for chromatic aberration. This technique is based
on the principles of diffraction and not on typical geometric optics (Veldkamp and McHugh, 1992). This correction
works because refraction causes blue light to be bent stronger than red, whereas diffraction causes red light to be bent
stronger than blue.
In order to get a perfect image, all the light rays emanating from each point of the object, must arrive at the
image plane by following equal optical path lengths. As
we observed with the camera obscura, the only way this
is possible is by curving the image plane (Figure 2-37).
However, unlike our retina, film and silicon imaging chips
are flat. Therefore if we want the image at the center of the
field and the edge of the field to be in focus at the same
time, we must use a lens that has been corrected for “curvature of field.” Lenses that are corrected to have a flat
field have the prefix F- or Plan-. A Plan-apochromat is the
most highly corrected lens.
An image is a point-by-point representation of an
object. We have learned how to determine the position, orientation, and magnification of an image formed by reflection in a mirror, or by refraction through a lens. We can
31
Chapter | 2 The Geometric Relationship between Object and Image
n 1.38
n 1.38
n 1.38
n 1.38
FIGURE 2-38 The lonely fungi obey the laws of geometric optics. In air, light is focused on the far side of the cylindrical sporangiophore, and the
fungus bends toward the light source. In a high refractive index medium, light is dispersed over the far side of the sporangiophore and is brightest on the
side closest to the light source. In this case, the fungus bends away from the light source.
determine the properties of an image graphically, using
characteristic rays, or analytically, using the Gaussian
lens equation. We have determined that light travels from
the object to the image as if it were taking the path that
takes the least time. As long as all the rays emanating from
each point in an object have the same optical path length
when they meet on a flat image plane, the image will be
perfect. However, we see that lenses can have spherical
and chromatic aberrations and they can cause curvature of
field, which results in an image that is not a perfect pointby-point replica of the object. In Chapter 3, I will show
that even if the lens system were perfect, the very nature
of light would result in an imperfect image. In Chapter 4,
I will show you how to select lenses that minimize these
aberrations while using a microscope.
GEOMETRIC OPTICS AND BIOLOGY
The principles of geometric optics can be applied to many
biological systems. Birds that catch fish in water and fish
that catch insects in air must have an instinctive understanding, far better than our own, of the laws of refraction.
One of the best understood examples of a biological
organism using geometric optics to complete its life cycle
is the sporangiophore of the fungus Phycomyces. This
cylindrical cell that makes up the sporangiophore typically
bends toward sunlight (Castle, 1930, 1932, 1938, 1961,
1966; Dennison, 1959; Dennison and Vogelmann, 1989;
Shropshire, 1959, 1963; Zankel et al., 1967). In 1918,
Blaauw suggested that this cylindrical cell might act like
a converging lens that focuses the light to the back of the
cell (Figure 2-38) and that light stimulates growth on the
so-called “dark side” resulting in the cell bending toward
the light.
Buder (1918, 1920) and Shropshire (1962) varied the
refractive index of the medium in which the cells grew and
found that when the refractive index of the medium was
less than the refractive index of the cell (1.38), parallel rays
caused the cell to bend toward the light. However, when
the refractive index of the medium was greater than that of
the cell, parallel rays caused the cell to bend away from the
light. This occurs because in the former case, the cell acts
like a converging lens and the light is focused on dark side
of the cell. In the latter case, the cell acts like a diverging
lens and the light is focused more on the light side of the
cell than on the dark side of the cell.
Plants also take advantage of geometric optics since
the epidermal cells of many plants form lenses that focus
the sun’s light onto the chloroplasts (Vogelmann, 1993;
Vogelmann et al., 1996) to enhance photosynthesis.
GEOMETRIC OPTICS OF THE HUMAN EYE
The two balls in our head, known as eyes are the interface
though which we receive visual information about the rest
of the world (Young, 1807; Huxley, 1943; Polyak, 1957;
Gregory, 1973; Inoué, 1986; Ronchi, 1991; Park, 1997;
Helmholtz, 2005). Information-bearing light enters our
eyes through the convex surface of the cornea, a transparent structure with a refractive index of 1.377. The cornea,
which is composed of cells and extracellular fibrous protein,
acts like a converging lens (Figure 2-39). The rays refracted
by the cornea pass through the anterior (between the cornea and the iris) and posterior (between the iris and the
crystalline lens) chambers filled with a dilute salt solution
known as the aqueous humor (n 1.337) and are further
refracted by the biconvex crystalline lens, which has an
index of refraction of 1.42–1.47. The rays refracted by the
crystalline lens pass through a jelly-like substance called
the vitreous humor (n 1.336) and come to a focus on the
photosensitive layer on our retina that contains color-sensitive cones used in bright light and light-sensitive rods used
in dim light. The image on the retina is inverted. Neurons
transmit signals related to the inverted image from the retina to the visual cortex of the brain. The brain then interprets the image and makes an effigy of the object that we
see with the mind’s eye. In creating this effigy, the brain is
able to make inverted images on the retina upright, but
is not able to lower a coin covered with water, unbend a
stick passing through a water–air interface, or place the
setting sun beneath the horizon.
The blue, green, gray, amber, hazel, or brown part of
the eye situated between the cornea and the crystalline lens
is known as the iris. The iris is a variable aperture whose
32
Light and Video Microscopy
Real image
projected
onto retina
(inverted
left/right
and
top/bottom)
Ciliary muscle
Cornea
Optical axis
Iris
Object in
field of vision
Optic
nerve
Retina
Lens
FIGURE 2-39 The cornea and lens of the human eye act as a converging lens that throws an image on the retina.
diameter varies between 2 mm and 8 mm, in bright light
and dim light, respectively. The hole in the center of the
iris through which light passes is called the pupil. The best
images are produced when the pupil diameter is 3 to 4 mm
because the central regions of the eye suffer from the fewest aberrations compared with the peripheral regions.
The length of the eye from the cornea to the retina is
approximately 23 mm. Together, the optical elements of the
eye act as a converging lens with a focal length of about
2 cm to project an image on the retina. The large difference
in refractive index between the air and the cornea means
that most (80%) of the refraction by the eye takes place at
the cornea. The crystalline lens accounts for the other 20
percent.
When we look at distant objects, the ciliary muscles
attached to the crystalline lens are relaxed, and if we have
normal vision, an “in-focus” image of the distant object
appears on the retina. When looking at objects up close,
the ciliary muscles contract, causing the crystalline lens
to become more rounded. This reduces the focal length
of the crystalline lens to about 1.8 cm in a process known
as accommodation so that “in-focus” images of the near
objects appear on our retina (Peacock, 1855; Wood and
Oldham, 1954; Robinson, 2006). In people over 40, a
loss in the ability to accommodate, or presbyopia, occurs
because the crystalline lens becomes too rigid and/or the
ciliary muscles become too weak. Presbyopia can be corrected with the convex lenses placed in reading glasses or
bifocals.
If our corneas are too convex (focal length 1.96 cm),
images of distance objects are not in focus on the retina,
but closer to the crystalline lens, and we are nearsighted
or myopic. Myopia can also result when the length of the
eyeball is too great. Nearsightedness can be corrected by
wearing spectacles with diverging lenses or through laser
surgery that reduces the convexity of the cornea.
If our corneas are too flat (focal length 2.04 cm),
images of near objects are not in focus on the retina,
but farther away, and we are farsighted or hyperopic.
Hyperopia can also result when the length of the eyeball
is too short. Farsightedness can be corrected by wearing
spectacles with converging lenses or through laser surgery
that increases the convexity of the cornea.
If either the cornea or the lens is not spherical, but ellipsoidal, horizontal objects and vertical objects are brought
to a focus at different image planes. This is known as astigmatism, and can be corrected through the use of cylindrical
lenses or laser surgery.
Together the optical elements of the eye make up a
compound converging lens that forms an image on the retina. When objects are placed at infinity, the eye, like any
other converging lens, forms images at the focal plane,
where the retina is located. When the objects are brought
closer and closer to the converging lens of the eye, the
image becomes more and more magnified; but it also forms
further and further from the lens since the retina is a fixed
distance from the lens, and the eye changes its focal length
through accommodation and forms an image on the retina.
However, the eye cannot accommodate without limit, and
consequently there is a minimum distance that an object
can be observed by the eye and still be in focus on the
retina. This distance is known as the distance of distinct
vision, the comfortable viewing distance, or the near point
of the eye. It is approximately 25 cm in front of the eye.
When we look at an object from a great distance away,
the rays emanating from the borders of the object make
33
Chapter | 2 The Geometric Relationship between Object and Image
α
25 cm
α
B
f
FIGURE 2-40 The closer an object is to our eye, the larger is the visual
angle made by the object and the eye, and the larger the image is on the
retina.
a miniscule angle at the optical center of the eye and the
image of the object formed on the retina is minute (Figure
2-40). When the object is moved closer to the eyes, the
rays emanating from the borders of the object make a
larger visual angle and the image on the retina becomes
slightly larger. When the object is placed 25 cm from the
naked eye, the rays emanating from the object make an
even larger visual angle at the optical center of the eye
and consequently the image on the retina is even greater.
However, if the object is microscopic, even if we bring it
to the distance of distinct vision, we will not be able to see
it because the visual angle will be too small to form a sizeable image on the retina. The visual angle must be at least
1 minute of arc (1/60 of a degree) for us to be able to form
an image of the object on our retina.
When the visual angle is too small, the microscopic
object can be observed through a microscope so that the
rays will make a large visual angle at the optical center of
the eye (Figure 2-41). With a microscope with 100× magnification, the image of the microscopic object on the retina will be as large as if the object were 100 times larger
than its actual size and placed at the distance of distinct
vision. The magnified apparent image that occurs at the
distance of distinct vision is known as the virtual image.
The microscope is thus a tool that can be used to project a larger and more magnified image of an object on the
f
FIGURE 2-41 When a small object is placed at the near point of the
naked eye, we still cannot see it clearly, because the visual angle is too
small and the image falls on a single cone. A lens placed between the
object and the eye produces an enlarged image on the retina. The size of
the image on the retina is the same as that that would be produced by a
magnified version of the object placed at the near point of our eye.
retina than would be projected in the absence of a microscope. According to Simon Henry Gage (1917, 1941):
In considering the real greatness of the microscope and the truly
splendid service it has rendered, the fact has not been lost sight
of that the microscope is, after all, only an aid to the eye of the
observer, only a means of getting a larger image on the retina
than would be possible without it, but the appreciation of this
retinal image, whether it is made with or without the aid of the
microscope, must always depend upon the character and training
of the seeing and appreciating brain behind the eye. The microscope simply aids the eye in furnishing raw material, so to speak,
for the brain to work upon.
According to Sigmund Freud (1989), “With every tool,
man is perfecting his own organs, whether motor or sensory, or is removing the limits to their functioning … by
means of the microscope he overcomes the limits of visibility set by the structure of his retina.”
WEB RESOURCES
I think you will enjoy the following web sites, which provide information,
animations, and Java applets about geometric optics.
●
●
●
●
http://www.educypedia.be/education/physicsjavalabolenses.htm
http://www.educypedia.be/education/physicsjavacolor.htm
http://www.educypedia.be/education/physicsjavalabooptics.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/ligcon.html
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Chapter 3
The Dependence of Image
Formation on the Nature of Light
In the last chapter I discussed geometric optics and the
corpuscular theory of light. In this chapter I will discuss
physical optics and the wave theory of light. Geometric
optics is sufficient for understanding image formation
when the objects are much larger than the wavelength of
light. However, when the characteristic length of the object
approaches the wavelength of light, we need the principles
of physical optics, developed in this chapter, to understand
image formation.
CHRISTIAAN HUYGENS AND THE
INVENTION OF THE WAVE THEORY
OF LIGHT
Up until now, we have assumed that light travels as infinitesimally small corpuscles along infinitesimally thin rays.
This hypothesis has been very productive; having allowed
us to predict the position, orientation, and magnification
of images formed by mirrors and lenses. In the words of
Christiaan Huygens (1690):
As happens in all the sciences in which Geometry is applied to
matter, the demonstrations concerning Optics are founded on
truths drawn from experience. Such are that the rays of light are
propagated in straight lines; that the angles of reflexion and of
incidence are equal; and that in refraction the ray is bent according to the law of sines, now so well known, and is no less certain
than the preceding laws.
dissolving, and burning matter, and it does so by disuniting the particles of matter and sending them in motion.
According to the mechanical philosophy of nature championed by Descartes, anything that causes motion must itself
be in motion, and therefore, light must be motion. Since
two beams of light crossing each other do not hinder the
motion of each other, the components of light that are set in
motion must be immaterial and imponderable. The motion
of the ether causes an impression on our retina, which
results in vision much like vibratory motion of the air causes
an impression on our eardrum, which results in hearing.
Huygens considered that a theory of light and vision might
have similarities to the newly proposed theory of sound
and hearing (Airy, 1871; Millikan and Gale, 1906; Millikan
and Mills, 1908; Millikan et al., 1920, 1937, 1944; Miller,
1916, 1935, 1937; Poynting and Thomson, 1922; Rayleigh,
1945; Helmholtz, 1954; Lindsay, 1960, 1966, 1973; Kock,
1965; Jeans, 1968).
Since hearing is important for communication and
the ability to enjoy the aural world around us, the studies
of sound and acoustics have been important to astute
observers and inquisitive people since ancient times. It is
a commonplace that there is a relationship between sound
and vibration. Pythagoras (sixth century BC) noticed that
the pitch of the sound emitted by a vibrating string was
related to the length of the string—low pitches came from
However, Huygens recognized a problem with the
assumption that light was composed of material particles
(Figure 3-1). He went on to say:
… I do not find that any one has yet given a probable explanation
of the first and most notable phenomena of light, namely why is
it not propagated except in straight lines, and how visible rays,
coming from an infinitude of diverse places, cross one another
without hindering one another in any way.
Huygens realized that light must be immaterial since
light rays do not appear to collide with each other. He
concluded that light consists of the motion of an ethereal
medium. Here is how he came to this conclusion: Fire produces light, and likewise, light, collected by a concave mirror, is capable of producing fire. Fire is capable of melting,
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
B
A
FIGURE 3-1 If light were composed of Newtonian corpuscles, corpuscles propagating from the bird to observer A should make it more difficult
for observer B to see the flower, since the corpuscles from the flower will
cause the corpuscles coming from the bird to scatter.
35
36
plucking long strings and high pitches came from plucking short strings. The long thick strings that produced low
notes vibrated with low frequency and the short thin strings
that produced high notes vibrated with high frequency. It
seemed reasonable to the ancients that the vibrations produced by the strings were transmitted through air to the ear
the way vibrations produced by stones thrown into water
were visibly transmitted across water. We can realize how
well developed the theory of acoustics must have been
when visiting an ancient theater or amphitheatre and experiencing its fine acoustic qualities.
Marin Mersenne in 1625 and Galileo Galilei in 1638
independently published theories of sound, both of which
stated that sound was caused by the vibration of strings
and other bodies, and that the pitch of a note depended on
the number of vibrations per unit time (i.e., the frequency).
Galileo came to this conclusion after he rubbed the rim of
a goblet filled with water and produced a sound—a sound
that could be visualized by looking at the ripples produced
in the water. He noticed that the number of ripples appearing on the surface of the water was related to the pitch of
the sound. Sauver and John Wallis, the famous brain anatomist, independently noticed that when a string was plucked
in various places along the length of the string, certain
regions, known as nodes, did not move, while the rest of
the string did. A single plucked string could produce a
simple vibration, known as the fundamental vibration.
It could also produce a complex vibration composed of a
series of harmonic vibrations or overtones. The harmonics,
which had higher pitches than the fundamental vibration,
were characterized as having an integral numbers of nodes.
A mathematical description of the movement of strings
and their creation of various pitches was given in the eighteenth century by Daniel Bernoulli, Jean d’Alembert, and
Leonhard Euler. Euler described the complex sound produced by a vibrating string as the superposition of the fundamental and harmonic vibrations.
The propagation of sound was also studied by the
ancients, including the architect Vitruvius, who in the
first century BC compared the propagation of sound with
the propagation of water waves. In 1660, Robert Hooke
discovered that sound can not travel in a vacuum when he
found that the intensity of the sound of a bell, placed in a
glass jar, decreased as he evacuated the air from the bell
jar with a vacuum pump. Gassendi, Mersenne, and others
assumed that the speed of light was infinite, and determined the speed of sound in air by shooting guns and measuring the time between when they saw the flash and when
they heard the explosion.
The speed of sound through air, which depends on the
temperature and wind speed, is approximately 340 m/s. In
general, the speed of sound through a medium depends
on the elasticity and density of that medium. By comparing the time it takes for sound to travel along long pipes
Light and Video Microscopy
with the time it takes sound to travel in air, in 1808,
J. B. Biot and others showed that the velocity of sound is
faster in liquids and solids than it is in air. Daniel Colladon
and Charles Strum determined the elasticity (compressibility) of water in 1826 by measuring the speed of sound produced by a bell under the water of Lake Geneva.
The fact that the ear is involved in the reception of sound
is well known and in 1650, Athanasius Kircher designed a
parabolic horn as an aid to hearing. In 1843 Georg Ohm
proposed that the ear can analyze complex sounds as many
fundamental pitches in the manner that a complex wave can
be expanded mathematically using Fourier’s theorem. By
1865 Hermann von Helmholtz gave a complete theory of
how the ear works and in 1961, Georg von Békésy won the
Nobel Prize for showing how the ear works.
Making the comparison between the mysterious properties of light and the better understood properties of sound,
Huygens (1690) went on to say:
We know that by means of the air, which is an invisible and
impalpable body, Sound spreads around the spot where it has
been produced, by a movement which is passed on successively
from one part of the air to another; and that the spreading of
this movement, taking place equally rapidly on all sides, ought
to form spherical surfaces ever enlarging and which strikes our
ears. Now there is no doubt at all that light also comes from the
luminous body to our eyes by some movement impressed on the
matter which is between the two; since, as we have already seen,
it cannot be by the transport of a body which passes from one to
another. If, in addition, light takes time for its passage—which
we are going to examine—it will follow that this movement,
impressed on the intervening matter, is successive; and consequently it spreads, as sound does, by spherical surfaces and
waves: for I call them waves from their resemblance to those
which are seen to be formed in water when a stone is thrown into
it, and which present a successive spreading as circles….
Since waves travel at a finite speed, it seemed before
1676 that wave theory was applicable to sound, but not
to light since it appeared that the speed of light was infinite (Descartes, 1637). However, in 1676, Ole Römer, an
astronomer who was studying the eclipses of Io, one of
the moons of Jupiter, proposed that the speed of light was
finite in order to make sense of the variation he observed
in the duration of time between eclipses. Since the relative
distance between Io and the Earth changed throughout the
year as the planets orbited the sun, Römer realized that the
discrepancies in his observations could be accounted for
if light did not travel infinitely fast; but it took light several minutes to travel from Io to the Earth, the exact time
depending on their relative distance. Although he never
published any calculations on the speed of light, from his
numbers, Huygens could calculate that the speed of light
was approximately 137,879 miles per second—more than
600,000 times greater than the speed of sound.
With this new data in hand, Huygens concluded
that light indeed travels as a wave (Figure 3-2). However,
light waves and sound waves differ in many respects. For
37
Chapter | 3 The Dependence of Image Formation on the Nature of Light
example, sound waves must be longer than light waves
since sound waves result from the agitation of an entire
body and light waves result from the independent agitation
of each point on the body. Huygens wrote, “… the movement of the light must originate as from each point of the
luminous object, else we should not be able to perceive all
the different parts of that object.” Moreover, “… the particles which engender the light ought to be much more
prompt and more rapid than is that of the bodies which
cause sound, since we do not see that the tremors of a body
which is giving out a sound are capable of giving rise to
light, even as the movement of the hand in the air is not
capable of producing sound.”
In order to transmit light from every point of an object,
the ether had to be composed of extremely small particles. Moreover, Huygens knew that the speed of sound
depended on the compressibility (elasticity) and penetrability (density) of the medium through which it moved.
The velocity of a sound wave or any mechanical wave is
equal to the square root of the ratio of the elasticity to the
density. He thus assumed that the speed of light would also
depend on the elasticity and density of the ether and consequently, the ether would have to be very elastic and not
very dense. He imagined what the properties of the ether
would be like (Figure 3-3):
When one takes a number of spheres of equal size, made of some
very hard substance, and arranges them in a straight line, so that
they touch one another, one finds, on striking with a similar
sphere against the first of these spheres, that the motion passes
as in an instant to the last of them, which separates itself from
the row, without one’s being able to perceive that the others have
been stirred. And even that one which was used to strike remains
motionless with them. Whence one sees that the movement
passes with an extreme velocity which is the greater, the greater
the hardness of the substance of the spheres.
He went on to say, “Now in applying this kind of movement to that which produces light there is nothing to hinder
us from estimating the particles of the ether to be a substance as nearly approaching to perfect hardness and possessing a springiness as prompt as we choose.” The ether
had some unusual properties. Not only must it be extremely
elastic, but it also must be very thin, since it could penetrate through glass. This conclusion came from an experiment done by Galileo’s assistant, Evangelista Torricelli,
who showed that light could penetrate through a tube from
which the air had been exhausted. It is ironic that, in order
to circumvent the problems he found associated with the
corpuscular nature of light, Huygens had to propose that
the medium through which light traveled was corpuscular.
Huygens concluded that each minute region of a luminous object generates its own spherical waves, and these
waves, which continually move away from each point,
can be described, in two dimensions, as concentric circles around each originating point. The elementary waves
A
B
C
FIGURE 3-2 According to Christiaan Huygens, light radiates from
luminous sources as waves. The waves must have small wavelengths
since we can resolve points A, B, and C in the candle.
A
B
C
D
FIGURE 3-3 According to Huygens, in order for light to travel so fast,
the aether must be composed of highly elastic diaphanous particles. The
particles must be smaller than the minimum distance between two clearly
visible points. The motion from sphere A is passed to sphere D without
any perceptible change in the intervening spheres B and C.
emanating from each particle of a luminous body travel
through the ether, causing a compression and rarefaction
of each ethereal particle. The excitation of each particle
causes each of them to emit a spherical wave that excites
the neighboring ethereal particles. Consequently, each
ethereal particle can be considered as a source of secondary wavelets whose concentric circles coincide with those
of the primary wave. The wavelets that coincide with each
other reinforce each other, producing an optically effective
wave. The optically effective wave can be demonstrated by
drawing a circle that envelopes the infinite number of circles centering about each point on the original front (Mach,
1926). This envelope, which overlies the parts of the wavelets that coincide with each other, represents the optically
effective front, which then serves as the starting line for
another infinite number of points that act as the source of
an infinite number of spherical waves (Figure 3-4). Thus
the propagation of light is a continuous cycle of two transformations—one involving the fission of the primary wave
into numerous secondary wavelets, and the other involving
the fusion of the secondary wavelets into a new primary
wave.
Huygens’ wave theory of light described the manner in
which light spread out from a point source and provided
a geometrical reason why the intensity of light decreased
38
Light and Video Microscopy
B
A
B
A
A
ct
ct
Primary
source
Secondary
sources
A
B
B
A
Plane wavefronts
Spherical wavefronts
FIGURE 3-4 According to Huygens, the propagation of light is a continuous cycle of two transformations—one involving the fission of the
primary wave into numerous secondary wavelets, and the other involving
the fusion of the secondary wavelets into a new primary wave.
R
R
R
r
R
i
r
r
A
i
r
r
i
i
B
FIGURE 3-5 The wave theory can explain the law of reflection.
According to Huygens, a wave front incident on a mirror produces secondary wavelets. By the time the last part of the incident wave strikes the mirror at B and begins producing secondary wavelets, the wavelets initiated
by the portion of the wave that first struck the mirror already at A have
produced many secondary wavelets. The secondary wavelets (R) formed
from each consecutive region of the mirror reinforce each other (r), leading to a wave front that propagates away from the mirror so that the angle
of reflection equals the angle of incidence. The incident wavelets are
represented with i’s and the reflected wavelets are represented with r’s.
with the square of the distance. Moreover, since each particle in the ether could simultaneously transmit waves
coming from different directions, Huygens’ wave theory
of light, as opposed to Newton’s corpuscular theory, could
explain why light rays cross each other without hindering
one another. “Whence also it comes about that a number
of spectators may view different objects at the same time
through the same opening, and that two persons can at the
same time see one another’s eyes.”
Newton’s corpuscular theory of light provided a clear
explanation of why light traveled in straight lines, but
it was not so clear how light, if it were wave-like, could
propagate in straight lines. Huygens realized that spherical
waves can be approximated by plane ways as they travel
far from the source, so he could provide some explanation
for why light traveled in straight lines. Huygens imagined
that when a spherical wave approached a boundary with an
opening, the secondary wavelets that passed through the
aperture would align and reinforce each other so that the
majority of the wave traveled straight through the opening and the few waves that bent around the edges of the
boundary would be “too feeble to produce light there.”
As we will see later in this chapter, Huygens explanation
is accurate only in cases where the characteristic length of
the opening is much larger than the wavelength of light.
In order to explain reflection using Huygens’ Principle,
imagine a wave front that impinges on a mirror where the
incident front makes an angle relative to the normal. The
first part of the wave to hit the mirror begins to produce
secondary wavelets, and then the next part of the wave to
hit the mirror produces secondary wavelets. By the time
the last part of the incident wave strikes the mirror and
begins producing secondary wavelets, the wavelets initiated by the portion of the wave that first struck the mirror
already have produced many secondary wavelets. The secondary wavelets formed from each consecutive region of
the mirror reinforce each other, leading to a wave front that
propagates away from the mirror at the same angle as the
incident wave approached (Figure 3-5).
Huygens used the wave theory of light to explain
refraction by assuming that “the particles of transparent
bodies have a recoil a little less prompt than that of the
ethereal particles … it will again follow that the progression of the waves of light will be slower in the interior of
such bodies than it is in the outside ethereal matter.” Thus,
the secondary wavelets formed in the refracting medium in
a given period of time will be smaller than the secondary
wavelets produced in air (Figure 3-6). The first part of the
incident wave to strike the refracting surface produces secondary wavelets, and then the next part of the wave to hit
the refracting surface produces secondary wavelets. By the
time the last part of the incident wave strikes the refracting surface and begins producing secondary wavelets,
the wavelets initiated by the portion of the wave that first
struck the refracting surface already have produced many
secondary wavelets. The secondary wavelets formed from
each consecutive region of the refracting surface reinforce
each other, leading to a wave front that propagates through
the refracting medium at an angle that follows the SnellDescartes law as well as Fermat’s Principle of least time.
Huygens’ wave theory could also explain the action
of lenses on light. Imagine a plane wave emanating from
a distant source striking a biconvex converging lens. Since
the speed of light is lesser in the glass than in the air, the
peripheral region of the wave travels faster than the central portion and the waves emerging from the lens are concave instead of planar. The converging lens transforms the
waves from no curvature to positive curvature. The concave
39
Chapter | 3 The Dependence of Image Formation on the Nature of Light
f
i
i
i
i
FIGURE 3-7 Because light travels more slowly through glass than
through air, a converging lens converts a plane wave to a spherical wave.
To visualize how a converging lens transforms spherical waves into plane
waves, imagine the source being placed at f, and then reverse the direction
of all the arrows to the left of f.
t
t
T
t
t
T
FIGURE 3-6 The wave theory can explain the law of refraction.
Huygens believed that the waves traveled slower in media with higher
refractive indices. This resulted in the wavelets forming closer together
in the medium with a higher refractive index and the consequent bending
of the wave toward the normal. The secondary wavelets (T) formed from
each consecutive region in the transmitting medium reinforce each other
(t), leading to a wave front that propagates into the transmitting medium
at an angle consistent with the Snell-Descartes Law.
waves leaving the lens come to a point at the focus (Figure
3-7). Now imagine the reverse situation with convex waves
emanating from the focus and striking the biconvex lens.
Again the peripheral region of the wave travels faster than
the central portion of the wave. Thus the waves that emerge
from the lens are planar. The converging lens transforms
the waves from negative curvature to no curvature.
In general, converging lenses (as well as concave mirrors), which have a positive radius of curvature, increase
the curvature of the incident waves. By contrast, diverging
lenses (as well as convex mirrors), which have a negative
radius of curvature, and which transform plane waves to
convex waves and concave waves to plane waves, decrease
the curvature of the incident waves (Millikan et al., 1944).
We can relate geometrical optics to wave optics by drawing lines that run perpendicular to the wave fronts. Each
line normal to the wave front represents a ray that radiates
out from the source and is composed of corpuscles. The
infinitesimal thinness of the rays is an approximation and
an abstraction as is the infinite lateral extension of plane
waves. Waves that have a finite wave width are intermediate between the two pictures of light and could represent
the radial extensions or widths of the corpuscular rays.
The wave theory of light can also explain why objects
viewed through inhomogeneous media appear to be in a
different place than they actually are (Figure 3-8). Imagine
a coin placed on the bottom of a dish of water. According
to the wave theory of light, the speed of light is slower in
water than it is in air, and consequently the spherical waves
emanating from each point in the coin are compressed.
That is, the wavelength in water is shortened relative to the
wavelength in air. When the waves hit the water–air interface, they decompress. That is, the wavelength becomes
O2
O1
S
m
n
P′
P
FIGURE 3-8 The wavelength of a light wave increases as the light
passes from water to air. This causes the waves to have a greater wavelength and curvature when in the air. Since we do not realize that the
wavelength and curvature change, we imagine that the object that produced the image on our retina is along a straight line, perpendicular to the
wave front that enters our eyes. This is the reason we see objects in water
as being at P instead of at P and why objects appear closer to us.
longer and the wave hits a point o2 instead of the point
o1, which it would have hit if the waves traveled the
same speed in air as they do in water. Because of the air,
the waves now have greater curvature than they would
have had, had the wavelength not changed at the surface.
Apparently our visual system is hardwired to believe that
light travels as plane waves at the speed of light in air
(which is negligibly different than the speed of light in a
vacuum). For this reason, we see the coin floating at P
instead of at its true location P. In his treatise, Huygens
showed how the wave theory can explain the apparent
position of the setting sun and other visual illusions.
THOMAS YOUNG AND THE
DEVELOPMENT OF THE WAVE THEORY
OF LIGHT
The wave theory was as good as the corpuscular theory in
describing reflection and refraction, but it did not provide
a satisfying description of shadows. Isaac Newton (1730)
thought that if light were a wave, then it should be able
40
to bend behind obstacles just as sound waves and water
waves are able to bend behind obstacles. Newton did not
realize that although all waves have similar behaviors,
the specific behaviors of waves depend on the relative
dimensions of the wave (e.g., their wavelength) compared
with the characteristic lengths of the structures they
encounter.
Casual inspection shows that water waves that would
bend behind a stick will not bend behind an ocean liner.
Science, however, advances when casual inspection is supplemented with attention to detail. Newton did not apply
his usually powerful observational and analytical powers
to understand the importance of relative lengths when it
came to waves. Indeed, when we look at the edges of an
ocean liner, we see that the water waves do bend around it.
Likewise when we look at the edges of an opaque object,
as Franciscus Maria Grimaldi (1665) did, we see that light
waves bend or diffract around the object.
Grimaldi noticed that the shadow formed by a small
opaque body (FE) placed in a cone of sunlight that had
entered a room though a small aperture was wider (MN)
than it would be (GH) if light propagated in straight lines
(Figure 3-9). Grimaldi found that the anomalous shadow
was composed of three parallel fringes. Grimaldi assumed
that these fringes were caused by the bending of light away
from the body. He called this effect, which differed from
reflection and refraction, the diffraction of light from the
Latin dis, which means “apart” and frangere, which means
“to break” (Meyer, 1949). Grimaldi noticed that the fringes
disappeared when he increased the diameter of the aperture
that admitted the light, and when the summer Italian sun
was bright enough, he could distinguish that the fringes
between M and N were brightly colored (Priestley, 1772;
Mach, 1926). Grimaldi also observed that light striking a
small aperture cut in an opaque plate illuminated an area
that was greater than would be expected if light traveled in
straight lines.
Robert Hooke (1705) and Isaac Newton (1730)
repeated and extended Grimaldi’s observations on diffraction by studying the influence of a human hair on an incident beam of light (Figure 3-10). Newton noticed that the
hair cast a shadow on a white piece of paper that was wider
than would have been expected given the assumption of the
rectilinear propagation of light. Newton concluded that the
shadow was broadened because the hair repelled the corpuscles of light with a force that fell off with distance.
Newton also observed the shadow cast on a piece of
white paper, by a knife-edge illuminated with parallel rays.
Newton noticed that the image of the knife-edge was not
sharp, but consisted of a series of light and dark fringes.
Then he placed a second knife parallel to the first so as
to form a slit. As he decreased the width of the slit, the
fringes projected on the white paper, moved further and
further from the bright image of the slit. By comparing the
position of the fringes formed at various distances from the
Light and Video Microscopy
GH Umbra
IG, HL Penumbra
A B
F
E
C
M
I G
H L N
D
FIGURE 3-9 Grimaldi saw that the shadow formed by a small opaque
body was larger than it should be if light traveled only in straight lines.
He noticed that the additional shadow was composed of colored fringes.
G
H
I
T
C
B
A
K
L
M
F
E
D
X
N
O
P
S
R
V
Q
FIGURE 3-10 Isaac Newton noticed that the shadow of a hair (x) was
larger than would be expected if light traveled in straight lines. He concluded that the broadened shadow occurred because the hair exerted a
repulsive force on the corpuscles that fell off with distance. Newton did
not see any light fringes inside the geometrical shadow.
slit, Newton concluded that the corpuscles repelled by the
knife-edges followed a hyperbolic path. Using monochromatic light, Newton noticed that the fringes made in red
light were the largest, those made in violet light were the
smallest, and those made in green light were intermediate
between the two.
After performing experiments with results that could
not be explained easily with his corpuscular theory,
Newton (1730) ended the experimental portion of his
Opticks with the following words:
When I made the foregoing Observations, I design’d to repeat
most of them with more care and exactness, and to make some
new ones for determining the manner how the Rays of Light
are bent in their passage by Bodies, for making the Fringes of
Colours with the dark lines between them. But I was then interrupted, and cannot now think of taking these things into farther
Consideration. And since I have not finish’d this part of my
Design, I shall conclude with proposing only some Queries, in
order to a farther search to be made by others.
In the queries at the end of the book, Newton (1730)
wondered:
Are not the Rays of Light in passing by the edges and sides
of Bodies, bent several times backwards and forwards, with
a motion like that of an Eel? and Do not several sorts of Rays
make Vibrations of several bignesses, which according to their
41
Chapter | 3 The Dependence of Image Formation on the Nature of Light
bignesses excite Sensations of several Colours, much after the
manner that the Vibrations of the Air, according to their several
bignesses excite Sensations of several Sounds? And particularly
do not the most refrangible rays excite the shortest Vibrations
for making a Sensation of deep violet, the least refrangible the
largest for making a Sensation of deep red …?
He went on to ask, “And considering the lastingness of
the Motions excited in the bottom of the Eye by Light, are
they not of a vibrating nature?”
Newton went on to conclude that light was not a wave,
but was composed of corpuscles that traveled through an
ether that could be made to vibrate. The vibrations were
equivalent to periodic changes in the density of the ether;
and these variations put the light corpuscles into “easy fits
of reflection or transmission.” Newton could not believe that
light was a wave because he felt that if light in fact did travel
as a wave, it should not only bend away from an opaque
object, but it should also bend into the geometrical shadow.
As a consequence of the great achievements of Isaac
Newton and the hagiographic attitude and less than critical
thoughts of the followers of this great man, the corpuscular theory of light predominated, and the wave theory of
light lay fallow for almost 100 years. The wave theory was
revived by Thomas Young (1794, 1800, 1801), a botanist,
a translator of the Rosetta stone, and a physician who was
trying his hand at teaching Natural Philosophy at the Royal
Institution (Peacock, 1855). While preparing his lectures,
Young reviewed the similarities between sound and light,
and reexamined the objections that Newton had made to
the wave theory of light. Young, who studied the master,
not the followers, concluded that the wave theory in fact
could describe what happens to light when it undergoes
diffraction as well as reflection and refraction. Here is how
Young (1804a) came to this conclusion:
I made a small hole in a window-shutter, and covered it with a
piece of thick paper, which I perforated with a fine needle. For
greater convenience of observation, I placed a small looking
glass without the window-shutter, in such a position as to reflect
the sun’s light, in a direction nearly horizontal, upon the opposite
wall, and to cause the cone of diverging light to pass over a table,
on which were several little screens of card-paper. I brought into
the sunbeam a slip of card, about one-thirteenth of an inch in
breadth, and observed its shadow, either on the wall, or on other
cards held at different distances. Besides the fringes of colours
on each side of the shadow, the shadow itself was divided by
similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed,
but leaving the middle of the shadow always white.
That is, Young observed something that Newton had
missed. Young noticed that the light in fact did bend into
the geometrical shadow of the slip of card (Figure 3-11).
Young went on to describe the origin of the white fringe in
the middle of the geometrical shadow:
Now these fringes were the joint effects of the portions of light
passing on each side of the slip of card, and inflected, or rather
diffracted, into the shadow. For, a little screen being placed a
few inches from the card, so as to receive either edge of the
shadow on its margin, all the fringes which had before been
observed in the shadow on the wall immediately disappeared,
although the light inflected on the other side was allowed to
retain its course, and although this light must have undergone
any modification that the proximity of the outer edge of the card
might be capable of occasioning. When the interposed screen
was more remote from the narrow card, it was necessary to
plunge it more deeply into the shadow, in order to extinguish the
parallel lines; for here the light, diffracted from the edge of the
object, had entered further into the shadow, in its way towards the
fringes. Nor was it for want of a sufficient intensity of light, that
one of the two portions was incapable of producing the fringes
alone; for, when they were both uninterrupted, the lines appeared,
even if the intensity was reduced to one-tenth or one-twentieth.
Young shared his ideas and results with Francois
Arago, who told him that Augustin Fresnel had also been
doing similar experiments on diffraction (Arago, 1857).
Subsequently a fruitful collaboration by mail ensued
FIGURE 3-11 Thomas Young
illuminated a slip of card with
parallel light and observed light fringes in the geometrical shadow of the
card.
Fringes of color
Sun
White light
Fringes of color
Aperture
Biconvex
lens
Slip of
card
Wall
42
Light and Video Microscopy
A
B
Max
Max
Min
Max
Min
Min
Max
Min
Max
2
Min
Max
Max
Min
Max
Crest
Trough
FIGURE 3-12 (A) According to Huygens’ Principle, the two edges of the card used by Young act as sources of secondary wavelets. The bright spots
appear where the wavelets reinforce each other. (B) Two slits in a card also act a sources of secondary wavelets forming alternating light and dark
fringes.
between Arago, Fresnel, and Young. Although Young was
a great experimentalist and theoretician, Fresnel was also a
great mathematician, and between 1815 and 1819, he constructed mathematical formulae that could accurately give
the positions of the bright and dark fringes observed by
Young in his experiments on diffraction. Fresnel’s formulae
were based on Young’s theory of interference (Buchwald,
1983; see later).
While Fresnel was working on his formulae, the
Académe des Sciences, chaired by Arago, announced that
the Grand Prix of 1819 would be awarded for the best
work on diffraction. Fresnel (1819) and one other contender submitted their essays in hopes of winning the
Grand Prix. The judges included Arago, who had come to
accept the wave theory of light, as well as Siméon Poisson,
Jean-Baptiste Biot, and Pierre-Simon LaPlace, who were
advocates of Newton’s corpuscular theory of light. After
calculating the solutions to Fresnel’s integrals, Poisson was
unable to accept Fresnel’s theory because if Fresnel’s ideas
about diffraction were true, then there should be a bright
spot in the center of the shadow cast by a circular mirror,
and to everyone’s knowledge, such a bright spot did not
exist. Poisson wrote (Baierlein, 1992), “Let parallel light
impinge on an opaque disk, the surrounding being perfectly transparent. The disk casts a shadow- of course- but
the very centre of the shadow will be bright. Succinctly,
there is no darkness anywhere along the central perpendicular behind an opaque disk (except immediately behind
the disk).”
Arago subjected Poisson’s prediction to a test, and
found that indeed there was a bright spot in the center of
the shadow. Arago wrote in a report about the Grand Prix
(Baierlein, 1992), “One of your [Académe des Sciences]
commissioners, M Poisson had deduced from the integrals
reported by [Fresnel] the singular result that the centre of
the shadow of an opaque circular screen must, when the
rays penetrate there at incidences which are only a little
more oblique, be just as illuminated as if the screen did not
exist. The consequence has been submitted to the test of
direct experiment, and observation has perfectly confirmed
the calculation.” Fresnel won the Grand Prix of 1819.
Although this was a victory for the wave theory of light, it
did not result in an immediate and wide acceptance of the
reality of the wave nature of light.
In order to understand how the fringes are formed by diffraction, we can use Huygens’ Principle and posit that the
edges of the card used by Young to diffract the light act as
sources of secondary wavelets (Figure 3-12). The bright
spots appear where the wavelets coincide with each other
and reinforce each other, producing an optically effective
wave. Each minute portion of a spherical wavelet can be considered to represent the crest of a sine wave (Figure 3-13).
By combining Young’s qualitative treatment of waves with
Jean d’Alembert’s mathematical treatment, Fresnel was
able to simplify the analysis of diffraction.
D’Alembert (1747) derived and solved a wave equation
that described the motion of a vibrating string. According
to d’Alembert, the standing wave produced by a vibrating
43
Chapter | 3 The Dependence of Image Formation on the Nature of Light
FIGURE 3-13 An infinitesimally thin section of the light
waves radiating from the edge of
the card observed from the side
Axis
of
propagation
z
(in an instant of time) will appear as a sine wave with
λ an amplitude (Ao) and a wavelength. The sine wave appears
from the edge of the card as if an
oscillator “cranked out” the sign
wave.
λ
A0
y
4
3
2
1
5
θ
6
12
7
1
2
3
4
5
6
7
8
9
10
11
12
11
8
9
10
Propagation in time
(at a given point in space)
string resulted from two traveling waves propagating in
opposite directions. He described the propagation of the
two waves with functions whose arguments included the
wavelength (λ, in m), the frequency (ν, in s1) of the wave,
and its speed (c, in m/s). The wavelength is the distance
between two successive peaks in a wave. The frequency is
related to the wavelength by the following formula, known
as the dispersion relation:
λν c
The arbitrary functions that satisfy d’Alembert’s wave
equation must be periodic, and typically sinusoidal functions,
including sine and cosine, are used to describe the propagation of sound and light waves (Crawford, 1968; Elmore and
Heald, 1969; French, 1971; Hirose and Lonngren, 1991;
Georgi, 1993) through space (x, in m) and time (t, in s).
Thus the time variation of the amplitude (Ψ) of a light wave
with wavelength λ and frequency ν at a constant position
x, or the spatial variation of the amplitude of a light wave
with wavelength λ and frequency ν at constant time t can be
described by the following equation (Figure 3-14):
Ψ (x, t ) Ψ0 sin 2π (x/λ ν t )
The spatiotemporal varying height of the sine wave,
whether a light wave or a water wave, is known as its
amplitude and Ψo is the maximal amplitude. The brightness or intensity of a light wave is related to the square of
its amplitude. We perceive differences in the wavelength of
light waves as differences in color. The minus sign is used
to describe a wave traveling toward the right and the plus
sign is used to describe a wave traveling toward the left.
Although traditionally light waves are treated as if they
have length but not width, Hendrik Lorentz (1924) insisted
that light must have extension. It is possible to model a
plane wave with nonvanishing width by using the angular frequency (ω, in radians/sec) instead of the frequency
and the angular wave number (k, in radians) instead of the
wavelength. The angular frequency is related to the frequency by the following equation:
ω 2πν
and the angular wave number is related by wavelength by
the following equation:
k 2π / λ
The dispersion relation, given in terms of angular parameters is:
ω/k c
The traveling wave is then described by:
Ψ (x, t ) Ψ0 sin ( kx ωt )
where ω can be interpreted as the angular frequency, in which
the quantity λ /2π rotates around a circle, such that the product of ω and λ /2π equal the speed of light. If such a wave
were to translate at velocity c along the axis of propagation,
λ /2π would represent the radius of the wave (see appendix).
Waves are not only described by their intrinsic qualities, including their velocity, wavelength (angular wave
number), frequency (angular frequency), and amplitude,
but also by relative or “social” qualities, including phase
(Ψ, dimensionless). The phase of a wave is its position relative to other waves. When two waves interact, their phase
has a dramatic effect on the outcome.
Young (in Arago, 1857) wrote:
It was in May of 1801, that I discovered, by reflecting on the beautiful experiments of Newton, a law which appears to me to account
for a greater variety of interesting phenomena than any other optical
44
Light and Video Microscopy
Amplitude
(at a given point in space)
c (wave velocity)
T
(oscillation
period)
λ
Observing
point
A
Time t
B
Axis of
propagation
FIGURE 3-14 (A) At a single instant of time, we see a wave as a spatial variation in amplitude. (B) Whether we visualize the wavelength of a wave or
the frequency of a wave depends on the mode of observation. At a single point in space, we see a wave as a time variation in amplitude.
principle that has yet been made known. I shall endeavour to
explain this law by a comparison:– Suppose a number of equal
waves of water to move upon the surface of a stagnant lake, with a
certain constant velocity, and to enter a narrow channel leading out
of the lake;– suppose, then, another similar cause to have excited
another equal series of waves, which arrive at the same channel
with the same velocity, and at the same time with the first. Neither
series of waves will destroy the other, but their effects will be combined; if they enter the channel in such a manner that the elevations
of the one series coincide with those of the other, they must together
produce a series of greater joint elevations; but if the elevations of
one series are so situated as to correspond to the depressions of the
other, they must exactly fill up those depressions, and the surface of
the water must remain smooth; at least, I can discover no alternative, either from theory or from experiment. Now, I maintain that
similar effects take place whenever two portions of light are thus
mixed; and this I call the general law of interference of light.
The eye cannot perceive the absolute phase of a light
wave; but it can distinguish the difference in phase between
two waves because the intensity that results from the combination of two or more waves depends on their relative
phase (Figure 3-15). When two waves are in phase, their
combined intensity is bright since the intensity depends on
the square of the sum of their amplitudes. This is known
as constructive interference. When two waves are onehalf wavelength out-of-phase, the two waves cancel each
other and darkness is created. This is known as destructive
interference. Any intermediate difference in phase results
in intermediate degrees of brightness. Young (1802) wrote:
“Wherever two portions of the same light arrive at the eye
by different routes, either exactly or very nearly in the
same direction, the light becomes most intense when the
difference in the routes is any multiple of a certain length,
and least intense in the intermediate state of the interfering
portions; and this length is different for light of different
colors.”
We use the principle of superposition to determine the
intensity of the resultant of two or more interfering waves
(Jenkins and White, 1937, 1950, 1957, 1976; Slayter,
1970). According to the principle of superposition, the
time- or position-varying amplitude of the resultant of two
or more waves is equal to the sum of the time- or positionvarying amplitudes of the individual waves. The intensity of the resultant is obtained by squaring the summed
45
Chapter | 3 The Dependence of Image Formation on the Nature of Light
A
λ
B
λ
FIGURE 3-15 (A) Constructive interference occurs between two waves that are in phase. The amplitude of the resultant is equal to the sum of the
individual amplitudes. Destructive interference occurs between two waves that are λ/2 out-of-phase. (B) The amplitude of the resultant vanishes. Since
the intensity of light is related to the square of the amplitude of the resultant, constructive interference produces a bright fringe and destructive interference produces a dark fringe.
amplitudes. The intensity of the resultant of two or more
waves can be determined graphically by adding the amplitudes and then squaring the sum of the amplitudes. The
intensity of the resultant wave can also be determined analytically. Consider two waves with equal amplitudes, both
with angular wave number k, traveling to the right; let
wave two be out-of-phase with wave one by the phase factor ϕ (in radians). Since 360° is equivalent to 2π radians,
one radian is equivalent to 57.3°.
Ψ (x, t) Ψo1 sin (kx t) Ψo1 sin (kx t ϕ )
Since sin A sin B 2 cos [(A B)/2] sin [(A B)/2],
this equation can be simplified to yield:
Ψ (x, t) 2 Ψo1 cos (/ 2) sin (kx t ϕ/ 2)
When the two waves are in-phase and ϕ 0, cos (0) 1
and
Ψ (x, t) 2 Ψo1 sin (kx t)
The resultant has twice the amplitude and four (22) times
the intensity of either wave individually. The resultant also
has the same phase as the individual waves that make up
the resultant. This is the situation that leads to a bright
fringe. When the two waves are completely out-of-phase,
where ϕ π, cos (π/2) 0 and
Ψ(x, t) 0
The resultant has zero amplitude and intensity (02). This
is the situation that leads to a dark fringe. The phase of the
resultant is not always the same as the phase of the component waves. The amplitude of the resultant of two similar
waves that are π/4 (45°) out-of-phase with each other is:
Ψ (x, t) 1.8476 Ψo1 sin (kx t 0.38)
The intensity (3.414) is given by the square of the amplitude and the resultant is out-of-phase with both component
waves. This is the situation that leads to the shoulder of a
fringe. The amplitude of the resultant of two similar waves
that are π/2 (90°) out-of-phase with each other is:
Ψ (x, t) 1.4142 Ψo1 sin (kx t 0.707)
The intensity (1.999) is given by the square of the amplitude and is almost indistinguishable from the sum of the
intensities of the component waves since the interference
is neither constructive not destructive. The resultant is outof-phase with the two component waves.
Let us continue to consider Young’s diffraction experiment in terms of Huygens’ Principle and the principle of
interference (Figure 3-16). Let the waves emanate from a
source and pass through a slit. Place a converging lens so
that the slit is at its focus and plane waves leave the lens
and strike the strip made out of cardboard. Each edge of
the card acts as a source of secondary wavelets. The waves
from each secondary source radiate out and interfere with
each other. Where the crests of the waves radiating from
the two sides of the card come in contact, they will constructively interfere. Where the troughs of each set of
waves come in contact, they will constructively interfere.
Where a crest from one set meets a trough from the other
set, they will destructively interfere. We can see that there
is a region, equidistant from both edges of the slip of card,
where the crests from one secondary wave interact only
with the crests from the other secondary wave. Thus in this
region, light interferes only constructively. These rays will
give rise to a bright spot on the screen known as the zerothorder band.
We can also see that just to the left or right of the middle, there are regions where the crests of one secondary
wavelet always meet the troughs of the other secondary
wavelet and thus they always destructively interfere. This
gives rise to one dark area on the left of the zeroth-order
band, and another on the right of the zeroth-order band.
Again as we move further from the middle of the slip
of card, we see that on the left, the crests of the wave from
the near edge meet the crests of the wave from the far
edge. The waves from the far edge are one full wavelength
behind the waves from the near edge. The waves constructively interfere and give rise to a bright band. Likewise,
on the right, we see that the crests of the wave from the
near edge meet the crests of the wave from the far edge
that are also retarded by one full wavelength. These waves
also constructively interfere and give rise to a bright band.
These are called the first-order bands.
In a similar manner, the second-order, third-order (and
so on) bright fringes are formed when the crests of each
secondary wavelet meet, but one wave is retarded by
m 2, 3 (and so on) full wavelengths relative to the other
one. The bright fringes (maxima) alternate with dark fringes
(minima). The maxima appear where the optical path
lengths (OPL) of the component waves differ by an integral
number (m) of wavelengths. The minima appear where the
46
Light and Video Microscopy
X
Max
x
N
q
Min
d
S1
S0
M
C
Max
P
2
S2
D
Min
Max
C
FIGURE 3-16 The slip of card can be modeled as two sources of
Huygens’ wavelets. Bright fringes are formed where the waves from the
two sources constructively interfere and dark fringes are formed where
the waves from the two sources destructively interfere.
A
O
FIGURE 3-17 The rays NX and PX are perpendicular to the wave
fronts emanating from N and P, respectively. If x is the first-order maximum, then PC is equal to 1λ.
opposite side to the length of the hypotenuse. The first-order
maximum occurs when PC (1)λ and must satisfy the
following condition:
d sin θ m λ
optical path lengths of the component waves differ by
m ½ wavelengths.
The zeroth-order band is the brightest, the first-order
bands are somewhat dimmer, the second-order bands are
dimmer still, and so on . We can explain this by saying that
each secondary wavelet is a point source of light whose
energy falls off with distance from the source of secondary
wavelets. Therefore there is the most energy in the light
that interacts close to the source and there is less energy in
the light that interacts further from the source.
The distance between the fringes depends on the size of
the object, the distance between the object and the viewing
screen, and the wavelength of light. If we know any three
of these parameters, we can deduce the fourth. How can we
determine the distance between the fringes? Let’s consider
an object of width d that is a distance D from the viewing
screen (Figure 3-17).
Waves arriving at point A from points N and P have
identical optical path lengths and are thus in-phase. At any
other point X on the screen, separated from A by a distance
x, waves from N and P differ in optical path length. The
value of this optical path difference (OPD) is:
Optical path difference PC
The maxima occur where the optical path difference
equals an integral number of wavelengths; that is, where
PC mλ, where m is an integer. Likewise, the minima
occur where the optical path difference equals m ½
wavelengths. Intermediate intensities occur where the
optical path difference equals (m n) wavelengths where
0 n ½.
It is true the PC d sin θ, since, for a right triangle,
the sine of an angle equals the ratio of the length of the
Note that NPC is the same as MPO, and since
NCP and OMP are right angles, and all triangles have
π radians (180°), then
<θ <MOP
MOP AOX because they are vertical angles.
Thus,
<AOX <θ
tan (AOX) tan θ ≈ x/D
As long as θ is small (that is D MO and D d), then
D OA. Using the small angle approximation:
sin θ ≈ tan θ ≈ x/D.
Therefore the maxima occur where d (x/D) mλ, or
x (D/d) m λ
and minima occur where
x (D/d) (m ½ )λ
Thus, the following three statements are true:
1. The smaller the object, the greater the distance
between the first-order band and the zeroth-order band.
Thus, a short distance in the object plane results in a long
distance in the diffraction plane, and a long distance in the
object plane results in a short distance in the diffraction
plane. This is known as the concept of reciprocal space.
2. The shorter the wavelength, the smaller the distance
between the first-order band and the zeroth-order band.
Thus diffraction can be used to separate the wavelengths
of light, and in fact, diffraction gratings are used to separate light into various colors (see Chapter 8). Moreover,
47
Chapter | 3 The Dependence of Image Formation on the Nature of Light
if the size of the object, the length between the object and
the screen, and the distance between the diffraction bands
are known, the wavelength of the light illuminating the
object can be determined. Thomas Young (1804a) determined the wavelengths of visible and UV waves with this
method.
3. The greater the distance from the object to the
screen, the greater the distance between the first-order
band and the zeroth-order band. Thus, the greater the
distance, the easier it is to distinguish a greater number of
diffraction bands.
Interference occurs because the intensity of a resultant wave depends on the square of the sum of the amplitudes of the component waves and not on the sum of the
squares of the amplitudes. When we consider two waves,
the intensity of one wave alone is proportional to Ψ12 and
the intensity of the other wave alone is proportional to Ψ22,
but the intensity of the two interfering waves is proportional to (Ψ1 Ψ2)2. Thus when Ψ1 Ψ2, the intensity
is 0. When Ψ1 Ψ2, the intensity is 4 Ψ1, and when Ψ1 and
Ψ2 have any other relationship, the intensity is intermediate between 0 and 4 Ψ. These relationships hold for any
number of waves where the intensity is proportional to the
square of the sum of the amplitudes of all the waves that
strike a given point.
I (Ψ1 Ψ2 Ψ3 Ψ4 … Ψn )2
Young also investigated the diffraction of light through
two slits. Again, we can determine the positions of the
bright and dark fringes graphically or analytically. If we
analyze the two-slit diffraction graphically using Huygens’
Principle, we consider each of the two slits to be sources
of secondary wavelets, and the bright fringes appear where
the crests of the waves emanating from both slits reinforce
each other, and the dark fringes appear where the crests of
the waves from one slit coincide with the troughs of the
waves from the other slit.
When we analyze two-slit diffraction analytically, we
use the same formulae as we used to describe the diffraction of light around a card, except that d represents the distance between the slits instead of the width of the card.
We can look at the distribution of light passing
around the card or through two slits in term of the radial
width (λ/2π) or radial diameter (λ/π) of a light wave
(see Appendix II). The amplitudes of the light that passes
through slit one (Ψ(r1, t)) and slit two (Ψ(r2, t)) are given
by the following equations:
Ψ (r1 , t) Ψo sin (kr1 t)
Ψ (r2 , t) Ψo sin (kr2 t)
where r1 is the distance from slit 1 to the screen and r2 is
the distance from slit 2 to the screen. The phase difference (ϕ) between the two waves is kr1 kr2 (k(r1 r2)),
which is equal to (r1 r2)(2π/λ). Consequently the sum of
the amplitudes can be written:
Ψ (r12 , t) Ψo [ sin (kr1 t) sin (kr1 t )]
Since sin A sin B 2 cos [(A B)/2] sin [(A B)/2],
Ψ (r12 , t) 2 Ψo cos (/ 2) sin (kr1 t / 2)
The resultant is a propagating wave. The properties of
propagation are determined by the sine term and the amplitude of the resultant is strongly influenced by the cosine
term (Hirose and Lonngren, 1991). Thus the amplitude
of the resultant wave depends on the phase difference
between the component waves according to the following
equation:
Ψ (r12 , t) 2 Ψo cos ((r1 r2 )(2π/ λ )/ 2)
and the intensity (I Ψ(r12, t)2) of the resultant wave is
given by
I 4 Ψo 2 cos2 ((r1 r2 )(2π/ λ )/ 2)
4 Ψo 2 cos2 ((OPD)(π/ λ ))
where OPD r1 r2. We could say that interference
effects are a function of the ratio of the OPD to the diameter of the wave. Since the OPD mλ and mλ d sin θ,
the interference effects for a given angle (θ) are a function
of the distance between slits and the diameter of the wave.
Diffraction usually is given as a function of the length
of light waves that have no radial dimension. However,
in this unorthodox introduction of wave width, we can
almost visualize a single wave wrapping around the card
or simultaneously going through the two slits. The smaller
the wave width, the more the light wave approximates a
light ray. The smaller the wave width and wavelength,
the more a light wave approximates a corpuscle of light.
The diffraction pattern of an object is related to the
shape of the object. Compare the diffraction patterns of a
slit (whose length is much greater than its width), a square
(which is a slit whose length and width are equal), and a
circle (which is a slit rotated π radians (180°) (Figure
3-18).
The diffraction pattern of a circular pinhole is called an
Airy disc, named after Sir George Airy. His observation
that the size of the image of a star depended on the diameter of the lens used as an object glass in a telescope led him
to study the diffraction pattern of circular apertures (Airy,
1866; Rayleigh, 1872). Airy found that maxima resulted
when the optical path difference from two diametrically
opposed points on the circle to the viewing screen was a
nonintegral number of wavelengths. The reason that the
maxima occur at nonintegral numbers is because the width
of a circular aperture varies from 0 to d and waves originating from the thin regions interfere with waves originating from the wide areas. The values of m [d sin θ/λ],
which correspond to minima or maxima of an Airy Disc,
48
Light and Video Microscopy
TABLE 3-1 Coefficients of Wavelength that Give
Rise to Minima and Maxima
Order
Minima (λ)
Maxima (λ)
0
0
0
1
1.220
1.635
2
2.233
2.679
3
3.238
3.699
4
4.241
4.710
FIGURE 3-19 The point spread function of an Airy disc. The maxima
occur at non-integral numbers.
function that describes damped periodic functions.
Friedrich Bessel used this function to understand the disturbance of the elliptical motion of one planet by another
planet (Smith, 1959). We will use the Bessel function to
describe the distribution of light intensity (I) in the plane
perpendicular to the optical axis when light hits a circular
aperture. The intensity at position x depends on the wavelength of light, the radius of the aperture, the distance of
the point from the axis, and the light intensity at the aperture. The light intensity at any point x away from the center
of the diffraction pattern is given by the following equation
(Menzel, 1955, 1960):
FIGURE 3-18
and a circle.
Fraunhöfer diffraction patterns of a vertical slit, a square,
I x I 0 [2 J1 (x)/x]2
where
are given in Table 3-1. The function that describes the distribution of intensities in an Airy disc often is called the
point spread function (Figure 3-19).
These coefficients can be obtained experimentally, or
they can be obtained analytically using one of the Bessel
functions. A Bessel function is a convenient and useful
x (π/ λ )d sin θ
and J1(x) is the Bessel function of the first kind. The Bessel
function, in general, is defined as:
J n (x) ∞
(1)k (x/ 2)n2 k
k! (k n)!
k 0
∑
49
Chapter | 3 The Dependence of Image Formation on the Nature of Light
When n 1, the Bessel function of the first kind is
written as:
J1 (x) ∞
(1)k (x/ 2)12 k
k! (k 1)!
k 0
∑
When the Bessel function of the first kind is expanded, it
looks like this:
(x/ 2)
(x/ 2)3
(x/ 2)5
1!2!
2!3!
1!
7
9
(x/ 2)
(x/ 2)
…
4!5!
3!4!
J1 (x) When we solve the factorials, it looks like this:
J1 (x) (x/ 2) (x/ 2)3 (x/ 2)5 (x/ 2)7 (x/2)9 …
2
12
144
2880
This equation gives an infinite series. When x is large
and positive, we can use the following asymptotic series to
simplify the answer:
J1 (x) (2 / π x)½ [P1 (x) cos (x (3π/ 4))
Q1 (x) sin (x (3π/ 4))]
where
P1 (x) 1 (12 )(3)(5) (12 )(32 )(52 )(7)(9)
2!(8x)2
4!(8x)4
(12 )(32 )(52 )(72 )(92 )(11)(13)
6!(8x)6
and
Q1 (x) (1)(3)
(12 )(32 )(5)(7)
1!(8x)
3!(8x)3
central disk that is surrounded by a minimum. The angular
position (θ) of the first minimum is obtained from the following equation:
(12 )(32 )(52 )(72 )(9)(11)
5!(8x)5
Thus, the maxima and minima can be obtained for
apertures of various diameters (d) illuminated with a given
wavelength (λ) using this equation:
sin θ 1.220 λ/d
where d is the diameter of the aperture. At small angles, sin
θ is equal to tan θ. And since tan θ x/D, where x is the
distance on the screen between the center and edge of
the central spot and D is the distance from the aperture to
the screen, then sin θ x/D and
x 1.220 λ D/ d
Thus circular apertures can be characterized by the following rules:
1. The greater the distance between the aperture and
the screen, the greater the diameter of the central spot.
2. The smaller the diameter of the aperture, the greater
the diameter of the central spot.
3. The shorter the wavelength, the smaller the diameter
of the central spot.
A biological specimen can be considered a series
of points, dots, and holes, and the image of a biological object can be considered a series of overlapping Airy
discs of various sizes. Consider the nucleus to be a large
pinhole (d 105 m), a mitochondrion to be a medium
pinhole (d 106 m), and a vesicle to be a small pinhole
(d 107 m) illuminated with 500 109 m light (radial
wave diameter 1.59 107 m). Table 3-2 gives the
angular position of the first minimum and first maximum
produced by microscopic objects of various sizes (Figure
3-20).
We can see from Table 3-2 that the smaller the aperture, the less the rays travel in straight lines. The larger
the aperture, relative to the radial wave diameter, the more
the diffraction pattern looks like the image of the aperture.
When I discussed the camera obscura or the pinhole camera in Chapter 1, I showed that the smaller the aperture, the
more distinct the image. However, there is a limit as to how
small the aperture can get before the image of each point
on the object is “inflated” by diffraction (Rayleigh, 1891).
As a rule of thumb, the optimal pinhole diameter (in μm)
I x I 0 [2 J1 (x ) / x ]2
where x (π/λ) d sin θ, and is the ratio at a given angle θ of
the diameter of the circular disc to the radial wave diameter.
The diffraction pattern of a circle consists of a central disk, which contains 84 percent of the intensity and
the first-order maximum, which contains 7 percent of the
intensity. The higher-order maxima contain 3 percent, 1.5
percent, 1 percent, and so on, of the light intensity transmitted by the aperture. For practical purposes, we can
consider the diffraction pattern of a circle to consist of a
X
A
d
θ
D
FIGURE 3-20 The angle described by the first order maximum depends
on the diameter of an organelle.
50
Light and Video Microscopy
TABLE 3-2 Angles Subtending the First Minimum
and Maximum Produced by Microscopic Objects of
Various Sizes
d
First minimum
(degrees)
107 m
6
5
10
First maximum
(degrees)
–
–
m
37.589
54.84
m
3.497
4.689
104 m
0.349
0.468
103 m
0.0349
0.047
102 m
0.0035
0.0048
10
FIGURE 3-21
for 0.5 μm light is (1.1) si, where si is the distance from
the pinhole to the object.
I have been discussing diffraction patterns of objects illuminated with plane waves, and the diffraction patterns are
viewed an infinite distance from the object. This is known
as far-field or Fraunhöfer diffraction. If we were to reduce
the wavelength of light to zero, the Fraunhöfer diffraction
pattern would turn into an image that exactly reproduced the
object. Fresnel diffraction, also known as near-field diffraction, occurs when an object is illuminated with plane waves
and the diffraction pattern is observed a short distance away
from the object (Fresnel, 1819). The Fresnel diffraction pattern is clearly recognizable as an imperfect and somewhat
fuzzy image of the object (Figure 3-21).
Young realized that, as long as the wavelength of light
was not infinitesimally short, the image of a specimen
would be affected by diffraction. That is, slits will appear
as fringes, squares will appear as crosses, and circles will
appear as Airy discs. Young (1804a) wrote:
The observations on the effects of diffraction and interference,
may perhaps sometimes be applied to a practical purpose, in
making us cautious in our conclusions respecting the appearances
of minute bodies viewed in a microscope. The shadow of a fibre,
however opaque, placed in a pencil of light admitted through a
small aperture, is always somewhat less dark in the middle of its
breadth than in the parts on each side. A similar effect may also
take place, in some degree, with respect to the image on the retina, and impress the sense with an idea of a transparency which
has no real existence: and, if a small portion of light be really
transmitted through the substance, this may again be destroyed
by its interference with the diffracted light, and produce an
appearance of partial opacity, instead of uniform semitransparency. Thus, a central dark spot, and a light spot surrounded by
a darker circle, may respectively be produced in the images of a
semitransparent and an opaque corpuscle; and impress us with an
idea of a complication of structure which does not exist.
If light is a wave, then what is waving and what is the
nature of the medium through which it propagates? In the
Fresnel or near-field diffraction pattern of a square.
early part of the nineteenth century, Young, Arago, and
Fresnel considered light, like sound, to be a mechanical longitudinal compression wave. Longitudinal waves,
which vibrate parallel to the direction of propagation, can
propagate in gases, liquids, and solids. However, after considering the polarization of light (see Chapter 7), Young
and Fresnel realized that light, unlike sound, must be, at
least in part, a transverse mechanical wave. Transverse
waves, which vibrate perpendicular to the direction of
propagation, can propagate only through a highly elastic solid medium or through a liquid medium subjected to
gravitational forces. This seemed to indicate that the luminous ether had to be elastic enough to propagate light from
distant stars without impeding the movement of the planets around the sun or causing the planets to snap back in
the direction they came from! In addition, the ether had
to be thin enough to pass though the glass walls of a vacuum jar.
Since the square of the velocity of a wave propagating through a mechanical medium is equal to the ratio of
the elasticity to the density of the medium, in order for
the speed of light to be 299792458 m/s, the elasticity had
to be enormously high and the density had to be infinitesimally low. David Brewster told John Tyndall (1873) that
he objected to the wave theory of light because “he could
not think the Creator guilty of so clumsy a contrivance as
the filling of space with ether in order to produce light.”
Throughout the nineteenth century, much effort was
expended trying to resolve the requirements of this enigmatic luminous ether though the merciless addition of
putative physical properties and the use of inexorable
mathematics (Airy, 1866; MacCullagh, 1880; Lodge,
1907, 1909, 1925; Lorentz, 1927; Whittaker, 1951, 1953;
Schaffner, 1972; Swenson, 1972; Hunt, 1991). Then, at the
turn of the twentieth century, Einstein (1905a) proclaimed
by fiat that the ether was unnecessary for the propagation
Chapter | 3 The Dependence of Image Formation on the Nature of Light
of light, if we accept, in exchange, the idea that space and
time are only relative concepts.
Although we can clearly see that Thomas Young gave
us great insight into the nature of light and its practical applications in microscopy and vision, in his lifetime,
this Englishman was a persona non grata, since he did
not accept the corpuscular nature of light proffered a century before by Newton. Newton was held in high regard in
England as can be seen by the following epitaph written
for Newton in 1727 by Alexander Pope:
Nature and Nature’s laws lay hid in night:
God said, “Let Newton be!” and all was light.
Thomas Young was viciously attacked anonymously
in the Edinburgh Review for being “Anti-Newtonian”
(Anonymous, 1803, 1804; Young, 1804; Peacock, 1855;
Wood and Oldham, 1954; Klein, 1970). The anonymous
reviewer (1803, 1804b), most likely Lord Brougham
(Tyndall, 1873), wrote about Young and his wave theory
of light:
A mere theory is in truth destitute of all pretensions to merit of
every kind, except that of a warm and misguided imagination. It
demonstrates neither patience of investigation, nor rich resources
of skill, nor vigorous habits of attention, nor powers of abstracting and comparing, nor extensive acquaintance with nature. It
is the unmanly and unfruitful pleasure of a boyish and prurient
imagination, or the gratification of a corrupted and depraved
appetite.
The anonymous reviewer went on to say:
We take our leave of this paper with recommending it to the
Doctor to do that which he himself says would be very easy;
namely, to invent various experiments upon the subject. As,
however, the season is not favourable for optical observation,
we recommend him to employ his winter months in reading the
“Optics”, and some of the plainer parts of the “Principia”, and
then to begin his experiments by repeating those which are to be
found in the former of these works.
Young decided that the Royal Institution was no place
for him and resigned from his post. However, his work has
held up over time, and it is an essential aspect of understanding image formation in the microscope. In 1850 Léon
Foucault (1850, 1862) measured the speed of light in air
and in water and found that it was slower in water than it
was in air, a finding that was consistent with the wave theory of light, but inconsistent with the corpuscular theory
of light championed by Newton (1730). This result, along
with the theoretical work done by James Clerk Maxwell
and the Maxwellians, led to a widespread acceptance of
the wave theory of light (Lloyd, 1873; Herschel, 1876;
Lommel, 1888). Since the corpuscular theory was able to
explain interference phenomena only by inventing ad hoc
hypotheses, the corpuscular theory was no longer thought
of as a contending theory, but as a “mob of hypotheses”
(Tyndall, 1873).
51
JAMES CLERK MAXWELL AND THE WAVE
THEORY OF LIGHT
Michael Faraday (1845) was looking for the relationship
between electricity, magnetism, and light, and eventually
found that he could influence the plane of polarization of
a light beam when he placed the glass through which the
beam traveled in a magnetic field (Tyndall, 1873; Thompson,
1901; Williams, 1987; Day, 1999). Other nineteenth century scientists, including Wilhelm Weber, also were interested in unifying electricity, magnetism, and optics. While
Maxwell was working on the equations of electricity (E)
and magnetism (B), he serendipitously found the relationship between electricity, magnetism, and light (Maxwell,
1891; Niven, 2003). These equations, known as Maxwell’s
Equations, combined an extended version of Ampere’s Law
( B μoJ μoεBo∂E/∂t), which relates the magnitude
of the magnetic field to the electrical currents, displacement
currents, and the magnetic permeability of the medium (μ);
Faraday’s Law ( E ∂B/∂t), which relates the magnitude of the electric field to a time-varying magnetic field;
Gauss’s Law of Electricity ( · E (ρ/εo)), which relates the
electric field to the charge density and electric permittivity ();
and Gauss’s Law of Magnetism ( · B 0), which states that
there are no magnetic monopoles (Heaviside, 1893; Hertz,
1893; Thomson, 1895; Poynting, 1920; Lorentz, 1923).
By combining these laws, Maxwell and the Maxwellians
(Campbell and Garnett, 1884; Lodge, 1889; Heaviside,
1892, 1922; Hertz, 1893; Maxwell, 1931; Cohen, 1952;
Everitt, 1975; Hunt, 1991; Yavetz, 1995; Darrigol, 2000;
Niven, 2003) showed that the electric (E) and magnetic (B)
fields, like sound, could be described by a wave equation:
∂ 2 E y /∂x 2 ∂ 2 E y /∂y 2 ∂ 2 E y /∂z2 o εo∂ 2 E y /∂t 2
∂ 2 Bz / ∂x 2 ∂ 2 Bz / ∂y 2 ∂ 2 Bz / ∂z 2 μ o εo∂ 2 Bz / ∂t 2
Combining the four laws of electricity and magnetism
resulted in equations for the electric and magnetic field that
had the same form as a wave equation. By solving the wave
equation, Maxwell found that the speed of electromagnetic waves in a vacuum is equal to (1/(oμo)), where o
is the electric permittivity of a vacuum (8.85 1012 s2
C2 m3 kg1) and μo is the magnetic permeability of a vacuum
(4π 107 m kg C2), and moreover, the speed turned out to
be 2.9986 108 m/s, which was the same value that Hippolyte
Fizeau (1849a,b) and Fizeau and Bréguet (1850) found for the
speed of light (Frercks 2000)! That is, when Maxwell solved
the wave equation to find the speed of propagation of an electromagnetic wave, he found that electromagnetic waves travel
at the speed of light. This meant to Maxwell, that light itself
must be an electromagnetic wave (Figure 3-22).
Fizeau measured the speed of light by passing light to
a distant mirror (8.6 km) through a rotating wheel with an
52
Light and Video Microscopy
x
TABLE 3-3 A comparison between Ke and n
Propagation
Ke
n
Air
1.000294
1.000293
Hydrogen
1.000131
1.000132
Helium
1.000034
1.000035
Carbon dioxide
1.00049
1.00045
Water
8.96
1.333
Fused silica
1.94
1.458
Substance
E
y
B
z
FIGURE 3-22 A light wave at a given instant of time according to
Maxwell. The electric (E) and magnetic (B) fields are transverse, in-phase
with each other, and orthogonal to each other.
opening cut into it. A pulse of light leaving the wheel traveled to the mirror where it was reflected back to the rotating toothed wheel. Fizeau adjusted the speed of rotation of
the wheel (N turns/second) so that the returning light pulse
either went through the hole or did not. From knowing
the distance the light traveled (D), the number of teeth
in the wheel (n), and the speed of rotation, Fizeau could
calculate the sped of light from the following formula:
c ΝnD
Fizeau found the speed of light to be 3.153 10 m/s,
a speed consistent with that found from astronomical measurements done by Römer and Bradley (Michelson, 1907,
1962; Jaffe, 1960; Livingston, 1973).
Maxwell (1865) was so excited when he saw this “coincidence” he said: “This velocity is so nearly that of light,
that it seems we have strong reason to conclude that light
itself (including radiant heat, and other radiations, if any)
is an electromagnetic disturbance in the form of waves
propagated through the electromagnetic field according to
electromagnetic laws.”
One important consequence of Maxwell’s electromagnetic wave theory of light for microscopists is that we can
use it to predict and understand the refractive index of various media (Maxwell, 1891). Since, according to Maxwell’s
wave equation, the velocity of light in a vacuum (c) is
given by:
c (ε0 μ o )1/ 2
then
n (εο μ o )1/ 2 / (εμ )1/ 2 (εμ )1/ 2 / (ε00 )1/ 2
[(ε / ε 0 )(μ/ μ 0 )]1/ 2
The dimensionless ratio of to o is known as the relative permittivity (Ke), which is a measure of the electric
characteristics of a substance; and the dimensionless ratio
of μ to μo is known as the relative permeability (Km), which
is a measure of the magnetic characteristics of a substance.
Therefore
n (K e K m )1/ 2
8
and the speed of light in a dielectric medium is given by:
v (εμ )1/2
where is the electric permittivity of the dielectric (in
s2C2 m3 kg1) and μ is its magnetic permeability (in m
kg C2). And since the refractive index (n) of a medium is
defined as:
n c/ v
Since most substances are only weakly magnetic
(except ferromagnetic materials), Km 1, which means
n √K e
This is known as Maxwell’s Relation, and it tells us that
the refractive index is a measure of the electrical properties
of a material. That is, it is a measure of concentration, distribution, and movement of the electrons in the material.
The concentration of electrons is roughly related to the
density of the substance.Table 3-3 compares Ke with n.
The discrepancies between the square root of the relative permittivity and the refractive index in Table 3-3
results from the fact that the relative permittivity is measured at 60 Hz, whereas the refractive index is measured
at 5 1014 Hz. When Ke of glass is measured with D.C.
fields, it is 12.61; when the field varies at a frequency of
1 Hz, the index of refraction decreases to 2.739, at 25 Hz,
Ke 2.51, and at 1.2 104 Hz, Ke 2.404. When the frequency of an electric field is increased to approximately
1010 Hz, Ke of glass falls to 2.04. Thus Ke decreases as the
frequency approaches that of visible light (1014 Hz; Bose,
1927) and in fact Ke approaches n. In most cases Ke has
been determined by ASTM (American Society for Testing
Materials) test methods at room temperature under standard conditions; however, like the values of the refractive
index, the values of Ke vary with temperature.
53
Chapter | 3 The Dependence of Image Formation on the Nature of Light
λ
FIGURE 3-23 According to Heinrich Hertz, incoming electric waves will cause an electron to oscillate. The energy of the oscillating electron can be
dissipated by the atoms or molecules that house the electron or the oscillating electron can act as a secondary source of electromagnetic waves by reradiating
the energy. Electromagnetic waves can also be radiated when the electrons oscillate as a result of other energy inputs (e.g., heat, friction, etc.).
Following Maxwell’s work, the wave theory of light
became the only accepted theory of light. However, light
was no longer treated as it was in the dynamical wave
theory, as mechanical waves traveling through a very
complicated and paradoxical ether as Huygens, Young,
Fresnel, Arago, McCullagh, Neumann, and Kirchhoff visualized them, but as electromagnetic waves (The Classical
Wave Theory), which may or may not have a mechanical
action. Maxwell still invoked the ether as a mechanical
medium necessary to transmit the electromagnetic waves
(Whittaker, 1951, 1953), but Hendrik Lorentz removed the
mechanical properties of the ether, leaving only its electrical permittivity and magnetic permeability.
We can now look at diffraction in terms of the electromagnetic theory of light. The edges of an obstruction or a
slit are composed of electrons in atoms or molecules that
can interact with the incident light. The electrons in the
material behave as oscillators whose phase and amplitude
of vibration depend on the electric field surrounding it. The
incoming electromagnetic wave drives the electrons into
oscillation and then the electrons reemit radiation at the
same frequency (Figure 3-23). The direction of the reemitted, scattered, or diffracted light is a function of the spatial
frequency of the object with which the light interacts.
We now know that gamma rays, X-rays, ultraviolet
rays, visible rays, infrared rays (heat), microwaves, and
radio waves are all electromagnetic waves that differ only
in their wavelengths and frequencies (Figure 3-24). Each
type of electromagnetic wave interacts with charged particles within atoms and molecules that are capable of
interacting with the frequency of the incident electromagnetic wave. Heinrich Hertz (1893) demonstrated that radio
waves could be reflected and refracted just like light waves.
Moreover, he showed that the electric field of the electromagnetic waves had transverse polarization as predicted
by Maxwell’s equations. Most textbook of optics present
optical phenomena in terms of the electromagnetic theory
of light (Stokes, 1884, 1885; Preston, 1895; Kelvin, 1904;
Schuster, 1904, 1909; Wood, 1905, 1914, 1961; Schuster
and Nicholson, 1924; Mach, 1926; Hardy and Perrin, 1932:
Drude, 1939; Robertson, 1941; Jenkins and White, 1957;
Strong, 1958; Bitter and Medicus, 1973; Hecht and Zajac,
1974; Born and Wolf, 1980), and many textbooks on electricity and magnetism are helpful in understanding optics
(Thompson, 1904; Thomson, 1909; Lorentz, 1923, 1952;
Haas, 1925; Jeans, 1927; Abraham and Becker, 1932;
Planck, 1932; Frank, 1940; Stratton, 1941; Skilling, 1942;
Harnwell, 1949; Panofsky and Phillips, 1955; Corson
and Lorrain, 1962; Jackson, 1962; Sommerfeld, 1964;
Jefimenko, 1966; Lindsay, 1969; Pauli, 1973; Shadowitz,
1975; Purcell, 1985; Griffiths, 1989; Heald and Marion,
1989; Pramanik, 2006). Textbooks concerning thermodynamics can also be consulted to understand optics since
Macedonio Melloni and John William Draper (1878) independently demonstrated that thermal radiation follows the
same laws as visible radiation. Currently almost the whole
spectrum of electromagnetic radiation is used in microscopes to study the microscopic structure of matter (see
Chapter 12).
ERNST ABBE AND THE RELATIONSHIP
OF DIFFRACTION TO IMAGE FORMATION
We have reached what I think is a really exciting point
where we can now apply the basic principles of geometric
54
Wavelength
Frequency (Hz)
Light and Video Microscopy
Gamma-rays
0.1Å
1019
{10.1Å nm
10
18
X-rays
1 nm
1017
400 nm
10 nm
1016
Ultraviolet
500 nm
Visible
nm
{1000
1 μm
14
600 nm
10
10 μm
Infra-red
1013
100 μm
1012
700 nm
μm
{1000
1 mm
11
10
1 cm
Microwave
1010
Radar
10 cm
109
1m
108
Radio, TV
10 m
107
100 m
106
1 when 0 x π
f (x ) 1 when π x 2π
100 nm
1015
of light spots found in the diffraction plane can be described
by a mathematical function called a Fourier transform. For
this reason, the back focal plane of the lens is commonly
called the diffraction plane or the Fourier plane.
Let’s assume that the object is an amplitude grating with
an alternating pattern of sharp dark bands and sharp transparent bands. The object can be described by a square wave with
an amplitude that varies between 1 and 1 (Figure 3-25).
The function that characterizes this square wave is:
AM
1000 m
FIGURE 3-24 The electromagnetic spectrum.
and physical optics to understand how a microscope works
and how it renders an image of a biological specimen. Let’s
assume that all the lenses in our microscope are perfect and
free from aberrations. However, even if our lenses were
perfect in reality, diffraction would still limit our ability to
render a perfectly faithful image of our specimen. This is a
result of the fact that the wavelength—and if you will, the
wave width—of light is finite and not infinitesimally small.
Diffraction is an extremely important concept in
microscopy. Interestingly, we still use Kirchhoff’s mechanical view of diffraction (Braddick, 1965; Baker and
Copson, 1987) to predict the position of spots since the
methods consistent with Maxwell’s equations require difficult mathematics (Sommerfeld, 2004) or unreasonable
physical assumptions (Bethe, 1944).
Normally, in the absence of a lens, an object illuminated
with plane waves forms a Fraunhöfer diffraction pattern at
infinity. However, when an object is placed in the object
space in front of a lens so that the lens forms an image in
the image space behind the lens, a diffraction pattern that is
equivalent to a Fraunhöfer diffraction pattern of the object
is produced at the back focal plane of the lens. The pattern
According to Joseph Fourier (1822), who was interested in modeling the movement of heat through a material of any shape, any shape can be described by a complex
wave, and that a complex wave is the sum of an infinite
series of sine waves. Consequently, we can approximate
the square wave with a sine wave that has the same period
or angular wave number as the square wave and an amplitude that varies between 1 and 1 (Figure 3-26).
We can increase the fidelity of the representation of
the square wave if we add to the fundamental sine wave,
a sine wave with a higher spatial angular wave number
and a smaller amplitude (Figure 3-27). We can increase
the fidelity of the representation even more if we add to
the two sine waves a third sine wave with an even greater
spatial wave number and a smaller amplitude (Figure 3-28).
We can increase the fidelity of the representation by adding more and more sine waves with higher and higher
spatial angular wave numbers or frequencies and smaller
and smaller amplitudes (Figure 3-29). A completely faithful representation requires the addition of an infinite number of sine waves. However, by summing a series of four
sine waves, we already have obtained a “reasonable” likeness of the square wave. According to Fourier’s Theorem,
the square wave can be described by the following equation:
f (x ) (4 / π)[(1/1) sin(1kx) (1/ 3) sin(3kx)
(1/ 5) sin(5kx ) (1/ 7) sin(7kx ) …]
where k is the fundamental spatial angular wave number
(in m1), and x is the position on the horizontal axis. We
use the term spatial angular wave number for k, since k
represents an inverse distance, however in most texts, the
spatial angular wave number is commonly called the spatial frequency.
Let’s analyze the Fourier Transform bit by bit. Notice
that the coefficient of each term follows the sequence 1/1,
1/3, 1/5, 1/7, 1/9, 1/11.... The coefficients in front of the
sine function determine the amplitude of the wave. The
coefficients of simple Fourier Transforms are either odd
or even. If the original function is symmetrical above and
below the x-axis, the coefficients are all even (and the function is composed of cosine waves instead of sine waves).
However, when the original function is not symmetrical,
Chapter | 3 The Dependence of Image Formation on the Nature of Light
55
1
π
0
2π
1
FIGURE 3-25 A square wave.
1
1
FIGURE 3-26 A sine wave that approximates the fundamental spatial angular wave number of the square wave.
1
1
FIGURE 3-27 The sum of two sine waves with different spatial angular wave numbers better approximates the square wave.
1
1
FIGURE 3-28 The sum of three sine waves with different spatial angular wave numbers approximates the square wave even better.
1
1
FIGURE 3-29 The sum of four sine waves with different spatial angular wave numbers approximates the square wave with high fidelity.
all the coefficients are odd (like our square wave, earlier)
and the function is composed of sine waves (like our square
wave, earlier). Complicated functions (like the wave that
would describe the arrangements of organelles in a cell)
have Fourier functions that are composed of sine waves
and cosine waves. In theory, every function, whether it is
periodic or nonperiodic, can be represented by the sum of an
infinite number of sinusoidal waves as long as the function
is everywhere finite and integratable.
Notice also that in the first term we take the sine of the
fundamental spatial angular wave number (k) of the sine
wave, which represents the fundamental spatial characteristics of the object. In the next terms, we take the sine of 3 k,
5 k, 7 k, and so on. So the math really says: We can approximate a square wave by adding sine waves together. The
rules are that we find the most fundamental spatial angular wave number that best describes the square wave. Then
we add sine waves with greater and greater spatial angular
56
wave numbers. The spatial angular wave numbers are preceded by a coefficient so that every time the spatial angular
wave number is multiplied by that coefficient, the amplitude is divided by that same coefficient. The fundamental
spatial angular wave number is related to the reciprocal of
the distance of an object that determines the position of the
first-order diffraction spot.
The spatial angular wave numbers of a square wave are
relatively simple and straightforward, however the spatial
angular wave numbers of more complex objects like the
cityscape shown in Figure 3-30, or the structure of a cell
can also be described by Fourier transforms, albeit more
complicated ones.
To understand image formation, we must understand the
relationship between the diffraction pattern and the image. The
terms of the Fourier transform, with greater and greater spatial
angular wave numbers, are equivalent to the diffraction spots
of higher and higher orders found farther and farther from the
principal axis. The small spatial angular wave number terms
of the Fourier transform are related to the lower-order diffraction spots and the large spatial angular wave number terms of
the Fourier transform are related to the higher-order diffraction spots. To make a perfect image we must add an infinite
number of Fourier terms, which is equivalent to capturing an
infinite number of orders of the diffracted light.
Ernst Abbe, while working for Carl Zeiss (Auerbach,
1904; Schütz, 1966; Smith, 1987), noticed in 1873 that
when an image is in focus, the diffraction pattern appears
in the back focal plane of the objective lens. When a specimen is illuminated, each point on the specimen can be
considered to act as a point source of light and give rise to
Huygens’ spherical wavelets. The light waves travel in all
possible directions from each point. The light, which travels
in a given direction, from each and every individual point
source, forms a collimated beam. Therefore light emanating
from the specimen can be considered to consist of a series
of collimated beams traveling in each and every direction.
In a perfect converging lens, by definition, a collimated
beam of light converges to a point at the back focal plane
of the lens. In a perfect lens, the light traveling parallel to
the optical axis focuses at the back focal point of the lens.
The other collimateds beams, which impinge on the lens,
from other directions converge at other points in the back
focal plane of the lens (Figures 3-31 and 3-32).
According to Abbe, points so, s1, and s2 at the back
focal plane act as point sources that give rise to Huygens’
spherical wavelets. The waves emanating from these points
interfere in an image plane to form an image of the original amplitude grating. Abbe realized that the image arises
directly from the diffraction spots on the back focal plane
and only indirectly from the points on the object. It is
as if the image is formed through two sequential optical processes. In the first process, the object diffracts the
illuminating light into the objective lens, and in the second
process, the objective lens moves the diffraction pattern
from infinity to the back focal plane of the lens. The light
Light and Video Microscopy
a
y
Cityscape
I (y,a)
y
Fundamental
Period
I (y,a)
y
Fourier
components
y
FIGURE 3-30 No matter how complicated an object is, it can be
resolved into its Fourier components.
emanating from the diffraction pattern in the back focal
plane of the objective lens interferes to form an image on
the image plane. The mathematical process that resolves the
object into components of various spatial frequencies in the
back focal plane of the objective is called a forward Fourier
transform. The mathematical process that recombines
57
Chapter | 3 The Dependence of Image Formation on the Nature of Light
Image Plane
Objective
Sub-stage
condenser
Transform
plane
Grating
G2
P1
s2
s1
s0
s1
s2
G1
P2
Object
plane
Focal
plane
f
FIGURE 3-31 The object (G) diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its
back focal plane. The spherical waves that emanate from the spots (s) at the back focal plane of the objective interfere with each other to produce an
image at the image plane (P). This diagram emphasizes the rays normal to the wave fronts.
Objective
s1
s0
Object
plane
Focal
plane
Image
plane
FIGURE 3-32 The object diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its back
focal plane. The spherical waves that emanate from the spots (s) at the back focal plane of the objective interfere with each other to produce an image at
the image plane. This diagram emphasizes the wave fronts.
the components of various spatial frequencies into an
image is called an inverse Fourier transform.
Physically, the illuminating light is diffracted by the
specimen and depending on the radius of the objective
lens and its distance from the specimen, fewer or more
orders of diffracted light are captured by the objective lens.
The objective lens then forms the diffraction pattern at its
back focal plane. Since the diffraction pattern lacks the
diffracted light of the orders that were not captured by
the objective lens, the diffraction pattern does not represent
58
Light and Video Microscopy
the diffraction pattern of the object, but of a somewhat
incomplete or blurred version of the object. The dark and
light regions of the image are formed by the interference of
waves emanating from the diffraction spots. The brightness
of a given spot depends on the amplitude and phase of the
interfering waves. The bright spots of the image are formed
where the wavelets originating from the back focal plane
constructively interfere and the dark spots occur where the
wavelets destructively interfere.
Let’s consider the formation of an image of a biological
specimen with a periodic structure such as a diatom. When
the diatom is illuminated, light radiates from each point
in the diatom in all possible directions. In Figure 3-33,
we will make use of the characteristic rays with which we
are familiar from Chapter 2. AB and AB are rays, perpendicular to their wave fronts, that strike the lens parallel
to the principal axis. AC is a ray, perpendicular to its wave
front, which travels through the front focal point. All other
rays parallel to AC will pass through the lens and converge at point D in the back focal plane. All the light rays,
perpendicular to their associated light wave fronts, which
leave the object parallel to AB, converge at point fi in the
back focal plane of the objective. Subsequently light rays,
with their associated wave fronts, diverge from these positions on the back focal plane to the image plane, where an
image is produced at the position where two rays and their
associated wave fronts (which originate at the same point
in the object) converge. Bright spots are formed where the
rays have optical path lengths that are equal to an integral
numbers of wavelengths. Dark spots are formed where the
rays vary by half-wavelengths.
In his initial experiments, Abbe noticed that when he
increased the diameter of the objective lens, he increased
the fidelity of the resulting image even though the apparent
cone of incident light (zeroth-order light) filled only a
small portion of the objective lens. Abbe figured that the
“dark space” of the objective lens must contribute to the
fidelity of the image. He proposed that specimens, whose
size were close to the wavelength of light, diffracted light
into the dark space of the objective lens. Thus, if the aperture were not large enough, some of these rays would not
enter the objective lens, and the diffraction pattern at the
back focal plane of the lens would not contain the higherorder diffraction spots. As a result of the incomplete capture of the diffracted light, the image was not a faithful
reproduction of the object.
He then said that the image actually is related to a fictitious object whose complete diffraction pattern exactly
matches the one collected by the objective lens. Through
experimentation he realized that the light (diffracted at
large angles) that is missed by the objective lens represents
the higher spatial angular wave numbers of the specimen,
and their removal results in an image that does not have
as much high spatial angular wave number information as
is present in the object. As it performs an inverse Fourier
transform on the diffraction pattern, the objective lens also
acts as a low pass filter that removes the higher spatial
angular wave number terms and the higher-order diffracted
light that they represent (Stoney, 1896).
Let us discuss in detail the experiments that serve at
the basis for Abbe’s theory of image formation. Abbe performed these experiments in collaboration with Carl Zeiss
and Otto Schott in order to produce the best objective lens
that could be made (von Rohr, 1920). Although excellent
objective lenses were already being made by craftsmen
working for small microscope companies, the high quality
objective lenses were obtained through trial and error and
without the benefit of physical theory.
B
A
V
A
fo
B
C
fi
D
C
Periodic
Object
(diatom)
Objective lens
Back
focal plane
Image plane
FIGURE 3-33 The object diffracts the illuminating light. The objective lens collects the diffracted light and produces a diffraction pattern at its back
focal plane. The spherical waves that emanate from the spots at the back focal plane of the objective interfere with each other to produce an image at the
image plane. This diagram emphasizes the characteristic rays.
59
Chapter | 3 The Dependence of Image Formation on the Nature of Light
In order to simplify the conditions used in image formation, Abbe used high contrast amplitude gratings for
specimens and observed their diffraction patterns in the
back focal plane of the objective lens and their images in
the image plane. When he observed amplitude gratings
consisting of widely spaced or narrowly spaced slits, Abbe
noticed that there was a mathematical relationship between
the amplitude grating and the diffraction pattern in that the
spacing between the dots in the diffraction pattern was
inversely proportional to the spacing between the slits in
the object (Figure 3-34).
Abbe also found that he could change the nature of the
image by altering the diffraction pattern. For example he
could block out the first order diffraction spots that result
from a widely spaced grating and the image would look as
if it came from a narrowly spaced grating (Figure 3-35).
Abbe also found that when he altered the diffraction pattern, in a process now known as spatial filtering, he
obtained a modified image.
Albert Porter (1906) extended Abbe’s experiment using
a grid for an object and obtained a diffraction pattern like
that shown in Figure 3-36 (Meyer, 1949; Bergmann et al.,
Object
Diffraction
pattern
Image
FIGURE 3-34 Ernst Abbe’s experiment viewing the image and diffraction pattern of a grating.
1999). Porter blocked out everything in the diffraction pattern except for the three central, horizontal spots, and saw
an image of vertical slits (Figure 3-37). When he blocked
out everything in the diffraction pattern but the three central, vertical spots, he saw an image of horizontal slits
(Figure 3-38). When he blocked only the central spot and
let the light from all the other spots to form an image, he
saw a bright grid on a dark background. When he blocked
out everything but the central spot, he saw a uniformly lit
background without any image at all and when he allowed
more and more orders of diffracted to pass and form the
image, the image became a more and more faithful representation of the object.
We can really see that the image is related directly to
the diffraction pattern in the back focal plane of the objective by making a mask that represents the diffraction
pattern of the grid. Then, without putting the grid in the
microscope, we insert the mask in the back focal plane of
the objective that mimics the diffraction pattern of the grid.
Even without the grid in the object plane, we see an image
of the grid in the image plane. Many more examples of spatial filtering can be found in Optical Transforms by Taylor
and Lipson (1964) and in Atlas of Optical Transforms by
Harburn et al. (1975). Ernst Abbe and Albert Porter established the relationships between the object, the diffraction
pattern, and the image by showing:
● Two different objects can be made to produce the
same image by altering the diffraction pattern.
● Two identical objects can be made to produce different images by altering the diffraction pattern.
● The removal of the diffracted light destroys the image.
We must collect at least the zeroth- and the first-order diffracted light in order to construct a bright-field image.
Block out
Object
Diffraction
pattern
Image
Object
FIGURE 3-35 Abbe used a mask to block out the first-order diffraction
spots produced by the coarse grating and obtained an image of the fine
grating.
Object
Diffraction
pattern
Image
FIGURE 3-36 Albert Porter’s extension of Abbe’s experiment. Porter
viewed the image and diffraction pattern of a grid.
Diffraction
pattern
Image
FIGURE 3-37 Porter produced an image of a vertical grating by masking certain diffraction spots produced by the grid.
Object
Diffraction
pattern
Image
FIGURE 3-38 Porter produced an image of a horizontal grating by
masking certain diffraction spots produced by the grid.
60
Light and Video Microscopy
● The more orders of diffraction that an objective lens
captures, the more faithful the image. The additional orders
can be represented mathematically by higher-order harmonics of a Fourier Transform. Each higher order diffraction
spot represents a higher-order spatial angular wave number.
● The image contrast is improved by the removal of
some of the zeroth-order light. Removing all the zerothorder light results in black objects appearing white, and
white objects appearing black. We will remove the zerothorder light completely when we do dark-field microscopy.
Abbe’s theory “applied not merely to very small
objects, to which he had first limited its application but that
it must supply the ultimate explanation of the images of all
objects seen by borrowed light; even of fence-poles, as he
fiercely put it in a reply to one of his critics” (Spitta, 1907).
Abbe’s studies and conclusions are central when it comes
to us incorporating Plato’s teachings and Bacon’s admonitions about the idols of the cave (see Chapter 1) when we
do microscopy. Artifacts introduced by diffraction alter the
relationship between the reality of the specimen and the
image of the specimen.
RESOLVING POWER AND THE LIMIT OF
RESOLUTION
The ability to see an isolated object is called detection.
There is not any lower limit to the size of a bright object
that can be detected against a black background as long
as the light radiated from the object is bright enough for
us to see or for a camera to capture. Resolving power, on
the other hand, is the ability to distinguish closely spaced
points as separate points. Our ability to resolve two bright
dots on a black background with the naked eye depends on
the distance the dots are from our eyes. When the closely
spaced dots are far from our eyes, they appear as a single
dot, but as we bring the dots closer and closer to our
eyes, the two dots appear to separate and we say we can
resolve the two dots as two separate dots. We can resolve
the two dots when they are close to us because we increase
the angle that subtends the rays that enter our eyes. The
greater the angular aperture, the greater the number of
diffraction orders emanating from a specimen we collect.
Consequently, the image of the specimen on our retina
becomes a more and more faithful representation of the
object.
Under ideal conditions, where the objects are bright on
a black background, our eyes have the power to resolve
two objects that are about 70 μm apart at a distance 25 cm
from our eyes. When objects are less than 70 μm apart,
our eyes are unable to collect more than the zeroth-order
diffracted light and there is no structure in the image on
our retinas. Seventy micrometers is the limit of resolution of the human eye. Squinting results in an increase in
contrast, but a decrease in the resolving power of the eye
(Figure 3-39).
The limit of resolution of a microscope is defined as
the smallest distance apart two points in an object may be,
with it still being possible to distinguish them as two separate points in the image. The resolving power of the light
microscope is limited by diffraction. In this chapter, I will
discuss three approaches used to characterize the resolving power of the light microscope—one by Ernst Abbe,
one by John Strutt, also known as Lord Rayleigh, and one
by Sparrow. In Chapter 12, I will describe the “near-field”
approach to increasing the resolving power of the light
microscope (Synge, 1928; Ash and Nicholls, 1972).
Abbe based his criterion for the limit of resolution
of a light microscope on his use of high-contrast amplitude gratings as objects. He illuminated the gratings with
axial, coherent light, and the objective lens captured the
diffracted rays to form a Fraunhöfer diffraction pattern at
Object
Angular
aperture
Light
α
FIGURE 3-39 The ability of the human eye to create a faithful image of an object by collecting as many orders of diffracted light as possible
depends on twice the angular aperture of the eye. The closer we move toward an object, the more diffraction orders we collect and the better we see the
object.
61
Chapter | 3 The Dependence of Image Formation on the Nature of Light
the back focal plane of the objective lens and an image of
the grating at the image plane. Abbe concluded that, in
order to resolve the bars of the grating, the objective lens
must be wide enough and/or close enough to the object to
catch the first-order diffracted rays (Figure 3-40). If the
spatial frequency of the specimen were too high for the
objective lens to capture the first-order diffracted light,
there would be no interference at the image plane, and a
spherical wave originating at the back focal plane of the
objective lens would illuminate the whole image plane.
The ability of the lens to catch the first order rays is
characterized by the angular aperture of the objective lens
(Figure 3-41). The angular aperture is defined by ⬔ACB.
If we define ⬔ACD as half the angular aperture and call it
α, then we see that tan α r/so, where r is the radius of the
lens and so is the distance between the object and the lens.
For infinity-corrected lenses, where the object is placed at
the focal point, tan α r/fo. If α is small enough, we can
use the small angle assumption: tan α sin α.
A light microscope has the resolving power to form a
distinct image of an amplitude grating with a distance d
between the black bands when the angle between the firstorder diffracted light and the zeroth-order diffracted light
equals the angular aperture of the objective lens. The sine
of the angle necessary to capture the first-order diffracted
light is given by the ratio of the wavelength of light to the
characteristic dimension of the object.
sin θ λ/d
The limit of resolution can be determined by replacing
θ with α, which yields:
This equation serves only as an estimate of the limit
of resolution, since it is based on the assumption of small
angles. Abbe (1881) noticed that this equation is limited
further by the assumption that the diffracted rays are not
refracted as they pass from the cover glass to the air on the
way to the objective lens. However, Abbe knew that when
microscopists replaced the air between the specimen and
the glass objective lens with immersion oil, they increased
the resolving power of the microscope (Figure 3-42). The
resolving power increases because the rays that were
refracted by the air out of the collecting range of the objective lens could enter the objective lens in the presence of
immersion oil with a refractive index of 1.515. Thus the
resolving power of the lens depended on both the angular
aperture and the refractive index of the medium between
the specimen and the lens.
Abbe incorporated the effect of the medium between the
specimen and the lens on the limit of resolution (d). Thus,
d λ/(n sin α )
Abbe (1881) gave the name numerical aperture (NA)
to n sin α. According to Abbe, the limit of resolution of
the microscope when illuminating the specimen with axial
coherent light is:
d λ/ NA
Given that the maximum angle that α can be is 90
degrees (sin α 1), and given that the medium that would
be most effective in refracting the diffracted rays into the
lens will have the same refractive index as the lens (1.515),
the maximal NA 1.5. Using blue light of 400 nm, the
limit of resolution of the light microscope will be:
d λ/(sin α )
d 400 nm / 1.515 264 nm
X
x
N
q
d
Light
source
M
P
Substage
condenser
Aperture
diaphragm
q
q
C
q
A
o
d sin θ
D
Stage
Objective
lens
FIGURE 3-40 According to Ernst Abbe, a microscope cannot resolve objects smaller than a certain length (d), because the angle of the first-order diffracted light is too great for that light to be captured by the objective lens.
62
A
Light and Video Microscopy
D
r
B
s0
α
C
FIGURE 3-41 The angular aperture (α) of a lens depends on the radius
(r) of the lens and the distance (so) between the object and the lens.
0
1
0
1
1
Waves travel
slower in oil than
in air:
oil
1
air
FIGURE 3-42 Because waves travel more slowly through oil than
through air, the angle between the first-order diffracted wave and zerothorder diffracted wave is smaller in oil than in air. This allows oil-immersion objectives to resolve finer details than dry objectives.
The resolving power of the light microscope can be
increased by using light of shorter wavelength. The wavelength can not be shortened without limit, because as the
wavelength decreases, the energy of each photon increases,
as will be discussed in Chapter 12, and consequently, the
short wavelength light can damage living specimens.
The resolving power of the light microscope can also be
increased by illuminating the object with oblique coherent
light (oblique illumination) by using a sub-stage condenser
(Figure 3-43). While the zeroth-order light travels through
one edge of the objective lens, the first-order light travels
through the opposite edge of the lens, effectively doubling
the angular aperture. In the case of oblique illumination, the
limit of resolution is estimated by the following formula:
d λ/(2 NA)
Given that the maximum angle that α can be is
90 degrees (sin α 1), and given that the medium that
would be most effective in refracting the diffracted rays
into the lens will have the same refractive index as the lens
(1.515), the maximal NA 1.5. Using blue light of 400 nm,
then the limit of resolution of the light microscope will be
about 132 nm.
In Chapter 4, I will discuss Köhler illumination, where
the specimen is illuminated with a cone of light whose rays
illuminate the specimen at a variety of angles. When illuminating the specimen with Köhler illumination, the limit
of resolution is given by the following inequalities:
0.5λ/ NA d < λ/NA
If lenses were to be made from materials with higher
refractive indices, then we could use immersion media
with higher refractive indices, and, consequently, we could
reduce the limit of resolution of the light microscope.
Lenses with a refractive index of 1.515 were chosen because
the early microscopists were restricted to using polychromatic sunlight to get bright enough images at high magnification (especially for making photomicrographs). This
required the development of achromatic or apochromatic
lenses made out of crown (n 1.5) and flint (n 1.6)
glass, which in combination, reduced the chromatic aberration; but had the unintended consequence of limiting the
resolving power of the microscope. However, now that
high-intensity, solid state, monochromatic light sources
are available, we could increase the resolving power of
the light microscope by using monochromatic light with
aspherical lenses made of high refractive index glass or
easy-to-mold high refractive index plastic. If we made
lenses out of plastics (Roukes, 1974) or other polymers that
have refractive indices of 2.5, the limit of resolution could
be as low as 80 nm. This is made even more feasible by the
development of solid state imaging chips that respond to
very low light levels (see Chapter 13).
Lord Rayleigh and Hermann von Helmholtz (Wright,
1906) took another approach to understanding the limit
of resolution of a microscope. They considered that each
point of an object acted as an independent point source of
light, much like the stars in the night sky. According to this
view, each point source of light sends out spherical waves
that illuminate the lens. Since the lens is an aperture, the
image of each point of light would actually be a diffraction
pattern of the lens (diameter 2r). Given that the apertures
of lenses are wide compared to the point sources in question, the diffraction fringes would be close to the image
that would have been made if the wavelength of light were
zero. However, even when the fringes are close, they still
exist, and consequently, each object point is inflated at
the image plane and surrounded by concentric fringes.
That is, they form a diffraction pattern that looks like an
Airy disc.
Rayleigh then considered how an image of two nearby
self-luminous dots would appear. Rayleigh assumed that
the light emanating from the two points were incoherent and thus did not interfere on the image plane (Figure
3-44). There may be some coherence between points that
are so close to each other, however.
The fact that a single point of light produces an Airy
disc when the light passes through the aperture of a lens
is significant when we want to localize objects such as
proteins or quantum dots that are below the limit of resolution of the light microscope. As a result of diffraction,
any point of light will be enlarged in the image plane. For
example, a 10 nm object will be inflated to about 218 nm
by an objective lens with a numerical aperture of 1.4. An
object smaller than the limit of resolution is delocalized as
63
1
0
α
Grating
(a)
Specimen
(b)
2)
1,
1
(0,
0
)
1,0
,–
2
(
1
(1,0,1)
Chapter | 3 The Dependence of Image Formation on the Nature of Light
Specimen
(c)
FIGURE 3-43 Illuminating a specimen with oblique illumination (b) effectively doubles the angular aperture of the objective lens compared with
axial illumination (a). Illuminating a specimen with a solid cone of light (c), as is done when using Köhler illumination, produces a composite image
composed of a mixture of high- and low-resolution images.
FIGURE 3-44 Two Airy discs that are clearly resolved in the image
plane (left) and two Airy discs that overlap in the image plane (right).
a result of diffraction and takes up more area in the image
plane than it should.
As the distance between the two self-luminous objects
decreases, the Airy discs overlap more and more, until
we are unable to distinguish whether we are looking at
one object or two. Lord Rayleigh suggested a criterion,
which can be used to determine whether or not we have
the ability to tell whether we are looking at one object or
two when their Airy discs overlap. Rayleigh suggested that
there is sufficient contrast to distinguish two points in the
image plane if, in intensity scans, the central maximum of
one point lies over the first minimum of the other (Figure
3-45). Under this condition, the intensity of the valley
between the two points is approximately 80 percent of the
intensities of the peaks. Since the first minimum occurs a
distance of 1.22λ away from the peak intensity, the limit of
resolution is given by the following formula:
d 1.220 (2 NA)
When using 400 nm light and a lens with an NA of 1.4,
the limit of resolution is 174 nm.The resolving power given
by Rayleigh’s criterion is less than that given by the Abbe
criterion because Rayleigh assumed that contrast must also
be considered when you consider resolution. Rayleigh
proscribed that there must be a 20 percent dip in intensity
between two points in order to resolve them. Thus, whereas
Abbe considered image formation to be diffraction limited,
Rayleigh considered image formation to be diffraction- and
contrast-limited.
C. Sparrow has shown that as long as the two peaks in
the image plane are separated enough to produce a minute
dip in intensity between the two points, the two points can be
resolved using analog and/or digital contrast-enhancement
techniques (see Chapters 13 and 14).
CONTRAST
In the absence of contrast, resolution is meaningless. If
there is not enough contrast to distinguish two points, it
does not matter how widely they are separated. Contrast
is defined as the difference in intensity between the image
point (Ii) and the background points (Ib). The percent contrast is given by the following formula:
% contrast (I b I i ) / I b 100%.
Absorption contrast is generated when the object or
the background differentially absorbs the incident light.
In terms of wave theory, absorption results in a reduction
in the amplitude of the waves. In absorption contrast, part
of the energy of the illuminating wave is absorbed by the
specimen and thus removed from the zeroth- and higherorder diffracted waves. When these waves reunite in the
image plane, the image is darker than the surround. Since
absorption often varies with wavelength, the specimen may
decrease the amplitude of a limited range of wavelengths
giving color contrast either naturally or through staining
64
Light and Video Microscopy
Clearly resolved
Rayleigh limit
Not resolved
FIGURE 3-45 According to Lord Rayleigh, two points that produce Airy discs can just be resolved in the image plane when the central maximum
of one point lies over the first minimum of the other. Under this condition, there is sufficient contrast to resolve the two points because the sum of the
point’s intensities midway between the peaks is about 80% of the intensity of each peak. When the points are too close, the Airy discs overlap so that
the intensity midway between the two points is equal to or greater than the intensity of the individual points.
Background
Specimen
Background point
0.95 I0
0.90I0
Specimen point
0.90 I0
Aperture (60%)
95% I0
B
I0
Aperture (60%)
0.60I0
Specimen
Background point
0.90I0
Specimen point
0.60 I0
Aperture (30%)
0.90I0
B
I0
FIGURE 3-46
0.90I0
I0
(a)
Background
S
Aperture (30%)
95% I0
0.60I0
(b)
S
0.90 I0
I0
Reducing the opening of the aperture diaphragm from 60° (a) to 30° (b) increases the scattering contrast of the image.
(Conn, 1933). Consequently, the image is a different color
than the surround. Since the absorption of visible light is
determined by the structure of the absorbing molecule,
absorption contrast provides information on the chemical
structure of the specimen. This can be quantified when
combined with microspectrophotometry.
Scattering contrast can arise from making use of the differential diffraction of light that occurs when objects with
different spatial angular wave numbers are illuminated.
An object with high spatial angular wave numbers diffracts
part of the incident intensity beyond the aperture of the
objective lens, and thus, its image appears darker than
the surround. Therefore contrast increases when the aperture of the objective lens decreases because fewer and
fewer diffraction orders are captured. The orders that are
not captured are not able to recombine to form the image.
Thus a transparent object would have no contrast if every
diffracted ray were captured by the objective lens.
Scattering contrast can be increased by decreasing the
effective NA of the objective. Increasing the contrast by
Chapter | 3 The Dependence of Image Formation on the Nature of Light
decreasing the NA directly decreases the resolution of the
light microscope. This is just one of the many tradeoffs
that occur in microscopy. Finding the best compromise
comes from experience.
In order to see how stopping down the aperture of the
objective lens increases the contrast (Figure 3-46), consider a point in a homogeneous background that transmits
100 percent of the intensity of the illuminating system (I).
Ninety and 95 percent of the light from this point is scattered within an angle of 30 and 60 degrees, respectively.
Consider a point in the specimen that absorbs 5 percent of
the light from the illuminating system and scatters 60 percent of the light within 30 degrees and 90 percent within 60
degrees. The percent contrast due to absorption would be 5
percent, according to the following formula:
percent contrast (1.00 I 0.95 I) / (1.00 I)
100% 5%
If we use a lens with a 60 degree aperture, then the
intensity of the surround is equal to 1.00I 0.95 0.95I,
the intensity of the specimen is equal to 0.95I 0.90 0.855I, and the percent contrast is 10 percent, according to
the following formula:
percent contrast (0.95I 0.855I) / 0.95I
100% 10%
When we close down the aperture, the resolving power
of the light microscope decreases and the limit of resolution becomes 282 nm according to the following formula:
limit of resolution 1.22(400 nm ) / (2 sin 60)
282 nm
If we reduce the aperture to a 30 degree angle, then
the intensity of the surround equals 1.00I 0.90 0.90I,
the intensity of the specimen 0.95I 0.60 0.57I, and
65
the percent contrast is about 37 percent, according to the
following formula:
percent contrast (0.90 I 0.57I) / 0.90 I
100% 36.67%
The limit of resolution, according to Rayleigh will
become 1.22(400 nm)/(2 sin 30°) 488 nm.
We have learned that the wave nature of light affects
our ability to resolve objects with the light microscope.
We have found that we can increase contrast and thus
detect transparent objects with the light microscope if we
decrease the aperture of the lens. However, as we increase
the contrast in this manner, pari passu, we decrease the
resolving power, and are not able to resolve the fine details
of the object. Resolution and contrast are complementary
properties.
●
Good resolution is meaningless in the absence of
contrast.
●
The conditions that tend to enhance contrast are
exactly those that tend to destroy resolving power.
One of the main goals of light microscopy is to increase
contrast while maintaining the diffracted-limited resolving
power of the light microscope. One of the advantages of
the light microscope over the electron microscope is that
living organisms can be observed in the light microscope.
Therefore it is our goal to increase contrast, while maintaining the diffraction-limited resolving power of the light
microscope in order to visualize living specimens and the
processes that occur within them.
WEB RESOURCE
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Chapter 4
Bright-Field Microscopy
Our naked eye is unable to resolve two objects that are separated by less than 70 μm. Perhaps we are fortunate that,
without a microscope, our eyes are unable to resolve small
distances. John Locke (1690) wrote in An Essay Concerning
Human Understanding,
We are able, by our senses, to know and distinguish things....
if that most instructive of our senses, seeing, were in any man a
thousand or a hundred thousand times more acute than it is by
the best microscope, things several millions of times less than the
smallest object of his sight now would then be visible to his
naked eyes, and so he would come nearer to the discovery of the
texture and motion of the minute parts of corporeal things; and in
many of them, probably get ideas of their internal constitutions:
but then he would be in a quite different world from other people: nothing would appear the same to him and others: the visible
ideas of everything would be different. So that I doubt, whether
he and the rest of men could discourse concerning the objects of
sight, or have any communication about colours, their appearances being so wholly different. And perhaps such a quickness
and tenderness of sight could not endure bright sunshine, or so
much as open daylight; nor take in but a very small part of any
object at once, and that too only at a very near distance. And if
by the help of such microscopical eyes (if I may so call them) a
man could penetrate further than ordinary into the secret composition and radical texture of bodies, he would not make any
great advantage by the change, if such an acute sight would not
serve to conduct him to the market and exchange; if he could not
see things he was to avoid, at a convenient distance; nor distinguish things he had to do with by those sensible qualities others
do. He that was sharp-sighted enough to see the configuration of
the minute particles of the spring of a clock, and observe upon
what peculiar structure and impulse its elastic motion depends,
would no doubt discover something very admirable: but if eyes
so framed could not view at once the hand, and the characters
of the hour-plate, and thereby at a distance see what o’clock it
was, their owner could not be much benefited by that acuteness;
which, whilst it discovered the secret contrivance of the parts of
the machine, made him lose its use.
Alexander Pope (1745) considered the same question in
An Essay on Man:
Why has not Man a microscopic eye?
For this plain reason, Man is not a Fly.
Say what the use, were finer optics given,
T’inspect a mite, not comprehend the heaven.
The eye is a converging lens that produces a minified
image of the object on the retina. The dimensions of the cells
that make up the light-sensitive retina limit the ability of
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
the human eye to resolve two dots that are closer than 70 μm
from each other. The retina contains approximately 120
million rods and 8 million cones packed into a single layer.
In the region of highest resolution, known as the fovea,
the cones are packed so tightly that they are only 2 μm apart.
Still, this distance between the cones limits the resolving
power of our eyes. If a point of light originating from one
object falls on only one cone, that object will appear as a
point. If light from two objects that are close together fall
on one cone, the two objects will appear as one. When
light from two points fall on two separate cones separated
by a third cone, the two points can be clearly resolved. The
resolving power of the eye can be increased slightly by eye
movements that vary the position of the cones.
The numerical value of the limit of resolution of the
human eye was first discovered by Robert Hooke in 1673.
Birch (1968) wrote:
Mr. Hooke made an experiment with a ruler divided into such
parts, as being placed at a certain distance from the eye, appeared
to subtend a minute of a degree; and being earnestly and curiously viewed by all the persons present, it appeared, that not any
one present, being placed at the assigned distance, was able to
distinguish those parts, which appeared of the bigness of a minute, but that they appeared confused. This experiment he produced, in order to shew, what we cannot by the naked eye make
any astronomical or other observations to a greater exactness
than that of a minute, by reason, that whatever object appears
under a lens angle, is not distinguishable by the naked eye; and
therefore he alleged, that whatever curiosity was used to make
the divisions of an instrument more nice, was of no use, unless
the eye were assisted by other helps from optic glasses.
In order for two points to appear as separate points,
light from those points must enter the eye forming an angle
greater than one minute of arc. Thus the object must be
brought very close to the eye. However, due to the limitation of our eye to focus at close distances, a specimen can
be brought up only to the near point of the eye, which is
about 25 cm from our eye (see Chapter 2, Figure 2-40).
A microscope makes it possible to increase the visual
angle, so that light, emanating from two near, but separate
points, can enter the eye, forming an angle that subtends
more than one minute of arc such that the light from the
two separate points fall on separate cones (Figure 4-1;
Gage, 1908). The eye of the observer plays an integral role
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Light and Video Microscopy
as the optical interface between the microscope and the
effigy of the specimen produced by the brain.
To make a very simple microscope, place an index card
that contains a minute pinhole, smaller than your pupil,
between your eye and an object closer than the near point
of your eye. Then look at an object that would be blurry at
this distance without the very simple pinhole microscope.
An object that was blurry at this close distance will appears
clear through the pinhole. Moreover, since it is close to your
eye, it also appears magnified, compared to how it would
look when it was placed at the distance where it would look
sharp without the pinhole. The pinhole acts as a microscope
by reducing the angle of the cone of light that comes from
each point in the object without decreasing the visual angle
of an object placed so close to your eye. Since, with the pinhole, the image on your retina is formed by cones of light
with smaller zones of confusion, objects closer than the near
point of your eye that would have formed blurry images on
the retina now form sharp images.
Thus, microscopes are necessary to create large visual
angles that allow us to resolve microscopic objects. We
need a microscope if we want to see a mite, or any other
microscopic aspect of the natural world. Indeed the microscope opened up a whole new world to seventeenth and
eighteenth century microscopists (Hooke, 1665, 1678, 1705;
Leeuwenhoek, 1673, 1798; Malpighi, 1675–1679, 1686;
B
A
A
A
f
B
B
FIGURE 4-1 A simple microscope placed in front of the eye increases
the visual angle, thus producing an enlarged image of a microscopic specimen on the retina. The specimen appears to be located at the near point
of the relaxed eye and magnified.
Grew, 1672, 1682; Swammerdam, 1758). Augustus de
Morgan (1872) wrote:
Great fleas have little fleas upon their backs to bite e’m,
And little fleas have lesser fleas, and so on ad infinitum.
According to Emily Dickinson (1924):
Faith is a fine invention
When gentlemen can see,
But microscopes are prudent
In an emergency.
The word microscope comes from the Greek words
μικρος (small) and σκοπιν (to see). The word microscope
was coined by Giovanni Faber on April 13, 1625. The brightfield microscope is, perhaps, one of the most elegant instruments ever invented, and the first microscopists used the
technologically advanced increase in the resolving power of
the human eye to reveal that the workmanship of the Creator
can be seen at the most minute dimensions (Hooke, 1665;
Grew, 1672, 1682; Leeuwenhoek, 1674–1716; Malpighi,
1675–1679; Swammerdam, 1758). The bright-field microscope also has been instrumental in revealing the cell as
the basic unit of life (Dutrochet, 1824; Schwann, 1847;
Schleiden, 1849), the structural basis for the transmission
of inherited characteristics (Strasburger, 1875; Flemming,
1880), and the microscopic basis of infectious diseases
(Pasteur, 1878, 1879; Koch, 1880; Dobell and O’Connor,
1921). Color plates 1 and 2 show examples of cork cells and
chromatin observed with bright-field microscopy.
The bright-field microscope also has had a tremendous
influence in physics and chemistry in that it made it possible for Robert Brown (1828, 1829) to discover the incessant
movement of living and nonliving particles, now known as
Brownian motion or Brownian movement (Deutsch, 1991;
Ford, 1991, 1992a, 1992b, 1992c; Rennie, 1991; Bown,
1992; Wheatley, 1992; Martin, 1993). In 1905, Albert
Einstein (1926) analyzed Brownian motion and concluded
that the movement occurred as a result of the statistical distribution of forces exerted by the water molecules surrounding
the particles. Jean Perrin (1909, 1923) confirmed Einstein’s
hypothesis by observing Brownian motion under the microscope and used his observations, along with Einstein’s
theory, to calculate Avogadro’s number, the number of molecules in a mole. Ernst Mach and Wilhelm Ostwald, who
were the last holdouts to accept the reality of atoms and
molecules, became convinced in the reality of molecules
from the work done on Brownian motion. These influential scientists were held back from accepting the evidence
of the existence of molecules from other kinds of physicochemical data because of their positivist philosophy, which
could be summed up by the phrase “seeing is believing.”
COMPONENTS OF THE MICROSCOPE
A simple bright-field microscope, like that used by
Leeuwenhoek (1674–1716), Jan Swammerdam, Robert
Brown, and Charles Darwin consists of only one lens, which
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Chapter | 4 Bright-Field Microscopy
forms a magnified, erect, virtual image of the specimen (Ford,
1983, 1985). By contrast, the compound microscope uses
two lens systems to form an image. The primary lens system
(object glass or objective lens) captures the light that is diffracted by the object and then forms a real intermediate image
that is further magnified by a second lens system, known as
the eyepiece or ocular.
There are currently two standard optical configurations.
Traditional objectives are designed to produce a real, magnified, inverted image 16 or 17 cm behind the objective
lens when the specimen is placed in front of the front focal
plane of the objective (Gage et al., 1891). Most microscope objectives manufactured today produce an image of
an object at infinity when the object is placed at the front
focal plane of the objective (Lambert and Sussman, 1965).
When infinity-corrected objectives are used, an intermediary lens, known as the tube lens, is placed behind the
objective lens. The tube lens focuses the parallel rays leaving the objective lens, and produces a real image at the
back focal plane of the tube lens. This arrangement, by
which parallel rays pass from the objective lens, minimizes
the introduction of additional aberrations introduced by
rays coming from every conceivable angle going through
extra optical pieces placed between the objective lens and
the ocular. Objectives that produce an intermediate image
160 mm or 170 mm behind the lens are marked with 160 or
170, respectively. Objectives that produce the intermediate
image at infinity are marked with .
Each objective lens is labeled with a wealth of information (Figure 4-2). The most prominent number signifies the
transverse magnification (mT) of the intermediate image.
Remember from Chapter 2, that
possible from spherical aberrations (Kepler, 1604; Descartes,
1637; Molyneux, 1692, 1709; Gregory, 1715, 1735; Smith,
1738; Martin, 1742, 1761, 1774; Adams, 1746, 1747,
1771, 1787, 1798; Baker, 1742, 1743, 1769; McCormick,
1987) and chromatic (Dollond, 1758; Amici, 1818; Lister,
1830; Beck, 1865; Abbe, 1887; Cheshire, 1905; Disney
et al., 1928; Clay and Court, 1932; von Rohr, 1936; Payne,
1954; Feffer, 1996)—aberrations that were once thought to
be absent in the human eye (Paley, 1803).
Due to dispersion, which is the wavelength-dependence
of the refractive index (see Chapter 2), a single lens will
not form a single image, but a multitude of images, each of
which is a different color and each of which is offset axially
and laterally from the others. For example, when we use an
aspheric objective that is not color-corrected, the microscopic
image will go from bluish to reddish as we focus through
the object. This chromatic aberration can be mitigated, but
not eliminated by using an achromatic doublet, which was
invented by Chester Moor Hall, John Dolland, and James
Ramsden. The achromatic doublet is made by cementing a
diverging lens made of high-dispersion flint glass to the converging lens made of low-dispersion crown glass. The flint
glass mostly cancels the dispersion due to the crown glass,
while only slightly increasing the focal length of the lens.
When we plot the focal length of an aspheric lens as a
function of wavelength, we get a monotonic plot, where
wavelengths in the blue range experience shorter focal
lengths, wavelengths in the red range experience longer focal
lengths, and wavelengths in the green range experience intermediate focal lengths (Figure 4-3). When we plot the focal
length of an achromatic lens as a function of wavelength, we
m T y i /y o si /so
Focus shift
Aspheric
The objective lenses often are surrounded by a thin band
whose color represents the magnification of the objective.
From the beginning, microscopists and inventors realized that microscopes do not magnify objects faithfully. In
fact the microscope itself introduces fictions or convolutions into the image that are not part of the object itself.
Over the years, lenses were developed that were as free as
Achromatic
0
0
400
500
600
700
400
Flat-field correction
Lateral magnification
Specialized
properties
Tube length
Cover glass
thickness range
Chromatic and spherical
aberration correction
Numerical aperture
Focus shift
Apochromatic
500
600
700
Superachromatic
0
0
Working distance
Magnification color
code
Correction collar
Cover glass
adjustment guage
FIGURE 4-2 Each objective is labeled with an abundance of useful
information.
400
500
600
Wavelength (nm)
700
400
500
600
Wavelength (nm)
700
FIGURE 4-3 Chromatic aberration means that the focal length of an
objective lens is wavelength dependent. There is a large variation in focal
lengths with wavelength in aspheric objectives, a smaller variation in achromatic objectives, an even smaller variation in apochromatic objectives,
and the smallest variation in superachromatic objectives.
70
get a parabolic plot, where the focal length for a wavelength
in the blue region (spectral line F) is similar to the focal
length for a wavelength in the red region (spectral line C).
Ernst Abbe developed an objective lens that introduced less chromatic aberration than the achromats and
coined the term apochromat, which means “without color,”
to characterize his lens design (Haselmann, 1986; Smith,
1987). He defined apochromats as lenses that had the same
focal length for three widely spaced wavelengths in the
visible range. Apochromats can be defined as objective
lenses whose differences in focal lengths do not exceed
λ/4 throughout the spectral range from 486.1 nm (spectral line F), through 546.1 nm (spectral line E) to 6563 nm
(spectral line C). However, this definition remains fluid
as microscope lens makers are striving to make “super”
apochromatic objective lenses that each have a single
wavelength-independent focal length all the way from the
ultraviolet to the infrared wavelengths.
More lens elements are required to effectively reduce
chromatic aberration and this increases the cost of the objective dramatically. Consequently, apochromats are the most
expensive lenses and achromats are the least expensive
objective lenses available in good microscopes. Microscope
makers make a variety of lenses that are more corrected
than achromats, but less corrected than apochromats. These
semi-apochromats and fluorites, which go by a variety of
manufacturer-specific names, are intermediate in cost.
A single lens also introduces spherical aberrations
because the rays that enter the peripheral region of the
lens experience a shorter focal length than do the paraxial
rays. Spherical aberration often is corrected at the same
time as chromatic aberration so that spherical aberration
in aspheric objective lenses is absent only for green wavelengths. Green light was chosen, not because it produces
diffraction-limited images with the highest resolution, but
because it is the color that people can see with the least
amount of eye strain. Spherical aberration is nearly absent
for all wavelengths for apochromatic objective lenses.
Again, the spherical aberration is intermediate in achromatic and semi-apochromatic objective lenses. Objectives
can be readily tested for chromatic and spherical aberration
by using a homemade Abbe-test plate (Sanderson, 1992).
The resolving power of the objective lens is characterized by its numerical aperture (NA; Chapter 3). The
numerical aperture of the lens describes the ability of the
lens to resolve two distinct points. The numerical apertures
of objectives typically vary from 0.04 to 1.40. Objectives
with NAs as high as 1.6 were made over a century ago
(Spitta, 1907), but were not popular as a result of their
requirement for special immersion oils and cover glasses.
However, objectives with NAs between 1.49 and 1.65,
which are used for Total Internal Reflection Fluorescence
Microscopy (TIRFM; Chapter12), are being reintroduced.
The NA of an objective is given by the small print number
that either follows or is printed under the magnification.
Light and Video Microscopy
The brightness of the image, in part, is proportional
to the square of the numerical aperture and inversely proportional to the square of the transverse magnification
(Naegeli and Schwendener, 1892; Beck, 1924).
Brightness (NA/m T )2
In order to produce a maximally bright image we may want
to use an objective lens with the highest possible NA and
the lowest possible magnification. However, the brightness
of the image does not only depend on the geometry of the
lens but also on the transparency of the optical glasses used
to construct the lenses (Hovestadt, 1902). In the past there
has been a tradeoff between the transparency of an objective lens and the number of corrections. For example, the
fluorites, which are composed of lens elements made of
calcium fluoride, were more transparent to the ultraviolet
light used for fluorescence microscopy than were the apochromats made with glass lens elements. Manufacturers are
striving to make highly corrected lenses that are transparent throughout the spectrum from ultraviolet to infrared.
Objective lenses must also be corrected so that the specimen is in sharp focus from the center to the edge of a flat
image plane. Objectives that are designed to produce flat
fields are labeled with F- or Plan-; for example, F-achromat
or Plan-Apochromat. The Plan-objectives are more highly
corrected for curvature of field than the F-objectives. It is
the nature of optics that it takes one lens element to produce
a magnified image of the object and many lens elements
to eliminate or perform a deconvolution on the aberrations
or convolutions introduced by the “imaging” lens element.
Following are some examples of the lens combinations used
to make highly corrected objective lenses (Figure 4-4).
Objectives are made with features that are useful for
doing specific types of microscopy. For example, some
objectives have an iris at the back focal plane, which can
reduce the NA of the objective. These objectives may have
the word Iris printed on them. This feature, which increases
contrast at the expense of resolution, is useful when doing
dark-field microscopy (see Chapter 6).
Some objectives are made out of completely homogeneous glass, known as strain-free glass. A lens made out
of strain-free glass does not depolarize linearly polarized
10x Achromat
10x Fluorite
10x Apochromat
FIGURE 4-4 Chromatic aberration is reduced by building an objective
lens with additional achromatic doublets and triplets.
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Chapter | 4 Bright-Field Microscopy
light that passes through the lens. These objectives may
have the word Pol printed on them. They are useful when
doing polarization microscopy (see Chapter 7).
The working distance of an objective lens is defined as the
distance between the front of the lens and the top of a cover
glass (Gage, 1917). Typically, the working distances, which
vary between 0.1 and 20 mm, are inversely proportional to
the magnifications and the numerical apertures of objective
lenses. However, some long working distance objectives are
made that also have high magnifications and numerical apertures. These objectives, which may be marked with an LD,
are especially useful for doing micromanipulation.
When doing micromanipulation, sometimes it is helpful to immerse the lens directly in the dilute aqueous
solution that bathes the specimen. Water immersion objectives, which are marked with a W, are good for this use.
Objectives also are made that can be used in solutions with
higher refractive indices, like glycerol. Glycerol immersion objectives are marked with a Glyc. Lastly, immersion
oils are used to increase the resolving power of the microscope. Objective lenses that are made to be used with oil
are marked with the word Oil. Some objective lenses can
be immersed in media with refractive indices from 1.333
to 1.515. Depending on the manufacturer, these objectives
are marked with Imm or W/Glyc/Oil.
Objectives are designed so that the cover glass acts as
the first lens in objectives that are corrected for spherical aberration. Most objectives used in transmitted light
microscopy are marked with 0.17, which means it is corrected for use with a 0.17 mm (#1½) cover glass. Some
objectives are made for use without cover slips and are
marked with 0. Objectives, which are insensitive to cover
glass thickness, are marked with -. Some objectives can
be used with a variety of cover glasses. These objectives
have a correction collar and may be marked with korr.
The cover glass introduces an increase in the optical path length of the diffracted rays that pass through it
(Figure 4-5). The magnitude of the increase depends on
the angle or order of the diffracted rays. The more oblique
the rays are; the greater the increase in optical path length.
The thicker the cover glass, the greater the difference
between rays emanating at different angles from the same
point. The highly diffracted rays appear to come from a
nearer object than the rays that are diffracted from a smaller
angle. Consequently, the different diffraction order rays will
be focused at different distances from the image plane. This
results in a zone of confusion instead of a single point, and
contributes to spherical aberration. The manufacturers of the
objective lenses design the objectives to compensate for the
increase in the optical path induced by a given cover glass
thickness. The Abbe Test Plate can be used to determine the
effect of cover glass thickness on spherical aberration.
One of the characteristics of objective lenses is their
cost; and unfortunately cost will probably play the biggest
part in your choice of objectives. As I discussed in the last
chapter, resolution and contrast are often competing qualities. However, as I will discuss in Chapter 14, we can use
analog or digital image processing to enhance the contrast
in electronically captured images. Thus, in our constant
tug of war between contrast and resolution, we can opt for
an objective that will provide the highest resolution and/or
the greatest brightness at the expense of contrast and then
enhance the contrast of the high resolution image using
image processing techniques.
A real image of the specimen formed by the objective
lens falls on the field diaphragm between the front focal
plane of the ocular and the eye lens of the ocular itself.
The ocular-eye combination forms a real image of the
intermediate image on the retina, which appears as a magnified virtual image 25 cm in front of our eyes. Since the
intermediate image is inverted with respect to the specimen, the virtual image also is inverted with respect to the
specimen. Oculars typically add a magnification of 5x to
25x to that produced by the objective. Moreover, a turret
that contains a series of low magnification lenses can be
inserted into the microscope just under the oculars. These
ancillary magnification lenses increases the magnification
of the virtual image by one or two times. Most oculars
used in binocular microscopes can be moved laterally to
adjust for your interpupillary distance. One or both oculars
will have a diopter adjustment ring, which can be turned to
compensate for difference in magnification between your
two eyes. When the interpupillary distance and the diopter
adjustment are set correctly, it is actually relaxing to sit in
front of a microscope all day.
When correcting aberrations in microscopes, designers take into consideration the objectives, tube lens, and
oculars. Depending of the objective lens, special matching
1
2
3
1
2
3
Cover glass
Object
Slide
FIGURE 4-5 The cover glass introduces spherical aberration. The
higher-order diffracted rays are refracted more than the lower-order diffracted rays, resulting in the point being imaged as a zone of confusion.
This occurs because the lower order-diffracted rays appear to come from
a position close to the object and the higher order-diffracted rays, when
they are traced back through the cover glass, seem to come from a position between the real object position and the objective lens. The greater
the cover glass thickness, the greater the amount of spherical aberration
that will be introduced by the cover glass. A correction for the spherical
aberration introduced by an objective lens also corrects the spherical aberration introduced by a cover glass of a certain thickness (e.g., 0.17 mm).
Objectives with correction collars can correct for the spherical aberration
introduced by a range of cover glass thicknesses.
72
Light and Video Microscopy
oculars may have to be used with it in order to obtain the
best image. There are several common types of oculars in
use, and they fall into two categories: negative and positive
(Figure 4-6). The Huygenian eyepiece, which was designed
by Huygens for a telescope ocular, is composed of two
plano-convex lenses. The upper lens is called the eye lens
and the lower lens is called the field lens. The convex sides
of both lenses face the specimen. Approximately midway
between the two lenses there is a fixed circular aperture
that defines the field of view and holds an ocular micrometer. This is where the intermediate image formed by the
objective lens is found. Since the object focus is behind
the field lens, the Huygenian eyepiece is an example of a
negative ocular. Huygenian oculars are found on relatively
routine microscopes with achromatic objectives.
The Ramsden eyepiece is an example of a positive ocular, whose object focal plane is in front of the field lens.
The Ramsden eyepiece consists of two plano-convex lenses
where the convex side of both lenses face the inside of the
eyepiece. The circular aperture that defines the field of view
and holds the ocular micrometer is below the field lens.
Compensating eyepieces, which can be either negative or
positive, contain a number of lens elements. Compensating
oculars are important for correcting the residual chromatic
aberration inherent in the design of some objective lenses
from the same manufacturer. As digital imaging techniques
develop (see Chapters 13 and 14), fewer and fewer people
are looking at microscopic images through the oculars and
more and more people are looking at the images displayed
on a monitor. Consequently, optical corrections to mitigate
aberrations are no longer included in the oculars. The corrections are completed in the objective lenses or the objective lens-tube lens combination.
A
B
FIGURE 4-6 A negative ocular (A) has the field diaphragm between
the eye lens and field lens. A positive ocular (B) has the field diaphragm
in front of the field lens.
Oculars may be labeled with a field of view number,
which represents the diameter (in millimeters) of the field
that is visible in the microscope when using those oculars.
The diameter of the field can be obtained by dividing the
field of view number by the magnification of the objective lens and any other lenses between the objective and
the ocular. This is helpful in estimating the actual size of
objects. The field of view numbers vary from 6.3 to 26.5.
The fields of view in a microscope equipped with an ocular
with a field of view number of 20, and 10x, 20x, 40x, and
100x objectives is 2, 1, 0.5, and 0.2 mm, respectively.
The total transverse magnification of the compound
microscope is given by the product of the magnification
of the objective lens (obj), the ocular (oc), and any other
intermediate pieces (int), including the optivar.
m total (m obj )(m int )(m oc )
In microscopy, there is a limit to the amount of magnification that is useful, and beyond which, the image quality
does not improve. This is reached when two points in the
image appear to send out rays that subtend one minute of
arc, which is the resolution of the human eye.
What is the maximum useful magnification of a light
microscope? Let us assume that the final image is formed
25 cm from the eye and the smallest detail visible in the
specimen is given by the following equation: d 1.22
λ/(2NA), and d 0.161 μm. Since the eye can just resolve
two points, 70 μm apart, the magnification necessary for
the eye to resolve two points (i.e., useful magnification) is
70 μm/0.161 μm 435x. It is uncomfortable to work at the
limit of resolution of the eye, so we typically use a magnification two to four times greater than the calculated useful
magnification, or up to 1740x. Higher magnifications can
result in a decrease in image quality since imperfections of
the optical system and vibration become more prominent at
high magnifications. As a rule of thumb, the optimal magnification is between 500 (NA) and 1000 (NA). However,
when working with good lenses and stable microscopes, it
is possible to increase the magnification to 10,000x (Aist,
1995; Aist and Morris, 1999).
The specimen is illuminated by the sub-stage condenser
(Wenham, 1850, 1854, 1856). There are a variety of substage condensers that have different degrees of corrections
(Figure 4-7). The Abbe condenser, which originally was
designed to provide an abundance of axial rays, is neither
Abbe
A
Aplanatic
B
Achromatic
C
FIGURE 4-7 Lens elements in sub-stage condensers. An Abbe chromatic sub-stage condenser (A), an aplanatic sub-stage condenser (B), and
an achromatic sub-stage condenser (C).
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Chapter | 4 Bright-Field Microscopy
achromatic nor aplanatic (Martin, 1993). Other condensers
designed to use oblique rays as well as axial rays are corrected for spherical aberration and/or chromatic aberration.
The aplanatic condenser is corrected for spherical aberration and the achromatic condenser is corrected for both
spherical and chromatic aberration.
A sub-stage condenser may contain a rotating ring with
annuli, prisms, or slits at its front focal plane that allows
us to do many forms of light microscopy, including darkfield and phase-contrast (see Chapter 6), differential interference contrast (see Chapter 9), and amplitude modulation
contrast (see Chapter 10). Some condensers are made with
long working distances, which are convenient to use when
performing micromanipulations on inverted microscopes.
The objectives, oculars, and sub-stage condenser usually
are supported by either an upright or inverted microscope
stand. The typical microscope, which is on an upright stand,
is ergonomically designed for most uses. However, inverted
microscopes make manual manipulations, including microinjection, microsurgery, and electrophysiological measurements much easier. The microscope stand often is overlooked
as an important part of the microscope. It provides stability
for photomicrography or video microscopy and flexibility to convert the stand for various types of optical microscopy. In the long run, it is worth getting the most stable,
flexible, and, consequently, most expensive microscope
stand. The stand contains the coarse and fine focus knobs
that raise or lower the nosepiece that holds the objectives.
The stage is where the specimen is placed. Inexpensive
glide stages let you position the specimen by sliding the stage
plate over a greased plate placed below it. In order to exactly
position a specimen, you need a stage that has controls to
translate the specimen in the XY direction. Such a stage may
be motorized and controlled by computers. Rotating stages
are useful for polarized light microscopy (see Chapter 7)
and other forms of microscopy that utilize polarized light or
depend on the direction of shear (see Chapters 9 and 10).
Originally the specimen in a bright-field microscope
was illuminated by sunlight and a heliostat, which rotated
with the speed of the rotation of the earth so that the sunlight would remain stationary with respect to the microscope. Alcohol, kerosene, and gas lamps were used on bleak
days or after the sun set at night. Eventually electric lights
became standard (Beale, 1880; Bracegirdle, 1993). Currently
a bright-field microscope is equipped with one or more electric light sources to illuminate the specimen (Davidson,
1990). The light source is usually a quartz halogen bulb,
although mercury vapor lamps, xenon lamps, lasers, and
light-emitting diodes may also be used in special cases.
The light source usually is placed between a parabolic
mirror and a collector lens. The light source is placed at the
center of curvature of the parabolic mirror so that the rays
that go backward are focused back on the bulb. The collector
lens is used to project an image of the filament onto the
front focal plane of the condenser (Köhler illumination) or
onto the specimen itself (critical or confocal illumination).
The diameter of the field illuminated by the light source
is controlled by the field diaphragm, and the number and
angle of the illuminating rays is controlled by the aperture
diaphragm.
THE OPTICAL PATHS OF THE LIGHT
MICROSCOPE
I will briefly discuss two types of microscope illumination:
Köhler and critical. In practice, Köhler illumination is used
in most microscopes, and a specialized form of critical
illumination is used in confocal microscopes. Köhler illumination provides a uniformly illuminated, bright field
of view, which is important when using an uneven light
source, like a coiled tungsten filament. At the end of the
nineteenth century, microscopists used sunlight or oil lamps
to illuminate their specimens, and very slow film to photograph them. The exposures needed to expose the film were
as long as five hours. Thus August Köhler (1893) was motivated to find a way to obtain the brightest image possible so
that he could continue his work investigating the taxonomic
position of the mollusk, Syphonaria, by taking good photomicrographs of the taxonomically important gills.
Köhler devised a method in which an image of the
source is formed by a converging lens, known as the collector lens, at the front focal plane of the sub-stage condenser, while an image of the field diaphragm is formed in
the plane of the specimen by the sub-stage condenser. The
sub-stage condenser produces collimated light beams, each
of which originates from a point on the source. Each point
on the source forms a collimated beam of light that illuminates the entire field of view. The points on the center of
the source form a collimated beam that is parallel to the
optical axis. The points farther and farther away from the
optical axis make collimated beams that strike the object
at greater and greater angles. Thus, the specimen is illuminated with a cone of light composed of both parallel and
oblique illumination (Evennett, 1993; Gundlach, 1993;
Haselmann, 1993).
In critical illumination, an image of the light source is
focused in the plane of the specimen. The illumination is
intense, but it is uneven unless a ribbon filament is used.
Critical illumination does not require a sub-stage condenser.
In critical illumination, each point in the object acts as a
point source of light. If the light radiating from two nearby
points is truly incoherent, it will form two overlapping
images of Airy discs, the intensity of which will be the sum
of the two intensities. Since light from two nearby points
will be somewhat coherent and will interfere, the intensity
of each point will not be exactly the sum of the two intensities, but will, in part, be described by the square of the sum
of the amplitudes of the light radiating from both points.
When the microscope is set up for Köhler illumination,
the following optical conditions result. The collector lens
focuses an image of the light source onto the front focal
74
plane of the sub-stage condenser where the aperture diaphragm resides. The sub-stage condenser turns each point
of light at its front focal plane into a beam of light whose
angle is proportional to the lateral distance of the point from
the principle axis. These beams of light are focused on the
rear focal plane of the objective by the objective lens itself.
The relative positions of the points of light on the back focal
plane of the objective are identical to the relative positions
they had when they originated at the front focal plane of the
sub-stage condenser. The ocular makes a real image of this
light disc at the eye point, also known as the exit pupil or
Ramsden disc of the ocular. The eye point is where we place
the front focal point of our eye. In Köhler illumination, light
originating from each and every point of the light source
illuminates our entire retina.
At the same time as the illuminating rays illuminate our
retina, the sub-stage condenser lens focuses an image of the
field diaphragm on the plane of the specimen. The objective
lens forms an intermediate image on the field diaphragm of
the ocular. Together, the ocular and the eye form an image of
the specimen on the retina. In Köhler illumination, the light
that falls on any point on the retina originated from every
point of the filament.
Köhler illumination gives rise to two sets of optical paths
and two sets of conjugate image planes—the illuminating
rays, which are equivalent to the zeroth-order diffracted
light, and the image-forming rays, which are equivalent to
the sum of the first-order and higher-order diffracted light
(Figure 4-8). When the microscope is adjusted for Köhler
illumination, we get the following advantages:
1. The field is homogeneously bright even if the source
is inhomogeneous (e.g. a coiled filament).
2. The working NA of the sub-stage condenser and the
size of the illuminated field can be controlled independently.
Thus, glare and the size of the field can be reduced without
affecting resolution.
3. The specimen is illuminated, in part, by a converging set of plane wave fronts, each arising from separate
points of the light source imaged at the front focal plane
of the condenser. This gives rise to good lateral and axial
resolution. Good axial resolution allows us to “optically
section.”
4. The front focal plane of the sub-stage condenser is
conjugate with the back focal plane of the objective lens, a
condition needed for optimal contrast enhancement.
To achieve Köhler illumination, the light source is placed
a distance equal to twice the focal length of the parabolic
mirror so that the rays that travel “backward” are focused
back onto the filament (Figure 4-9). The collector lens produces a magnified, inverted, real image of the light source
onto the front focal plane of the sub-stage condenser where
the aperture diaphragm resides. That is, any given point of
the filament is focused to a point at the aperture diaphragm.
Light and Video Microscopy
Light emanating from a point in the plane of the aperture
diaphragm emerges from the sub-stage condenser as a plane
wave (Figure 4-10). All together, the points in the front focal
plane of the sub-stage condenser give rise to a converging
set of plane waves. The angle of each member of the set of
plane waves is related to the distance of the point to the center of the aperture. In order to produce radially symmetrical
cones of light from the sub-stage condenser, the filament in
the bulb should also be radially symmetrical.
The plane waves emerging from the sub-stage condenser
traverse the specimen and enter the objective lens. The
objective lens converts the plane waves to spherical waves,
which converge on the back focal plane of the objective lens.
Thus each point at the back focal plane of the objective lens
is conjugate with a corresponding point in the plane of the
sub-stage condenser aperture diaphragm as well as a point
on the filament. The sub-stage condenser and the objective
together form a real inverted image of the filament at the
back focal plane of the objective (Figure 4-11).
The back focal plane of the objective lens and the front
focal plane of the sub-stage condenser can be visualized
by inserting a Bertrand lens between the oculars and the
objective, or by replacing an ocular with a centering telescope. The ocular forms a real minified image of the uniformly illuminated back focal plane of the objective lens at
the eye point. The eye point is located just beyond the back
focal point of the ocular, and it is where the front focal
point of the eye is placed. The object (i.e., the filament
in this case) and the image (of the filament) lie in conjugate planes. In Köhler illumination, the light source, the
aperture diaphragm, the back focal plane of the objective
lens, and the eye point of the ocular lie in conjugate planes
called the aperture planes. In each of these planes, the light
that does not interact with the specimen, that is the zerothorder light, is focused.
Now I will trace the path of the waves that interact with
the specimen. These are called the image-forming waves
and they represent the superposition of all diffracted waves.
When the microscope is set up for Köhler illumination, the
condenser lens forms a minified, inverted real image of
the field diaphragm on the specimen plane. Each point
on the field diaphragm is illuminated by every point of
the filament (Figure 4-12). The specimen is then focused
by the objective lens, which produces a magnified,
inverted image of the specimen and the field diaphragm in
the optical tube, past the back focal plane of the objective.
This plane is just behind the front focal plane of the ocular
(Figure 4-13).
The lenses of the ocular and the eye together form an
image on the retina as if the eye were seeing the virtual
image of the specimen (Figure 4-14). These four conjugate
planes are called the field planes. With Köhler illumination
there are two sets of conjugate planes, the aperture planes
and the field planes (Figure 4-8). The two sets of conjugate
planes are reciprocally related to each other.
75
Chapter | 4 Bright-Field Microscopy
Retina
Eye
Eyepoint
foc
Eyepiece
fob
Objective
Specimen
Sub-stage condenser
f
Aperture
diaphragm
Field diaphragm
Collector
lens
fs
Filament
FIGURE 4-8 Paths of the illuminating rays (A) and the image forming rays (B) in a microscope set up with Köhler illumination. The conjugate aperture
planes are shown in (A) and the conjugate field planes are shown in (B).
f
FIGURE 4-9 The lamp is placed at the center of curvature of a concave
mirror to capture the backward-going light. The collecting lenses focus an
image of the filament onto the aperture plane at the front focal plane of
the sub-stage condenser.
To find illuminating rays between the light source and
the specimen plane (Figure 4-15):
1. Draw two or three characteristic rays from each
of three points on the filament. Find the image plane. For
Köhler illumination, we move the filament and collector
lens so that the image plane is on the aperture diaphragm.
2. Draw two to three characteristic rays from each of
three points on the image of the filament on the aperture
diaphragm. Since the aperture diaphragm is at the front
focal plane of the sub-stage condenser, all rays from a single
point come through the condenser as parallel pencils of
light. Draw each pencil till it reaches the objective lens.
To find image-forming rays between the light source and
the specimen plane:
3. Draw two or three characteristic rays from two or
three points on the field diaphragm to the image plane,
where the specimen is placed. For Köhler illumination, the
sub-stage condenser is adjusted so that the image plane is
identical to the specimen plane on the stage.
76
Light and Video Microscopy
f
f
Sub-stage
condenser
Sub-stage
condenser
FIGURE 4-10 Light emanating from all the points in the plane of the aperture diaphragm give rise to a converging set of plane waves. The angle
of each plane wave relative to the optical axis of the microscope is a function of the distance of the point giving rise to the plane wave from the
optical axis.
Objective
Sub-stage
condenser
Front
focal plane
of sub-stage
condenser
Back focal
plane of
objective
FIGURE 4-11 Together, the sub-stage condenser and the objective lenses produce an image of the filament at the back focal plane of the objective.
f
f
Specimen
on stage
Field
diaphragm
Sub-stage
condenser
FIGURE 4-12 The sub-stage condenser focuses an image of the field diaphragm onto the focused specimen. Each and every point of the filament contributes to illuminating each and every point on the field diaphragm and the specimen.
As the aperture diaphragm is closed, points 1 and 3 and
bundles 1 and 3 are eliminated. Thus, the angle of illumination and the NA of the condenser are decreased. As the
field diaphragm is closed, the size of the viewable field is
decreased.
USING THE BRIGHT-FIELD MICROSCOPE
When using a microscope, it is as important to prepare
your mind and eyes as it is to prepare the specimen and
the microscope (Brewster, 1837; Schleiden, 1849; Schacht,
1853; Gage, 1941). Chapters 1 through 3 set the foundation for preparing your mind. In order to prepare your eyes,
make sure that you are comfortable sitting at the microscope. Adjust your seat to a comfortable height. Adjust
the interpupillary distance of the oculars for your eyes.
Set the diopter adjustment to correct for any optical differences between your two eyes. Make sure that the
room is dark, and your eyes are relaxed. Focusing with a
relaxed eye will prevent eyestrain and prolong your eyes’
ability to accommodate.
Place the specimen on the stage, and focus the specimen with the coarse and fine focus knobs using a low
magnification objective. Then close down the field diaphragm, and adjust the height of the sub-stage condenser
until the leaves of the diaphragm are sharply focused in
the specimen plane. Center the sub-stage condenser if the
77
Chapter | 4 Bright-Field Microscopy
field diaphragm is not in the center of the field. Open the
field diaphragm so that the light just fills the field. This
will minimize glare, which is light that is out of place,
just as dirt is matter that is out of place. Then adjust the
aperture diaphragm to give optimal contrast and resolution. The cone of light that enters the objective typically
is controlled by the aperture diaphragm. Determine which
Intermediate image plane
Tube lens
Range
with infinite
image distance
Ports to
insert various
accessories
position gives optimal resolution and contrast. Repeat the
process with higher magnification objectives. There is no
need to raise the objectives before rotating them into the
optical path, since all the objectives are parfocal and will
give a nearly in-focus image at the position the lower magnification lens gave a focused image. Many excellent books
describe the theory and practice of the microscope (Martin,
1966; Slayter, 1970; Zieler, 1972; Rochow and Rochow,
1978; Kallenbach, 1986; Spencer, 1982; Richardson, 1991;
Oldfield, 1994; Murphy, 2001).
Abbe (1889, 1906, 1921), a physical (and social) experimentalist and theorist, recommended using small cones of
light because “the resulting image produced by means of a
broad illuminating beam is always a mixture of a multitude
of partial images which are more or less different and dissimilar from the object itself.” Moreover, Abbe did not see
any reason for believing “that the mixture should come
nearer to a strictly correct projection of the object ... by
a narrow axial illuminating pencil” since the image of an
object actually is formed by double diffraction. The image
of an object illuminated with a cone of light will be formed
from many different diffraction patterns, and the image
will be “a mixture of a multitude of partial images.”
On the other hand, many leading microscopists, including E. M. Nelson and the bacteriologist, Robert Koch,
suggested that using a broad cone of light instead of axial
illumination gives a more faithful image without ghosts.
Here is what Nelson (1891) had to say:
The sub-stage condenser is nearly as old as the compound
Microscope itself. The first microscopical objects were opaque,
and in very early times a lens was employed to condense light
upon them. It was an easy step to place the lens below the stage
when transparent objects were examined.
Objective lens
On the Continent, where science held a much more important
place, the real value of the Microscope was better understood,
and it at once took an important place in the medical schools.
But the increase of light due to the more perfect concentration
of rays by achromatism enabled objects to be sufficiently illuminated by the concave mirror to meet their purposes. Therefore,
we find that on the Continent the Microscope had no condenser.
Object plane
FIGURE 4-13 The objective lens produces an intermediate image of the
specimen and the field diaphragm at the field plane of the ocular. If the
objective is marked with a 160 or 170, the field plane is 160 or 170 mm
behind the objective. If the objective is marked with an , the objective
lens produces an intermediate image at infinity and a tube lens is inserted
so that the intermediate image is produced at the field plane of the ocular.
England followed the Continental lead, and now the “foolish
philosophical toy” has entirely displaced in our medical schools
the dog-Latin text-book with its ordo verborum. But the kind of
f
f
FIGURE 4-14 The intermediate image is formed between the focal plane and the eye lens of a Ramsden ocular. Together, the eye lens and the eye
produce a real image of the specimen, any reticle in the ocular and the field diaphragms on the retina. Without the eye lens, the visual angle of the intermediate image would be tiny. With the eye lens, the visual angle is large and we imagine that we see the specimen enlarged 25 cm from our eye.
78
Aperture diaphragm
Field diaphragm
Light and Video Microscopy
1
3
2
2
3
f0
fi
1
2
1
f0
Collector
lens
3
fi
of condenser
Sub-stage
condenser
Specimen
plane
Objective
FIGURE 4-15 Adjusting the field diaphragm changes the size of the field and adjusting the aperture diaphragm changes the angle of illumination.
Microscope adopted was not that of the English dilettanti, but the
condenserless Continental. It may be said that the Microscope
for forty years—that is, from the time it was established in the
schools in, say, 1810 to 1880, has been without a condenser.
This paper I consider to be the most dangerous paper ever published, and unless a warning is sounded it will inevitably lead
to erroneous manipulation, which is inseparably connected with
erroneous interpretation of structure.
In 1880 a change came from two separate causes—first, the rise
of bacteriology; secondly, the introduction of a cheap chromatic
condenser by Abbe in 1873.
If you intend to carry out his views and use narrow-angled cones,
you do not need a condenser at all—more than this, a condenser
is absolutely injurious, because it affords you the possibility of
using a large cone, which, according to Prof. Abbe, yields an
image dissimilar to the object. If there is the slightest foundation
for Prof. Abbe’s conclusion, then a condenser is to be avoided,
and when a mirror is used with low powers care must be exercised to cut the cone well down by the diaphragm.
Taken by itself, the introduction of the Abbe condenser had not
much effect, but as Zeiss’s Microscopes had for some time been
displacing the older forms, and when the study of bacteriology
arose, oil-immersion objectives of greater aperture than the old
dry objectives (especially those of the histological series) were
used, illumination by the mirror was soon discovered to be inefficient, so a condenser became a necessity. The cheap Abbe condenser was the exact thing to meet the case.
The real office of the sub-stage condenser being a cone-producer,
the first question that arises is, What ought to be the angle of the
cone?
This is really the most important question that can be raised
with regard to microscopical manipulation. To this I reply that a
3/4 cone is the perfection of illumination for the Microscope of
the present day. By this I mean that the cone from the condenser
should be of such a size as to fill 3/4 of the back of the objective
with light, thus N.A. 1.0 is a suitable illuminating cone for an
objective of 1.4 N.A. (dark grounds are not at present under consideration). This opinion is in direct opposition to that of Prof.
Abbe in his last paper on the subject in the December number of
the R.M.S. Journal for 1889, where he says:‘The resulting image
produced by means of a broad illuminating beam is always a mixture of a multitude of partial images which are more or less different (and dissimilar to the object itself). There is not the least
rational ground—nor any experimental proof—for the expectation
that this mixture should come nearer to a strictly correct project to
the object (be less dissimilar to the latter) than that image which is
projected by means of a narrow axial illuminating pencil.’
Let me at the place state that I wish it to be distinctly understood
that I am not, in this paper, attacking Prof. Abbe’s brilliant discovery that the image in the Microscope is caused by the reunion of
rays which have been scattered by diffraction, neither do I question what I venture to think is his far more brilliant experiment,
which exhibits the duplication of structure, when the spectra of the
second order are admitted, while those of the first are stopped out.
I regard these facts as fundamental truths of microscopy.
What is a microscopist to do when the experts disagree? Trust experience. According to Spitta (1907):
The situation then is exceedingly difficult to deal with; for, when
the result of direct experiment, conducted with all the refinement
and skill of a master hand like that of Mr. Nelson, coupled with
a full scientific appreciation of the situation, seems to point absolutely and directly in the opposite direction to the teaching of a
mathematical expert and philosopher such as the late Professor
Abbe, undoubtedly was, one who has never been surpassed, if ever
equaled, in acuteness of thought coupled with resourcefulness of
investigation in all matters concerning the microscope—we repeat,
when these opinions are positively at variance, the onlooker is
compelled, from shear inability, to wait and consider. We are
bound to confess, however, after several years of attention to this
difficult and far-reaching problem, the weight of evidence in our
79
Chapter | 4 Bright-Field Microscopy
opinion, taken for what it is worth, certainly rests in favor of Mr.
Nelson’s view, and we venture to suggest that, perhaps, the data
upon which the learned Professor built his theoretical considerations may not have included a sufficient “weight” to the teachings
of actual experiment; and hence that, although the theory deduced
was undoubtedly correct, the data from which it was made were
insufficiently extensive. For example, bacteriologists seem mostly
agreed that the Bacillus tuberculosis is probably not an organism
likely to have a capsule under ordinary conditions, and yet with
a narrow cone, whether the specimen be stained or unstained, a
very pronounced encircling capsule, as bright and clear as possible
to the eye, appears in every case; yet, as the cone is steadily and
slowly increased, so does this mysterious capsule disappear! ...
The question then arises, how far can we reduce the aperture of the
sub-stage diaphragm without the risk of introducing false images?
To this we reply that, speaking in general, it must not be curtailed
to a greater extent than a cutting off of the outer third of the back
lens of any objective as seen by looking down the tube of the
instrument, the ocular having been removed.
Objective lens
x
θ
y
Object plane
Y
d
FIGURE 4-16
Depth of field.
Given the two definitions of x,
x y tan θ λ ( 4NA).
After solving for y we get:
DEPTH OF FIELD
y λ /((4 NA)(tan θ))
Geometrical optics tells us that there is an image plane
where the specimen is in focus. Physical optics tells us that
even if we used aberration-free lenses, each point in the
object plane is inflated by diffraction to a spheroid at the
image plane, and consequently, the resolution that can be
obtained at the image plane is limited. Putting these two
ideas together, we see that there is a distance in front of
and behind the image plane where we will not be able to
resolve whether or not the image is in focus. The linear
dimension of this region is known as the depth of focus.
The depth of field is a measure of how far away from either
side of the object plane an object will be in focus at the true
image plane. Thus, the numerical aperture will affect both
the depth of focus and the depth of field (Slayter, 1970).
The depth of field (or axial resolution) is defined as the
distance between the nearest and farthest object planes in
which the objects are in acceptable focus (Delly, 1988).
Here we derive the relationship between depth of field and
the numerical aperture (NA) using Abbe’s criterion and
simple trigonometry (Staves et al., 1995). According to
Abbe’s criterion, the minimum distance (d) between two
points in which those two points can be resolved is:
d λ/(2 NA)
We make the assumption that d is the zone of confusion
surrounding a point and represents the size of an object that
will be in acceptable focus at the nearest and farthest object
plane. The depth of field (Y) is the distance between the
plane of nearest and farthest acceptable focus (Figure 4-16).
Let x d/2 and y Y/2. Using the Abbe criterion for
resolution, an object that has a linear dimension of d will
appear as a point as long as 2x λ/(2NA). The largest that
x can be is x λ/(4NA). Given the definition of tangent
(tan θ x/y),
x y tan θ
Since depth of field (Y) is equal to 2y,
Y λ /((2 NA)(tan θ))
Remember that tan θ (sin θ)/(cos θ). Multiply the right
side of the equation by one (n/n):
tan θ (n sin θ)/(n cos θ)
Since NA (n sin θ), then
tan θ NA/(n cos θ)
Remember that cos2θ sin2θ 1, and cos2 θ (1sin2 θ).
Thus,
cos θ √ (1 sin 2 θ)
After substitution, we get
tan θ NA/[n √ (1 sin 2 θ)]
Since n n2,
tan θ NA/[ √ (n 2 (1 sin 2 θ))]
Distribute the n2 on the right side to get
tan θ NA/[ √ (n 2 n 2 sin 2 θ)]
Simplify, since n2sin2θ (n sin θ)2 NA2:
tan θ NA/[ √(n 2 NA 2 )]
Substitute into Y λ/((2NA)(tan θ)):
Y λ[ √(n 2 NA 2 )]/[(2 NA)(NA)]
Simplify:
Y λ[ √ (n 2 NA 2 )]/(2 NA 2 )
80
Light and Video Microscopy
This equation relates the depth of field to the numerical
aperture of the objective lens. This equation is based on
the validity of the Abbe criterion, the assumption that the
“zone of confusion” is equal to d, and the use of illumination where the full NA of the lens is utilized. This equation
states that the depth of field is proportional to the wavelength of light and decreases as the numerical aperture of
the objective lens increases. Thus for a narrow depth of
field, as is prerequisite for the observation of a localized
plane, we need an objective lens with a fairly high numerical
aperture.
When θ approaches 90 degrees and NA approaches n,
the objective lens tends to form an image at a single plane.
This is known as optical sectioning. The higher the NA of
the objective, the smaller the depth of field and the more we
are able to optically section. As the NA increases, the contrast and depth of field decrease, which makes it more difficult to see the specimen. When you first observe a specimen,
it is good to close down the aperture diaphragm and get the
maximal contrast and depth of field. As you get to know a
specimen, you should aim for the greatest axial and transverse resolution.
As we will discuss later in the book, the depth of field
can be decreased using illumination methods, such as twophoton confocal microscopy (see Chapter 12), and image
processing methods (see Chapter 14).
OUT-OF-FOCUS CONTRAST
I have been discussing the observation of specimens that
show amplitude contrast or sufficient scattering-contrast.
However, highly transparent objects would be almost invisible in a perfectly focused, aberration-free microscope that
captures most of the diffracted rays. However, the brightfield microscope can detect pure phase objects when you
defocus the specimen (Figure 4-17). The contrast arises
because waves that originate from nearby points in the
specimen are partially coherent and can interfere before
and behind the image plane. The degree of interference and
the intensity of the light at these other planes depend on the
relative phase and amplitude of the interfering waves. Since
the relative amplitude and phase of these waves depend on
the nature of the points from which they originate, they
contain some information about the object. So slightly
defocusing allows us to see a pure phase object in a brightfield microscope. In the next chapter, I will discuss ways of
viewing perfectly focused images of phase objects.
USES OF BRIGHT-FIELD
MICROSCOPY
The bright field microscope can be used to characterize
chemicals (Chamot, 1921; Schaeffer, 1953), minerals (Smith,
1956; Adams et al., 1984), natural and artificial fibers in textiles (Schwarz, 1934), food (Winton, 1916; Vaughan, 1979;
Flint, 1994), microorganisms (Dobell, 1960), and cells and
tissues in higher organisms (Lee, 1921; Chamberlain, 1924;
Kingsbury and Johannsen, 1927; Conn, 1933; McClung,
1937; Johansen, 1940; Jensen, 1962; Berlyn and Miksche,
1976; Harris, 1999). It has been used in the study of The
Shroud of Turin, and in the identification of art forgeries
(McCrone, 1990; Weaver, 2003).
Bright-field microscopy has long been used to furnish strong evidence in criminal trials (Robinson, 1935).
Typically hair and fibers are identified with a light microscope to see, for example, if the hair of the accused is at the
crime scene or if the hair of the victim or a fiber from the
victim’s house carpet can be found on the accused (Smith
and Glaister, 1931; Rowe and Starrs, 2001). Moreover, since
plants have indigestible cell walls, the food that an autopsied homicide victim last ate can readily be identified (Bock
et al., 1988). Light microscopes are becoming useful in the
United States’ counterterrorism program (Laughlin, 2003).
s2
Image plane
Out-of-focus image plane
s1
Objective
s2
s1
FIGURE 4-17 Out-of-focus contrast in an invisible object. The waves
coming from the closely spaced points s1 and s2 in a transparent image
interfere below the image plane to provide enough contrast to make the
nearly-faithful, out-of-focus image visible.
CARE AND CLEANING OF THE LIGHT
MICROSCOPE
First of all, try to keep the microscope and the area around
it clean, but let’s face it, we live in a world of dirt and dust.
When dirt and dust do fall on the microscope, localize the
surface that contains the dirt or dust by rotating or raising
or lowering the various components of the microscope and
looking through the microscope. The surface that has the
dirt on it is the one, which when moved, causes the dirt
to move. Remove what dust you can with a dust blower.
The dirt can be removed by breathing on the lens, or wetting the lens surface with distilled water of a lens cleaning solution used for cleaning camera lenses. Then gently
wipe the lens using a spiral motion moving from the center
Chapter | 4 Bright-Field Microscopy
of the lens toward the edge with “no-glue” cotton-tipped
cleaning sticks or lint-free lens paper. Immersion oil can be
removed the same way. Be careful if you use organic solvents to clean the objectives because the cement that holds
a given lens together may dissolve in that solvent. Each
microscope manufacturer has its own recommendations on
which solvents to use. You can easily check how clean the
front surface of the objective lens is by inspecting them by
looking through the wrong end of the ocular.
WEB RESOURCES
Molecular Expressions. Exploring the world of optics and microscopy:
http://micro.magnet.fsu.edu/
81
Nikon U: http://www.microscopyu.com/
Olympus Microscopy Resource Center: http://www.olympusmicro.com/
Carl Zeiss Microimaging: http://www.zeiss.com/micro
Leica Microsystems: http://www.leica-microsystems.com/
The Moody Medical Library’s Collection of Microscopes can be viewed
online at: http://ar.utmb.edu/areas/informresources/collections/blocker/
microscopes.asp
Microscopy UK: http://www.microscopy-uk.org.uk/index.html
McCrone Research Institute: www.mcri.org
Southwest Environmental Health Sciences Center Microscopy & Imaging
Resources on the web: http://swehsc.pharmacy.arizona.edu/exppath/
micro/index.html
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Chapter 5
Photomicrography
Photomicrography is the technique of taking pictures
through the microscope. It is almost as old as photography
itself. Some of the first photomicrographs were taken in
1839 by J. B. Reade, and by William Henry Fox Talbot,
the inventor of the positive-negative photographic process
(Arnold, 1977). Prior to the invention of photography, all
images viewed with the microscope could be captured for
posterity only with the aid of an artist’s pencil or pen. The
camera lucida, a drawing aid that was invented by William
Wollaston in 1808, was not applied to the microscope until
1880, more than 40 years after a photographic camera was
first used.
The goal of photomicrography is to form a complete and
faithful point-by-point reproduction of an object on paper.
(I will discuss digital images more fully in Chapters 13
and 14). Two things should be kept in mind when taking
a photomicrograph. First and foremost, a photomicrograph
is a research record that documents, through illustration,
a particular phenomenon or structure. Second, photomicrographs are also art, and should look beautiful. Remember,
though, that although it is important to make each picture
as beautiful as possible, the most important aspect of the
photomicrograph is the scientific content, and the artistic
approach should enhance and not replace or distract from
the scientific content. Photographic techniques are used
for quantifying light intensities as well as for the qualitative application of recording an image. However, when
recording an image for qualitative purposes, the quantitative aspects of photomicrography should be kept in mind
to optimize the image quality because the image intensities should be related to the intensities of each point of the
object.
I would like to emphasize that a photomicrograph
can be only as good as the image produced by the microscope. So when taking photographs of a microscopic
object, make sure that there is no dust on the microscope or slide, shut off the room lights, focus accurately,
use Köhler illumination, close the field diaphragm to the
appropriate size to prevent glare, and make the best possible choice (compromise) for the diameter of the aperture
diaphragm.
Light and Video Microscopy
Copyright © 2009 by Academic Press Inc. All rights of reproduction in any form reserved.
SETTING UP THE MICROSCOPE FOR
PHOTOMICROGRAPHY
When we look through the oculars of a microscope we see
a virtual image approximately 25 cm from our eyes. The
oculars produce a virtual image because the intermediate image formed by the objective falls between the focal
plane of the ocular and the eye lens of the ocular itself. The
virtual image cannot be captured on film; consequently,
when doing photomicrography, we must change the optical
setup that we use for viewing the image with our eyes, and
we must project a real image on the film (Figure 5-1).
A clever person can turn an ocular into a photographic
eyepiece that creates a real image beyond the back focal
plane of the lens by pulling out the ocular a little from
its normal position and fixing it in its new position with
tape. In this position, the intermediate image formed by
the objective lens falls in front of the front focal plane of
the ocular. This leads to the formation of a real image.
This is how a solar microscope works. A solar microscope is a microscope that projects an image of a specimen illuminated by sunlight (or an artificial light source)
onto a screen so that many people can view the image
(McCormick, 1987). Photo eyepieces, with magnifications from about 2x to 6x, are constructed with the correct
Virtual
image
Intemediate
image
Eye
Real image
on
retina
Specimen
Objective
Eyepiece
Specimen
Objective
Real image
on
Photo
film plane
eyepiece
FIGURE 5-1 Using a photo eyepiece to produce a real image on the
film (or imaging tube or chip) plane.
83
84
geometry to project a real image onto film or the imaging
chip of a digital camera.
We can estimate the total magnification of the image
on the negative by multiplying the magnification of the
objective lens by the magnification of the projection lens
and any other tube length factor. The magnification of the
printed image is given by multiplying the magnification
of the image on the negative by the magnification used to
print the picture. It is more accurate and convenient to photograph a stage micrometer on the microscope stage using
the same objectives used to observe the specimens of interest, and then print the negatives of the stage micrometer
using the same magnification used to make the prints. We
must also take a picture of a stage micrometer when using
a digital camera and ensure that we are using the same
optical and digital zoom values for photomicrography
and calibration. The optical zoom increases the amount
of detail that can be captured in the photograph, whereas
the digital zoom only enlarges the details obtained using the
optical zoom.
I discussed depth of field in Chapter 4, but for photomicrography, depth of focus is also important. The depth of
field is the total axial distance from the object plane where
we see the object in focus at the image plane. The depth of
focus is the total axial distance from the image plane where
we can place film or an imaging chip and still capture the
image in focus. In the light microscope, the depth of focus,
which is in the micrometer range, is approximately equal to
the depth of field (Slayter, 1970).
A microscope that has been focused correctly for visual
observation is not necessarily in focus for photographic
recording. Always focus the camera! You will always get
in-focus pictures if you focus the camera with a relaxed
eye. I imagine I am in a peaceful field or lying on a beach
in order to relax my eyes before I focus the camera. When
we look at an image visually, our eyes should be completely
relaxed; yet, when we focus up and down, we may squint or
strain our eyes, and our eyes may accommodate to put outof-focus objects in focus. Squinting reduces the numerical
aperture of our eyes and thus increases the depth of focus.
The ability of our eyes to accommodate is disadvantageous
for photomicrography because an object may appear in
focus to our accommodated eyes, but is out-of-focus on the
film, because the film does not have the ability to accommodate. Digital cameras, on the other hand, have the ability to
accommodate when used in auto focus mode.
When using a film camera, we must focus the camera
telescope so that the virtual image we see is parfocal with the
film plane. Always focus the reticule of the camera by moving the diopter adjustment toward you. Never focus out, then
in, then out, and so on, because your eye will accommodate.
Move the diopter adjustment toward you, when you pass the
in-focus point, screw it back in, look toward infinity, and
try again. Repeat until you can end by stopping at perfect
focus. At the risk of being repetitive, relax your eyes!
Light and Video Microscopy
For black-and-white photography, an achromatic objective lens used with a green interference filter is perfect.
However, instead of using a green filter, which takes advantage of the achromat’s correction for spherical aberration,
you may want to use a complementary-colored filter to
increase the contrast of a low-contrast colored object. In this
case, it would be better to use a fluorite or apochromatic
objective lens. Using orange filters instead of green filters
will increase contrast of regions that are stained blue, while
reducing resolution. Using a blue filter instead of a green
filter may increase resolution and contrast in yellow/orange
specimens, but the spherical aberration will reduce the
image quality when using a blue filter with an achromatic
lens. Everything is a compromise. Microscopy, like politics,
is the art of compromise. When doing black-and-white photography, the type of lamp used is not important as long as
it is bright enough. The brightness of the lamp can be varied
by adjusting the voltage.
When doing color photography, it is best to use an apochromatic objective lens. The lamp is important when doing
color photography. The color temperature of an illuminator
is determined by comparing the spectrum of colors it radiates to the spectrum of colors that come from a black body
heated to a given temperature (see Chapter 11). To achieve
the correct color balance in the photograph, the color temperature of the film must match the color temperature of the
illuminator. The color temperature of the film is a measure
of the film’s sensitivity to each color. The voltage of the
lamp determines its temperature and its temperature determines the spectrum of the emitted light. Since changing the
voltage changes the color temperature of the lamp, the voltage of the lamp should remain constant when you do color
photography. The intensity can be reduced by inserting neutral density filters into the light path. These filters have an
unvarying cross-section for visible light and thus uniformly
decrease the intensity all across the visible spectrum.
Daylight film is the most versatile for photomicrography, but using daylight film requires using a lamp that
has the same color temperature as the sun (5500–6000 K).
This color temperature is obtained with xenon arc lamps
(5500 K). However, the most typical lamps found in light
microscopes are tungsten-halogen lamps. These have
color temperatures of only 2800 to 3400 K. Type A films
are made for tungsten-halogen lamps, which have a color
temperature of 3400 K, and type B film is made for tungsten lamps, which have a color temperature of 3200 K. The
voltage necessary to maintain a given color temperature
increases as a bulb ages. The color temperature of a given
bulb can be converted to the color temperature of a given
film by using filters that alter the spectrum of the illuminating light (Delly, 1988).
In a digital camera, the white balance controls let you
adjust the color temperature so that the color temperature
of the digital camera is matched with the color temperature
of the illuminating light. Digital cameras have settings that
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Chapter | 5 Photomicrography
include automatic, daylight, and incandescent, which may
be good matches to the color temperature of the microscope’s illuminating system. Minor adjustments can also be
made to the daylight and incandescent settings to slightly
blue-shift or red-shift the color temperature of the digital
camera. If you cannot balance the color temperature correctly, you can always input a preset white balance to the
camera by allowing the illuminating light to pass through a
clear portion of the slide.
Vibration is a concern to the photomicroscopist.
Vibration can come from several sources, including the
camera, humans, and building construction. Many microscopes were made especially for photomicrography. These
microscopes had a heavy base and the camera either was
built into the microscope or mounted lower than the center of gravity to minimize vibration problems. Mounting a
camera above the microscope is inherently unstable, unless
the camera is not very heavy. To minimize problems with
vibration, a heavy camera can be supported mechanically.
It is possible to take pictures on a microscope with
your own 35 mm camera on the microscope. However, if
the camera has a focal plane shutter, it will vibrate during
the exposure and thus blur the image. When using cameras with focal plane shutters, it is necessary to decrease
the light intensity and increase the exposure time to “burn
in” a good image while the shutter is open. Cameras with
shutters that are composed of leaves can be used successfully for photomicrography since the vibration is equal in
all directions and thus cancels out. Due to the lightness of
digital cameras and their lack of mechanical shutters, they
do not suffer from vibration problems.
Buildings may cause a lot of vibration. You can help
solve this vibration problem by using a commercially available vibration-free table, or by putting the microscope on a
heavy table with a lot of mass. An excellent vibration-free
table can be made inexpensively by making a table with cinder block legs, and covering the cinder blocks with a layer
of lab bench. Then put some bicycle inner tubes pumped up
to a few pounds of pressure on top of that lab bench. Then
mount a second lab bench over the inner tubes. I have used
a bench like this. It is excellent and inexpensive if the raw
materials are available to you. Some people prefer tennis
balls to the inner tubes. If vibration still remains a problem,
you must use the fastest exposures possible.
Vibration has plagued photomicroscopists from the beginning. Following is an excerpt from Robert Koch’s (1880)
book, Investigations into the Etiology of Traumatic Infective
Diseases, which describes his problems with vibration:
With respects to the illustrations accompanying this work I must
here make a remark. In a former paper on the examination and
photographing of bacteria I expressed the wish that observers
would photograph pathogenic bacteria, in order that their representations of them might be as true to nature as possible. I thus
felt bound to photograph the bacteria discovered in the animal
tissues in traumatic infective diseases, and I have not spared trouble in the attempt. The smallest, and, in fact, the most interesting
bacteria, however, can only be made visible in animal tissues by
staining them, and by thus gaining the advantage of colour. But
in this case the photographer has to deal with the same difficulties as are experienced by photographing coloured objects, e.g.,
coloured tapestry. These have, as in well known, been overcome
by the use of coloured collodion. This led me to use the same
method for photographing stained bacteria, and I have, in fact,
succeeded, by the use of eosin-collodion, and by shutting off
portions of the spectrum by coloured glasses, in obtaining photographs of bacteria which had been stained with blue and red
aniline dyes. Nevertheless, from the long exposure required and
the unavoidable vibrations of the apparatus, the picture does not
have sharpness of outline sufficient to enable it to be of used as a
substitute for a drawing, or indeed even as evidence of what one
sees. For the present therefore, I must abstain from publishing
photographic representations; but I hope at a subsequent period,
which improved methods allow a shorter exposure, to be able to
remedy this defect.
SCIENTIFIC HISTORY OF PHOTOGRAPHY
The fact that light coming through a small hole in a cave,
tent, room, or even the leaves on a tree casts an inverted
image on the opposite wall has been known since antiquity
(Aristotle, Problems XV:11 in Barnes, 1984). In medieval
times, a chamber with a pinhole was used to view eclipses
of the sun (Eder, 1945). The camera obscura, which literally means dark chamber, was later exploited by the
Renaissance artists as a drawing aid (da Vinci, 1970). The
camera obscura was made by putting a small pinhole on
one side of a darkened room. Light emanating from an
object or scene outside the pinhole formed an inverted
image of the illuminated objects outside the hole. An
image of the object was captured by tracing the image on a
piece of paper, which was attached to the wall opposite the
pinhole. Girolamo Cardano suggested in his book De subtilitate, written in 1550, that a biconvex lens placed in front
of the aperture would increase the brightness of the image
(Gernsheim, 1982). Daniel Barbaro (1568) suggested putting an aperture in front of the lens so that only the part of
the lens with the least aberrations would be used.
The camera obscura was popularized by Giambattista
della Porta in his book, Natural Magic (1589), and by
the seventeenth century, portable versions of the camera
obscura were fabricated and/or used by Johann Kepler for
drawing the land he was surveying and observing the sun,
and by Johann Zahn, Athanasius Kircher, and others in order
to facilitate drawing scenes far away from the studio. By the
eighteenth century, the insides of these cameras were painted
black and a mirror was installed at a 45-degree angle so that
the image could be viewed on a translucent screen right side
up. An artist would aim the camera lens at the object and
manually trace the image on a thin piece of paper, which was
placed over the translucent glass.
The optical properties of camera obscura lenses were
improved by William Hyde Wollaston, George B. Airy, and
Joseph Petzval in the beginning of the nineteenth century
86
(Eder, 1945). The development of aberration-free lenses
with large apertures allowed shorter exposure times due
to the greater amount of light that was captured by these
“fast” lenses. However, before the invention of a photographic plate, the ability to capture the elusive image of a
picturesque scene on paper required the drawing skills of
an artist. Automatic capture of the image had to wait for
the invention of light-sensitive plates and film (Newhall,
1937, 1949).
Discoveries that led to the invention of light-sensitive
plates proceeded independently of the development of the
camera obscura (Vogel, 1889). The ability of light to change
the color or hue of matter has been known since ancient
times. The most obvious example is that sunlight causes
skin to tan. It also causes fabric to bleach. Aristotle knew
that light caused plants to turn green, and the yellowish
secretion of snails (Murex) to turn purple. The purple dye
became the famous purple of Tyre (Eder, 1945). It was only
a matter of time before this process could be developed to a
stage where images formed by the camera obscura could be
permanently captured.
In 1727, Johann Heinrich Schulze discovered that silver
salts were sensitive to light. He came across this discovery accidentally while trying to produce a phosphorescent
stone. He found that sunlight caused a mixture of chalk,
silver, and nitric acid to change from whitish to deep purple
due to the reduction of silver ions to metallic silver. After
discovering the scotophore (carrier of darkness) instead of
a phosphor (carrier of light), Schulze wrote that “often we
discover by accident what we could scarcely have found
by intention or design” (in Eder, 1945). Schulze concluded
that the sun’s light and not its heat was the effective agent
since the heat of a fire had no such effect. In a later experiment, Schulze covered one side of the bottle with a stencil
cut out of opaque paper, and found that when he exposed
the stencil side to sunlight and then carefully removed the
stencil, a temporary image was formed by the mixture.
Karl Wilhelm Scheele (1780) separated sunlight into
its component colors with a prism and found that blue rays
were more effective than red rays in reducing the silver
salts (by taking up phlogiston). This work was repeated by
Jean Senebier in 1782. By 1801, Johann Wilhelm Ritter
(1968), stimulated by Sir William Herschel’s (1800a,
1800b) discovery of invisible heat rays beyond the red
end of the spectrum, found invisible rays beyond the blue
end of the spectrum by showing that the invisible rays of
the spectrum were very effective in reducing silver salts.
Thomas Young (1803) used paper impregnated with silver
and his diffraction apparatus to measure the wavelength of
the invisible UV light.
In an attempt to capture images formed in the camera
obscura, Thomas Wedgwood worked with Humphry Davy
to make photosensitive plates. They made these photosensitive plates by soaking paper or white leather in solutions
Light and Video Microscopy
of silver nitrate and letting them dry. They found that the
images formed by the camera obscura were too faint to
cause the silver nitrate to turn black. They did find, however, that these photosensitive plates were sensitive enough
to capture images produced with a solar microscope, and
suggested that this will “probably be a useful application
of the method.” Unfortunately, the paper was not very sensitive and thus it had to “be placed at but a small distance
from the lens” (Wedgwood and Davy, 1802). They did
find that their technique could be used to transfer images
of paintings made on glass to the photosensitive paper
or leather. But, since the areas through which the light
passed caused the photosensitive plate to turn black, while
the regions of the object through which no light passed
remained white, the images were dark-light reversed.
Unfortunately, the images were not permanent and had to
be viewed by candlelight or else the whole image would
eventually turn black.
Joseph Nicéphore Niépce was finally able to capture an
image from the camera obscura on silver chloride-treated
paper in 1816 using a technique he named heliography.
However, these images could not be fixed either. By 1822
Niépce could capture a permanent image with the camera
obscura by coating glass plates with bitumen of Judea, a
form of asphalt dissolved in Dipple’s oil. Dipple’s oil is a
complex substance obtained by distilling animal tissues,
especially bones. Exposure of the plates to light in the camera obscura caused the bitumen of Judea to become insoluble in lavender oil. The areas not exposed to light remained
soluble. Thus a reversed image appeared when the plate
was washed with lavender oil. These plates captured permanent images, although they were not very light-sensitive
and required several-hour-long exposures (Newhall, 1937,
1949; Mack and Martin, 1939; Eder, 1945; Arnold, 1977).
In 1829, Niépce joined forces with Louis Jacques
Mandé Daguerre in order to develop more sensitive plates.
Daguerre accidentally had found that a silver spoon left
lying on an iodized silver plate left an image of itself on
the plate. Following this discovery, Daguerre coated copper plates with highly polished silver and then exposed the
plates to iodine vapor, which resulted in the formation of
silver iodide. Daguerre discovered that he could form a
latent image on these plates after only a few-minute exposure in the camera obscura. The latent image was formed
by the light-induced formation of silver metal. A permanent image could be formed from the latent image by a
development process that he could perform in the dark.
Daguerre’s development process consisted of treating the
exposed plates to the vapors of heated mercury.
Daguerre accidentally found that mercury vapor could
develop the latent images when he put undeveloped plates
into a cupboard and found that when he took them out
they had developed an image. They developed an image
because some mercury had accidentally spilled in the
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Chapter | 5 Photomicrography
cupboard giving off mercury vapor (James, 1952). The
mercury vapor formed a whitish amalgam with the metallic
silver. The unused silver iodide was washed away, and the
resulting image appeared as a positive if the Daguerreotype
was held such that the underlying silver did not reflect any
light into the viewer’s eyes. At the correct viewing angle,
the white portion of the image traveled to the eye as a
result of diffuse reflection, and the black (silver) portion of
the image missed the eye due to specular reflection. The
Daguerreotype process went through many improvements
and was of great scientific and commercial value; unfortunately it allowed the formation of only one image.
This disadvantage was overcome by Fox Talbot (1839b,
1839c, 1844–1846). Talbot exposed a piece of silver halidecoated paper in the camera obscura to the light emanating
from the object to form a negative image. After development, this piece of paper, which would be waxed or oiled to
make it transparent, would be placed between the sunlight
and an unexposed piece of silver halide-coated paper. In this
way, a positive image would appear on the second piece of
paper. This process could be repeated indefinitely to produce
multiple copies of a single image. Talbot used the negativepositive process to capture images of landscapes, architecture, people, sculpture, and art taken with a camera obscura.
While developing this technique for use with a solar
microscope, Talbot (1839b) developed paper that was
very sensitive to light, and exposures as short as one-half
second could be used. His technique involved first soaking the paper in a weak solution of common salt, wiping
it dry, and then spreading a dilute solution of silver nitrate
on one side of the paper. Upon drying, the paper was ready
to use (Talbot, 1839c). He achieved a very light-sensitive
paper when he included a potassium bromide rinse in the
photographic paper-making process. In 1839, J. B. Reade
(1854) surmised that silver-impregnated leather was more
sensitive to light than silver-impregnated paper because of
the chemicals used to tan the leather. Thus he applied an
extract from galls (i.e., gallic acid), a solution used to tan
leather, to paper to increase its sensitivity to light.
Taking steps to decrease the time needed to record
the image, Talbot found that he could reduce the time by
100-fold if he exposed dry plates to light and subsequently
developed them in gallic acid and silver nitrate. In 1851
Justus Liebig and Henri Victor Regnault independently
found that pyrogallic acid was a faster developer than gallic acid, and by 1861 J. Mudd introduced pyrogallol as a
developer. Major C. Russell introduced an alkaline form of
this developer, which worked best with the very light-sensitive silver bromide.
The photographs made with the negative-positive process developed by Talbot could not be made permanent
until a fixative was invented that would prevent the unexposed silver halide grains from turning black. Washes with
NaCl worked partially; however in 1819, John Herschel
discovered that silver halide could be effectively solublized by hyposulfite of soda (sodium thiosulfate). In 1839,
he started using sodium thiosulfate, which is known as
fixer, to remove the silver salts that had not reacted with the
starlight he was photographing (Herschel, 1840). Herschel
introduced many terms into photography, including positive, negative, fixed, and photograph (Sutton, 1858).
By 1839, cameras, film, paper, developers, and fixers
had reached a stage where photography could be used for
portraits, capturing scenery, and taking pictures of wars. In
1839, J. B. Reade captured the first permanent image of a
flea taken with a microscope (Wood, 1971a, 1971b), and
over the next few years, Alfred Donné, Léon Foucault,
Josef Berres, J. B. Dancer, and Richard Hogson captured
permanent images taken with the microscope (Eder, 1945).
Following the development of bright artificial light sources,
high numerical aperture sub-stage condensers, new methods of illumination, and faster films, photography also
could be used by all microscopists to capture microscopic
images. E. B. Wilson (1895), Starr (1896), and Slater and
Spitta (1898) presented some of the first photographically
documented biology books. Walker (1905) illustrated
mitosis in his textbook, with photomicrographs that could
be viewed as stereo pairs.
Removing and replacing a lens cap manually to expose
the film was no longer practical when high-speed films
that reduced the exposure time from minutes to less than a
second became available. Initially, mechanical leaf-shutters
were placed in front of the camera lens, but eventually they
became part of the lens system. In single lens reflex (SLR)
cameras, in which lenses could be interchanged freely, the
shutter was moved to the focal plane.
GENERAL NATURE OF THE
PHOTOGRAPHIC PROCESS
The photographic emulsion of the film consists of small
grains (about 0.05 μm in diameter) containing silver bromide crystals suspended in a gelatin matrix (James, 1952).
The emulsion usually is supported by a plastic film. The
silver bromide crystals are light sensitive. Upon exposure
to light, the silver bromide crystals are altered to form a
latent image. Chemical processing then turns the latent
image into a visible image.
The steps in the latent image formation are not completely known (Neblette, 1952). It is possible that light
causes the irreversible ejection of an electron from the
bromide ion. In this photoelectric process, radiant energy
is converted into the kinetic energy of the electron. The
electron is then trapped by AgS contaminants in the AgBr
crystal lattice. The electron then reduces the Ag to Ag0
(which is metallic silver). The precipitation of the free Ag0
produces the latent image.
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Light and Video Microscopy
(a)
(b)
(d)
(c)
(e)
FIGURE 5-2 Stages in the photographic process. The object (a), the unexposed film (b), the exposed film with a latent image (c), the developed film
(d), and the fixed film (e).
hν.
Step I:
AgBr → Ag Br 0 e (trapped by AgS)
Step II:
Ag e → Ag0
During the development process, the film is washed
in organic reducing agents related to hydroquinone
(Figure 5-2). The silver salts, which are near the metallic
silver that forms the latent image, are reduced by the developer. The quinones in the developer act as reducing agents
at alkaline pH. A stop bath, composed of acetic acid, is
used to terminate the development and to stop the cascading
reactions by acidifying the solution. Fixer is then used to
remove the unexposed, undeveloped silver salts while leaving the reduced silver on the film. The fixer is composed
of sodium or ammonium thiosulfite (S2O2). The fixing process is very complicated due to the many oxidation states of
thiosulfite. It is approximated by the following reaction:
AgBr Na(S2 O2 ) → Ag(S2 O2 ) NaBr
The film is then washed with water to eliminate the
fixer and unreduced silver. All the products are soluble in
water and are removed in the wash. The film subsequently
is dried and printed. To make color films, dyes are coupled
to the silver halide grains.
Photographic density is a quantitative measure of the
blackening of the photographic emulsion. Photographic
density (D) is defined by the following equation:
D log(I 0 /I)
where I0 is the incident intensity, and I is the intensity
transmitted through the film. The photographic density is
another term for absorbance. Therefore, according to the
Beer-Lambert Law, the photographic density is equal to
cd, where characterizes the ability of the silver grains
to interact with light and is known as the extinction coefficient or molar cross-section (in m2/mol), c is the concentration of silver grains (in mol/m3), and d is the thickness
of the film (in m) (Figure 5-3).
Films usually are characterized by a Hurter and
Driffield curve, which often is referred to as an H-D curve
or a characteristic curve. An H-D curve is a plot of the
photographic density of a film as a function of the log of
exposure. The exposure (E, in photons/m2) is equal to the
product of the incident light intensity (I, in photons m2
s1) and the time (t in s):
E It
This relationship, which shows the reciprocal relationship between intensity and time, is known as the BunsenRoscoe Law, and film should be tested only in the exposure
range where this reciprocity law holds (James, 1980).
When exposures are either extremely long or extremely
short, reciprocity does not hold and in both cases the influence of light is lower than expected. At low light levels or
very short times, the chance of a grain capturing light is so
low that doubling the time or light intensity has no effect
(this is one aspect of the quantum nature of light; a single photon can’t reduce thousands of silver grains, a little
bit each). At high light levels or long exposure times, the
chance of a grain capturing light is so high, that doubling
the time doesn’t expose any more grains: the system is
saturated.
89
Chapter | 5 Photomicrography
High contrast
emulsion
I
Optical density
Io
εcd
FIGURE 5-3 According to the Beer-Lambert Law, the photographic
density is equal to the product of the extinction coefficient, the concentration, and the thickness.
D
Optical density
C
A
B
Log exposure
FIGURE 5-4
Characteristic curve for film.
Therefore, we must consider the H-D curves as being
characteristic curves of the film in cases when reciprocity
holds. The characteristic curves of various films are available from the manufacturers. The speed and contrast of a
film for exposure by a given light source and upon development under a fixed set of conditions are specified by the
characteristic curve. Figure 5-4 shows the general form of
the H-D curve.
Some degree of blackening occurs at zero exposure; this
is known as the fog density of the film (A). The fog density
arises from the development of grains that have not interacted with light. The distance A-B is known as the toe of
the curve. The film is relatively insensitive to light in this
region—this is the region of underexposure. The optical
density increases linearly with the log of the exposure
between points B and C. This is the range where films
should be used. If all the portions of the object produce
an exposure within this range, then the photographic density level of each point in the image will be proportional to
the brightness of each conjugate point in the object. This
condition must be met when doing densitometry or when
comparing two images quantitatively. The quantitative
measurement of photographic density is known as densitometry and it is not uncommon to use a microdensitometer to quantitatively determine the amount of blackening
of a film.
The speed of the film is a measure of the size of the
toe of the curve. The higher the speed the smaller the toe,
the lower the speed, the more the toe extends to the right.
The speed is related to the size of the grains. For a given
Medium contrast
emulsion
Low contrast
emulsion
Log exposure
FIGURE 5-5 Characteristic curves for film with the same speed, but
different levels of contrast.
emulsion type, the larger the grain, the faster the film will be.
Larger grains produce more extensive blackening of the
image compared to smaller grains for the same number of
incident photons.
The film speed is given in ISO numbers. ISO stands for
the International Organization for Standardization, which
has superseded the American Standards Association (ASA),
the Deutsches Institut für Normung (DIN), and the GOST,
which was the system used by the former Soviet Union, all
of which had scales for film speed. Fast film is necessary
when photographing dim objects typically encountered
when doing fluorescence microscopy. Fast film is also necessary when the organism is moving or there is a vibration
problem. Because the film speed is proportional to the size
of the grains and the resolution of the film is inversely proportional to the size of the grains, the speed and resolution
are complementary properties of a film. There is always a
tradeoff, but the tradeoff can be minimized by studying the
characteristics of various films.
The contrast of the film is related to the slope of the
linear portion of the curve. The slope of the linear portion
of the characteristic curve also is known as the gamma of
the film. The steeper the curve, the larger is the difference
in photographic density for small differences in exposure
and thus the greater the contrast. Figure 5-5 shows the H-D
curves of three films that have the same speeds but different
contrasts.
Notice that higher contrast can be obtained only by
reducing the range of exposures in which the contrast is
produced. When we use high-contrast films, we must be
very careful in selecting exposures. The development process can also change the contrast of an emulsion. Figure 5-5
then can represent the characteristic curves of the same
film developed under different conditions. A high-contrast
film is usually important in microscopy since the microscope generally produces a low-contrast image. Image
contrast can also be increased by using a high-contrast
developer during processing. A gamma of 1.0 will give a
one-to-one correspondence between the brightness of the
object and the density of the image.
The characteristic curve of a digital camera can be varied using image adjustment controls. Digital cameras have
90
an ISO option, which varies the sensitivity of the camera
just as the ISO determined the sensitivity of the film.
Digital cameras also have contrast and brightness controls
that are useful for increasing the contrast of low-contrast
specimens.
George Eastman who, like Ernst Abbe (1906, 1921),
was also a practicing social philosopher, founded Kodak
and pioneered the development of film (Ackerman, 1930;
Brayer, 1996; Mattern, 2005). Film comes in many sizes,
although 35 mm (24 36 mm) is the most commonly used
for photomicrography since it is convenient, inexpensive,
and there are many kinds available. However, it is possible to obtain higher resolution in a final enlarged print by
using larger (e.g., 4 5 in., 5 7 in.) film formats.
Light and Video Microscopy
(a)
(b)
THE RESOLUTION OF THE FILM
Resolution ultimately is limited by the granularity of the
film. Since the smaller the grain size, the better the resolution, but the slower the film, we must make a trade off
between resolution and speed. The resolution of film is
given in lines per millimeter (lpm). It is determined by
photographing a high-contrast object (white bars on a
black background with a contrast of 1000:1). In film,
a “line” consists of one black and one white line, and
thus represents a pair of lines and is equivalent to a “line
pair” used to measure the resolution of electronic imaging devices. The limit of resolution of a film for a lowcontrast biological object will be about 40 to 60% of the
value given for a high-contrast object. Kodak technical
pan 2415 is a high resolution film (320 lpm) with excellent contrast. However, it is very slow (ISO 25) and thus
not good for dim or moving objects or microscopes with a
vibration problem.
How much film resolution in necessary? Suppose we
view an object, illuminated obliquely with 550 nm light
using a 100 x (NA 1.4) objective. The limit of resolution will be about 0.2 μm. When the intermediate image
is magnified 5 x by a projection lens, the total transverse
magnification becomes 500 x. The apparent limit of resolution at the image plane is thus 0.2 500 100 μm or
0.1 mm. This is equivalent to 10 lpm. The resolutions of
today’s films and imaging chips are much greater than
the resolution limit of the light microscope. As I will discuss later, it is important to use high-resolution film when
you want to enlarge the negative for reproduction in a
quality journal.
The Modulation Transfer Function (MTF) is a measure
of how faithfully the image detail represents the object
detail. In this case it is a measure of how the image detail
of the film represents the real image projected on it. It is
equivalent to the real component of the Optical Transfer
Function (OTF). The real component of the optical transfer
function characterizes the amplitude relations between the
FIGURE 5-6 (a) A sinusoidal test object used to determine the modulation transfer function and (b) the film image of the test object used to
determine the modulation transfer function.
object and the image, and the imaginary component characterizes the phase relations between the two. Here, the modulation transfer function relates the contrast of the image
in the film to the contrast of the object photographed.
The MTF is given by:
MTF (Hmax Hmin )/(H max H min )
(Hmax Hmin )/(H max H min )
where H is the intensity of light incident on the film and
H is the intensity of light passing through the film. The
subscripts min and max represent the minimum and maximum intensities, respectively. This equation usually is
multiplied by 100% to give the MTF in percent response.
Figure 5-6 shows a typical MTF square wave test object (a)
and image (b).
The test object is made so that the contrast
((Hmax Hmin)/(Hmax Hmin)) is constant throughout
the grating (Figure 5-7). The intensity modulation within
the image is measured by scanning the film with a
densitometer and the variations in density ((Hmax Hmin)/
(Hmax Hmin)) are plotted as a function of the spatial angular wave number of the test object. The percent
response is plotted as a function of spatial angular wave
number. It is convenient to plot the percent response as
a function of the spatial angular wave number using a
log-log plot so that the function will intersect the x-axis
instead of approaching asymptotically (Figure 5-8). Thus
the resolution of the film can be described as the point on
the modulation transfer curve where two lines can just be
resolved visually (that is, according to Rayleigh’s criterion,
two objects can be resolved if there is a dip in intensity
between them of 20%, or a 20% response). The resolution
of a film often is given as a number in lines per mm that
91
Chapter | 5 Photomicrography
Hmax Hmin
M
give a larger high-quality image. The resolution and size of
the film determines how magnified a journal-quality print
can be.
Hmax Hmin
A
B
C
H
EXPOSURE AND COMPOSITION
Distance along test object
(a)
M Hmax Hmin
Hmax Hmin
A
B
C
H
Distance along film image of test object
(b)
FIGURE 5-7 Graphical description of densitometer measurements of
the test object (a) and image (b) used to calculate the modulation transfer
function.
Modulation transfer function
A
100
Response (%)
B
50
C
20
10
5
5
10
20
50
100
200
Spatial wave number (mm1)
FIGURE 5-8 Log-log plot of the percent response vs. spatial angular
wave number.
can be separated visually in the photographic image of a
standard test object.
When a photograph is going to be reproduced for
a journal, it is first digitized through a computer analyzing system and then printed. The printed photograph is
composed of numerous dots, characterized by 256 or
more gray values that go from pure black to pure white.
The distance between the dots varies with the journal,
but they range from 6 to 11 dots/mm. In other words, the
limit of resolution of a photograph in a journal is about
6 to 11 lines/mm. As a consequence, any photograph with a
limit of resolution equal to 6 to 11 lpm is of journal quality.
If we use film that has a resolution of 100 lpm, we can
enlarge the negative about 10 times. A larger format film
with the same resolution can be magnified 10 times to
When using the exposure meter in a camera to determine
the correct exposure, remember that the exposure selected
by the camera is only an estimate. If the camera has an
averaging meter, the meter determines the average exposure
for a circle with a diameter of approximately 18 mm in the
center of the film. The exposure is based on the assumption that the objects are gray and spread evenly throughout
the field (Figure 5-9). When this is the case, the exposure
will be good. However, when a bright-field background is
dotted with fairly dense specimens, the camera will “think”
that the specimen is bright, and the predicted exposure will
be too short. If we do not want a thin low-contrast negative
or a dark low-contrast print, we must increase the exposure
time. If bright objects are scattered in a dark field, then
the exposure meter will “think” we need more light than
we really need, and the predicted exposure will be long.
If we do not want a dark low-contrast negative or a bright
low-contrast print, we must make the exposure faster than
the predicted exposure.
A “spot” meter determines the correct exposure for the
exact spot it is targeting. Digital cameras give the option of
using a built-in average, spot, or center-weighted exposure
meter. It is often better and more efficient to take a series
of exposures in order to get the optimal results. Digital
cameras make it easy to find the correct exposure for a
given specimen by automatically taking a series of exposures with different shutter speeds, apertures, or both.
The composition or framing of a photograph to a large
degree depends on what you put on the microscope slide.
There are two tricks that you can do to optimally frame
the specimen. One is to rotate the stage, and the other is to
rotate the camera.
Michael Davidson (1990, 1998) has created beautiful “landscapes” by photographing crystals, using multiple exposures. He calls these photographs microscapes.
Microscapes can be viewed online at http://www.microscopy.
fsu.edu/microscapes/index.html.
Here is how you can make a microscape:
1. Expose the foreground. Use a low-power objective with crossed polars (see Chapter 7). The image will
be completely black. Place a slide that has some recrystallized chemicals so that the birefringent image is only
on the bottom one-third to one-half of the field. To make
“wheat fields” in the foreground, use ascorbic acid crystals or recrystallized ascorbic acid. To make “plants at the
edge of a lake,” use DNA. To make a “sandy, rocky beach,”
use ascorbic acid that has been crystallized slowly from
92
Light and Video Microscopy
Measuring area
Specimen and background
Dark specimens are
sparcely distributed on
bright background
within the
metering region
0.25X
Dark specimens on a
bright background take
up about one fourth
of the metering region
0.5X
Specimen is evenly distributed
within the metering region.
Bright specimens on a
dark background
take up about one half
of the metering region
Bright specimens on a
dark background take up
about one fourth of the
metering region
Bright specimens are
sparcely distributed
on a dark background
within the metering region
FIGURE 5-9
Exposure adjustment
dial setting
1X
2X
4X
Use the
ISO
sensitivity
dial
How to correct the exposure for specimens that are not gray and uniform.
an aqueous ethanol solution and then smear it across the
microscope slide as it dries. To make “sea oats,” use meltrecrystallized ascorbic acid. To make a canyon, use sulfur
crystals.
2. Cut a mask out of black poster board that exactly
follows the outline of the crystals in the first exposure.
Place the mask over the field lens, which is a conjugate
plane to the specimen. This prevents the region exposed by
the first exposure from being reexposed.
3. Expose the mountains, seas, sky, and more. To make
“mountains,” use recrystallized chemicals, including xanthin or HEPES. To make a “sky,” place a low-intensity blue
filter in the light path. Using bright-field optics, expose the
remaining film. Short exposures make a dark blue “sky”
and long exposures make a light blue “sky.” “Skies” can
also be made by using a sheet of polyethylene between
crossed polars or by defocusing a bead of epoxy resin
using polarization optics and a full wave plate.
4. Expose a sun or moon. Close the field diaphragm
until you get the size of the “sun” or “moon” you want.
Move the substage condenser to put the sun or moon in the
desired position. Lower the substage condenser to defocus the field diaphragm leaves until the “sun” or “moon”
appears to be a circle. Place a color filter in the light path
to make the “sun” orange, yellow, or red. If you insert a
diffraction grating in the light path you will spread out the
image and get “redder” colors. Use an exposed piece of
Polaroid HC film for a diffraction grating.
5. Expose stars or clouds. To make “stars,” place a
sealed microscope slide that contains a solution of polybenzyl-1-glutamate on the stage. Using a 10 x objective
lens, move the slide so that no “stars” are over the “sun”
93
Chapter | 5 Photomicrography
or “moon.” Make sure the microscope is set up for Köhler
illumination again and then expose the film. “Clouds” can
be made by imaging defocused cibachrome bleach crystals
under crossed polars for a long time to wash out any color.
Image these crystals on the upper one-third of the slide.
Most importantly, experiment! The photomicrographs can
also be pieced together to form a panoramic landscape
(Thurgood, 1995).
THE SIMILARITIES BETWEEN FILM AND
THE RETINA
The retina is composed of rods and cones. The retinal rods
make up a surface that is analogous to a sheet of blackand-white film, and the cones make up a surface that is
analogous to a sheet of color film. The rods and cones,
along with their accompanying neurons, are analogous to
the silver halide grains in the film. The rods, which are
used in dim light conditions (scotopic vision), can detect
the presence of only 100 photons, which is only about
39 aJ of energy. The rods are used to detect differences in
the brightness of an object in dim light, and the cones are
used to distinguish the colors of an object in bright light
(photopic vision). There are three kinds of cones: one
senses violet-indigo-blue light (400–500 nm), one senses
green-yellow light (450–630 nm), and one senses orangered–far-red light (500–700 nm).
James Clerk Maxwell, who had a deep interest in
color vision, produced, along with his colleague Thomas
Sutton, a red, a green, and a blue photograph of a colored
tartan ribbon. In a lecture he gave at the Royal Institution
in 1861, he superposed the three photographs to obtain a
fully colored image of the tartan ribbon and thus proved
that all the colors could be produced by the three primary colors, and these primary colors, as Thomas Young
(Peacock, 1855) originally proposed, represent the three
different color-sensors in our eyes (Glazebrook, 1896;
Everitt, 1975; Niven, 2003). Other scientists who had
a deep interest in color vision include Isaac Newton,
Wolfgang Goethe, Ernst Mach, Hermann von Helmholtz,
and Erwin Schrödinger.
WEB RESOURCES
Nikon’s Small World Photomicrography Competition: http://www.
nikonsmallworld.com/
Molecular Expressions: Images from the Microscope: http://micro.
magnet.fsu.edu/micro/about.html
Georg N. Nyman’s Website of Photomicrographs: http://www.gnyman.
com/Photomicrography.htm
Stephen Durr’s Website of Photomicrographs: http://www.btinternet.com/
~stephen.durr/
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Chapter 6
Methods of Generating Contrast
The resolving power attainable with the bright-field microscope is meaningless when we look at invisible, transparent, colorless objects typical of biological specimens. We
can make such transparent specimens visible by closing
down the aperture diaphragm; but when doing so, contrast is gained at the expense of resolving power. A goal of
the light microscopist is to find and develop methods that
increase contrast while maintaining the diffraction-limited
resolving power inherent in the light microscope. In this
chapter I will describe four methods (dark-field, Rheinberg
illumination, oblique, and annular illumination) that can
increase contrast in the light microscope by controlling the
quality and/or quantity of the illuminating light when the
microscope is set up for Köhler illumination. When using
these four methods, the illumination is controlled by the
aperture diaphragm situated at the front focal plane of the
sub-stage condenser. I will also describe a method, known
as phase-contrast microscopy, which can increase contrast
and maintain resolving power by manipulating the light at
the back focal plane of the objective lens as well as at the
front focal plane of the sub-stage condenser (McLaughlin,
1977). Color plates 3 through 6 give examples of specimens observed with dark-field illumination, oblique illumination, and phase-contrast microscopy.
DARK-FIELD MICROSCOPY
All that is required for dark-field microscopy is to arrange
the illuminating system so that the deviated (first- and
higher order diffracted light) rays, but not the illuminating
(zeroth-order diffracted light) rays enter the objective lens
(Gage, 1920, 1925). Dark-field microscopy is as old as
microscopy itself, and Antony von Leeuwenhoek, Robert
Hooke, and Christiaan Huygens all used dark-field microscopy in the seventeenth century. Leeuwenhoek (in Dobell,
1932) wrote, “… I can demonstrate to myself the globules
in the blood as sharp and clean as one can distinguish with
one’s eyes, without any help of glasses, sandgrains that one
might bestrew upon a piece of black taffety silk.”
Hooke wrote (in Martin, 1988), “If the flame of the
candle were directly before the microscope, then all those
little creatures appeared perfectly defined by a blackline,
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
and the bodies of them somewhat darker than the water;
but if the candle were removed a little out of the axis of
vision all those little creatures appeared like so many small
pearls or little bubbles of air, and the liquid in which they
swam appeared dark.”
Huygens wrote (in Martin, 1988), “I look at these animals not directly against the light but on turning the microscope a little which makes them appear on a black ground.
One can best discover by this means the smallest animals
living and can also distinguish best the parts of larger
ones.”
When dark-field illumination is desired, the specimen
usually is illuminated with a hollow cone of light. In the
absence of a specimen, the illuminating light does not
enter the objective lens because the numerical aperture of
the sub-stage condenser is larger than the numerical aperture of the objective (Lister, 1830; Reade, 1837; Queckett,
1848; Carpenter, 1856). Special sub-stage condensers are
made for dark-field microscopy; however, for low magnifications, a clever and frugal person can create the hollow
cone of light by inserting a “spider stop” or a black circular piece of construction paper in the front focal plane of
a sub-stage condenser designed for the bright-field microscope. A clever or frugal person with a phase-contrast
microscope can create a dark-field microscope by using
the 100x phase-contrast annular ring in combination with
a 10x or 20x objective. A high-contrast dark-field image
can also be obtained by removing the undeviated, zerothorder diffracted light by inserting an opaque stop in the
central region of any plane that is conjugate with the aperture plane, including the back focal plane of the objective
and the eye point (Figure 6-1). A dark-field image can also
be produced by a bright-field microscope connected to a
digital image processor that removes the low-frequency
components of the Fourier spectrum in a process known as
spatial filtering (Pluta, 1989; Chapter 14).
In order to ensure that the rays emanating from the
sub-stage condenser are as oblique as possible, we must
raise the sub-stage condenser as high as it goes and open
the aperture diaphragm to its full capacity. We can also put
water or immersion oil between the sub-stage condenser
and the glass slide. Water is used for convenience; immersion oil is used for better resolution. The liquids reduce
95
96
Light and Video Microscopy
Objective
Stage
FIGURE 6-1 To achieve dark-field illumination, the specimen must be
illuminated with a hollow cone of light that is too wide to enter the objective lens.
Objective
Without
oil on
condenser
With oil
on condenser
Sub-stage condenser
FIGURE 6-2 Oil placed between the condenser and the slide allows us
to use an objective lens with greater numerical aperture when using darkfield illumination.
or eliminate the refraction that takes place at the air-glass
interface. When refraction occurs at the air-microscope
slide interface, the illuminating rays are refracted toward
the optical axis of the light microscope. This means that
an objective lens will capture more of the illuminating rays
when there is air between the top lens of the sub-stage condenser and the microscope slide than when there is water
or oil there. Thus when we place water or oil on top of
the sub-stage condenser, we get better contrast with an
objective lens with a low numerical aperture or can use an
objective lens with a higher numerical aperture to get better resolution (Figure 6-2).
Sub-stage condensers that are especially made for darkfield microscopy are designed to transmit only the most
oblique rays (Wenham, 1850, 1854, 1856). Dry dark-field
condensers are made to be used with objectives with numerical apertures up to 0.75, and the oil immersion dark-field condensers are made to be used with objectives with numerical
apertures up to 1.2. The dry dark-field condensers use prisms
that are cut in such a manner that the light that enters the
prism is reflected internally so that the light leaving the prism
exits at a very oblique angle. Some oil immersion dark-field
sub-stage condensers use a convex mirror to bring the light
to a concave parabolic mirror, which acts as the main lens
(Figure 6-3). Mirrors, unlike glass lenses and prisms, have
virtually no chromatic aberration.
Since the dark-field condition requires that the numerical aperture of the objective be smaller than the numerical aperture of the sub-stage condenser, an objective with
a variable aperture or iris is very useful for dark-field
microscopy. A variable iris in the objective lens lets us
adjust the numerical aperture of the objective so that it is
“just” smaller than the numerical aperture of the sub-stage
condenser and thus obtain optimal resolution and contrast.
Once an object is inserted into the dark-field microscope,
the illuminating light that interacts with the specimen is deviated by refraction and/or diffraction. The refracted and/or
the first- and higher-order diffracted rays are the only rays
that are able to enter the objective. These rays recombine to
make the image, and the specimen appears bright on a dark
background. Dark-field microscopy is best suited for revealing outlines, edges, and boundaries of objects. It is less useful
for the revealing internal details of cells unless there are a lot
of highly refractile bodies in a relatively transparent cytosol.
The more oblique the illuminating rays are, the easier it
is to detect the presence of very minute objects. Of course
the upper limit of obliquity is having the illuminating rays
pass perpendicular to the optical axis of the microscope,
Microscopes, known as ultramicroscopes, have the darkfield condenser set so that the illuminating rays emerge
from the condenser at a 90 degree angle with respect to
the optical axis. Typical dark-field microscopes can detect
cilia, which are 250 nm in diameter, and single microtubules, which are 24 nm in diameter (Koshland et al.,
1988); the ultramicroscopes can detect particles as small as
4 nm (Siedentopf and Zsigmondy, 1903; Hatschek, 1919;
Chamot, 1921; Ruthmann, 1970). The volume of a particle
is estimated by counting the number of particles in a solution containing a preweighed amount of substance of a
known density (Kruyt and van Klooster, 1927; Weiser,
1939). The linear dimensions can then be ascertained by
making an assumption about the shape of the particle.
Dark-field microscopes often are used to visualize particles whose size is much smaller than the limit of resolution.
How is this possible? Doesn’t the wavelength of light limit
the size of a particle that we can see? No, this is a very
important point; the limit of resolution is defined as the
minimal distance between two object details that can just
be recognized as separate structures. Resolving power is
truly limited by diffraction. But the concept of the limit of
resolution does not apply to the minimal size of a single
particle whose presence can be detected because of its light
scattering ability. The limit of detection in a dark-field
microscope is determined by the amount of contrast attainable between the object and the background. To obtain
maximal contrast, the rays that illuminate the object must
be extremely bright, and the zeroth-order rays must not
97
Chapter | 6 Methods of Generating Contrast
Objective
Oblique illuminatingrays
Objective
Diffracted
rays
Specimen
Oil
Specimen
Immersion
dark-field
condenser
Sub-stage
condenser
Dark-field
stop
A
Dark-field
stop
B
FIGURE 6-3 Two kinds of dark-field condensers.
Objective
Oblique rays
coloring specimen
Central rays
coloring background
Rays from annular ring
Rheinberg filter
FIGURE 6-4
Annular ring,
E.g. Red
Background
color
Central stop,
E.g. Green
Color for
light scattered in
this direction
Color for
light scattered in
this
direction
Rheinberg illumination and Rheinberg filters.
be collected by the objective lens. Moreover to obtain the
maximal contrast it is important to have scrupulously clean
slides, since every piece of dust will act as a glaring beacon of light. Conrad Beck (1924) says that dirt is “matter
out of place” and glare is “light out of place.”
We can infer the presence of minute objects using the
naked eye. In a dark room, pierced by a beam of sunlight,
we can detect the scattering of light by tiny motes of dust
in the beam as long as we do not look directly into the
beam. In fact, John Tyndall made use of this optical phenomenon to determine whether or not the room in which he
was working while he was performing his experiments on
the refutation of the theory of spontaneous generation was
dust-free. For this reason, the phenomena of scattering by
microscopic objects and the ability to detect minute objects
by scattering is often referred to as the Tyndall Effect and
Tyndall scattering, respectively (Gage, 1920, 1925).
RHEINBERG ILLUMINATION
Rheinberg illumination is a variation of dark-field
microscopy first described by Julius Rheinberg in 1896.
Rheinberg discovered this method when he accidentally placed colored glass filters in the sub-stage ring
(Spitta, 1907). Rheinberg called this type of illumination
“multiple or differential color illumination.” It is also
known as optical staining since when we use Rheinberg
illumination, the image of a normally colorless specimen is
made to appear colored without the use of chemical stains.
Zeiss introduced Rheinberg illumination under the name of
Mikropolychromar in 1933.
When Rheinberg illumination is desired, the central
opaque stop of the dark-field microscope is replaced with a
transparent, colored circular stop inserted into a transparent
ring consisting of a contrasting color (e.g., a red annulus
surrounding a green circle). The Rheinberg stop is placed
in the front focal plane of the sub-stage condenser. With
Rheinberg illumination, the illuminating rays that pass
through the annular ring are too oblique to pass through
the objective lens and consequently, the background in the
image plane is formed only from the illuminating rays that
pass through the central area of the circular stop. In order
to get the color of the annular ring in the image plane,
the light originating from the annular ring must be deviated by refraction and/or diffraction so that it passes into
the objective lens. Since the deviated rays originate from
the illuminating light passing through the annular ring, the
specimens appear to be the color of the annular ring. If we
were to observe a protist like Tetrahymena with a microscope equipped with a Rheinberg filter with a green central stop inside a red annulus, the protist would appear red
swimming in a green background (see Strong, 1968). If we
were to use a yellow annulus around a blue central stop, the
protist would appear yellow in a sea of blue (Figure 6-4).
98
Light and Video Microscopy
Optic axis
Homemade Rheinberg filters are easy to make
(Rheinberg, 1896; Needham, 1958; Taylor, 1984). To make
Rheinberg filters, cut circles and rings from colored plastics
used for theatre lighting with a cork borer. Then cement
them with mounting medium to a piece of glass that fits
in the filter holder at or near the front focal plane of the
sub-stage condenser. For best results, the edges of the adjacent colors should be covered with an opaque border about
3 mm in width.
Tricolored Rheinberg filters can be made where the
annulus is composed of four sectors (Hewlett, 1983).
Contrasting colors are placed in the adjacent sectors. For
example red, green, red, green. The central stop then is
filled with a third color, perhaps blue. Tricolored Rheinberg
illumination is particularly effective in objects that show
striking periodicity, like diatoms and textiles, including
silk, where the warp appears in one color and the woof
in another. In designing Rheinberg filters, you are limited
only by your imagination.
Contrast can be increased when we use Rheinberg illumination by adding several layers of the colored filter to
the central portion or by adding a neutral density filter to
the central portion. In this way a dim image of the specimen will not be lost in a bright background. Contrast can
also be increased by putting a polarizer over the central
stop, and then rotating another polarizer placed between
the light source and the Rheinberg filter in order to
decrease the brightness of the background and increase the
contrast of the specimen (Strange, 1989; Chapter 7).
Rheinberg-like filters can also be made by putting
together two semicircular sheets of colored material with
contrasting colors. The sheets should slightly overlap.
Stage
This yields a kind of oblique illumination (Walker, 1971;
Carboni, 2003).
OBLIQUE ILLUMINATION
Oblique or anaxial illumination, like dark-field illumination, is also as old as microscopy itself (Goring and
Pritchard, 1832; Brewster, 1837; Naegeli and Schwendener,
1892). Oblique illumination is a great way to produce good
contrast in images of transparent specimens. The contrast
not only comes without a loss in resolving power, but
with a gain in resolving power. With oblique illumination,
the image of invisible colorless, microscopic specimens
appears three-dimensional, although the image is actually a
pseudo-relief image and does not represent the true threedimensional structure of the specimen.
Oblique illumination is created by allowing light from
only one portion of the light cone exiting the sub-stage
condenser to illuminate the specimen. This is accomplished
by blocking all but one portion of the oblique rays coming
from the front focal plane of the sub-stage condenser. The
unwanted rays can be blocked with your fingers or with a
sector stop. Older microscopes were equipped with a translatable (i.e., decenterable) aperture diaphragm that was
capable of illuminating the specimen with axial or oblique
illumination (Figure 6-5).
A clever and frugal person with a phase-contrast microscope can readily produce oblique illumination by slightly
moving the rotating turret of the phase-contrast condenser
from the bright-field position to just slightly off-center and
adjusting the aperture diaphragm to give the best pseudorelief image.
Zeroth order
1st order
Stage
Secondary
axis
Objective
Stage
Sub-stage
condenser
FIGURE 6-5 Two ways of producing oblique illumination.
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Chapter | 6 Methods of Generating Contrast
I would like to emphasize that the image formed by
oblique illumination appears three-dimensional; but the
three-dimensional impression we get is just an introduced
artifact and bears no relationship to real shadow effects.
According to geometrical optics, the image plane is parallel to the object plane only when the illuminating rays
are parallel to the optical axis. As the illuminating rays
become more and more oblique, so does the image plane.
The inclination of the image plane results in small objects
being overfocused at one edge and underfocused at the
other edge. This results in a pseudo-relief image (James,
1976). According to physical optics, the defocusing results
in constructive interference on one side (the bright side)
of an image and destructive interference on the other side
(dark side).
There is currently no complete theory to explain the
appearance of the image obtained using oblique illumination. Ellis (1978) has a theory that takes only diffraction
into consideration, and Hoffman (1977) has a theory that
only takes refraction into consideration. I will discuss the
diffraction theory in this chapter after I discuss phasecontrast microscopy, and I will discuss the refraction theory in Chapter 10.
One advantage of using oblique illumination is that the
resolving power of the light microscope is up to twice of
what it would be with Köhler illumination (Figure 6-6).
The only disadvantage is that the image must be viewed
with caution since the (would-be) diffracted rays from one
side of the object do not contribute to the formation of the
image, and consequently a single image will not represent
all asymmetrical specimens. On the other hand, oblique
illumination makes it easy to discover and visualize asymmetries that may have gone undetected with bright-field
illumination. In order to distinguish between asymmetries and symmetries in the specimen when using oblique
illumination, it is important to rotate the specimen or the
direction of illumination. The specimen can be rotated if
the microscope is equipped with a rotating stage, and the
direction of illumination can be rotated by rotating the sector stop or the translatable aperture diaphragm.
In the nineteenth century, most microscopes were
equipped with either a decenterable sub-stage condenser
or a decenterable aperture diaphragm for doing oblique
illumination. However, in the late nineteenth century, the
optical attachments that made it possible to do oblique
illumination became victims in the sub-stage condenser
battle between the “axial-ists,” like Abbe, and the “coneists,” like Nelson and Koch. Microscope manufacturers
took sides with the axial-ists, and oblique illumination
was unintentionally lost in the process. Oblique illumination has been reinvented many times since then (Hoffman
and Gross, 1975; Hoffman, 1977; Ellis, 1978; Hartley,
1980; Kachar, 1985; Inoué and Spring, 1997; Piekos,
1999). Snowflakes look sensational when they are photographed on a cold microscope slide using oblique illumination (Kepler, 1611; Nakaya, 1954; LaChapelle, 1969;
Blanchard, 1998; Libbrecht, 2007). In 1991, almost 100
years after the battle between the cone-ists and the axialists, Zeiss introduced a type of oblique illumination known
as variable relief contrast (Varel).
PHASE-CONTRAST MICROSCOPY
The human eye has the ability to detect differences in
intensity and/or in color, and we see images when the
points that make up those images vary in intensity or color
compared with the background. The bright-field microscope can be considered an amplitude-contrast microscope,
which can be used to visualize microscopic specimens that
absorb light, thus reducing the amplitude of the waves and
the intensity of the light. When a specimen differentially
absorbs visible light of different wavelengths, the brightfield microscope renders a colored image. The human eye
cannot, however, detect differences in the phase of waves.
Transparent specimens with variations in refractive index,
Objective lens
0
0
0
0
Diffracted orders
0
Specimen
Condenser lens
Axial
Köhler
Oblique
FIGURE 6-6 Comparison bet-ween axial, Köhler, and oblique illumination. The numbers on the diffracted rays indicate the diffraction order. With
Köhler illuminate the zeroth-order rays that enter the left side of the objective lens, will coexist with the negative first-order diffracted rays from the
axially-illuminated specimen and the negative second-order diffracted rays from the specimen illuminated with oblique rays that enter the right side of
the objective lens.
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Light and Video Microscopy
or more correctly, variations in the optical path length
(OPL), are able to differentially retard waves; but since we
cannot detect the differences in phase with the naked eye,
the object remains invisible. The phase-contrast microscope is able to convert differences in the optical path
length between regions of a specimen into differences
in intensity, thus making transparent specimens visible
(Richards, 1950).
The phase-contrast microscope was invented by Fritz
Zernike in 1934 (Zernike, 1942a, 1942b, 1946, 1948;
Turner, 1982). Like many new discoveries (F. Darwin,
1887; C. Darwin, 1889; Planck, 1936, 1949; Cornford,
1966; Wayne and Staves, 1996), his invention was not
immediately accepted by the powers that be. Zernike
(1955) describes how his new invention was received by
the Zeiss works:
With the phase-contrast method still in the first somewhat primitive stage, I went in 1932 to the Zeiss works in Jena to demonstrate it. It was not received with as much enthusiasm as
I had expected. This may be explained by the following facts.
The great achievements of the firm in practical and theoretical
microscopy were all the result of the work of their famous leader
Ernst Abbe and dated from before 1890, the year in which Abbe
became sole proprietor of the Zeiss works. After 1890 Abbe was
absorbed in administrative and social problems, and partly also in
other fields of optics. Indeed his last work on microscopy dates
from that same year. In it he gave a simple reason for the difficulties with transparent objects, which we now see was insufficient. His increasing staff of scientific collaborators, evidently
under the influence of his inspiring personality, formed the tradition that everything worth knowing or trying in microscopy had
already been achieved.
Eventually people realized the importance of the
phase-contrast microscope for visualizing living, unfixed,
and unstained cells, and Zernike won the Nobel Prize
for his discovery in 1953.
The optical path length is equal to the product of
the refractive index and the thickness of the specimen
(see Chapter 2). It often is given in units of nm. The optical
path length can be expressed as the phase angle (in degrees
or radians) by multiplying the optical path length by unity,
where 1 360°/λ or 1 2π/λ. These relations hold when
we define the wavelength of a sinusoidal wave in terms of
a circle. The optical path length can also be expressed as
the phase change (in λ) by dividing the optical path length
by λ, where represents the wavelength of the illuminating
light.
An amplitude object (b) decreases the amplitude of
the incident light waves (a) that propagate through it and a
phase object (c) changes the phase of the incident light that
propagates through it (Beyer, 1965; Figure 6-7). Mixed
objects can influence both the amplitude and the phase of
the incident light.
The optical path length of a phase object differs from
the optical path length of the surround if there is a difference in the refractive index and/or the thickness. According
to Maxwell’s relation (see Chapter 3), the refractive index
of a substance is a measure of an electrical property of a
substance known as the dielectric constant or relative permittivity. The optical path length is a measure of the degree
of interaction between the light and the electrons in the
specimen compared to the degree of interaction between
the light and the surround.
In most biological samples, the refractive index is
related to the concentration of dry mass in the sample. The
dry mass of biological samples is predominantly made
Background
Amplitude object
Phase object
FIGURE 6-7 Amplitude objects reduce the amplitude of the incident wave, but phase objects influence the phase of the wave without changing the
amplitude.
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Chapter | 6 Methods of Generating Contrast
up of proteins, lipids, nucleic acids, and carbohydrates,
and each of these macromolecules is composed primarily
of light atoms, including carbon, oxygen, hydrogen, and
nitrogen held together by single bonds. As a first approximation, all the electrons in these light atoms and in the
bonds between them have similar electrical properties, and
consequently they interact with light in a similar manner.
The specific refractive increments of these macromolecules
are similar because the electrical properties are similar.
The specific refractive increment, which characterizes the
degree of interaction of the macromolecules with light, is
defined as the increase in the refractive index per one percent increase in the dry mass. Since biological specimens
are predominantly composed of these macromolecules
with similar specific refractive increments, the refractive
index of a specimen is related to its dry mass.
The specific refractive increment is a characteristic
of each molecule that describes how much the refractive
index of an aqueous solution increases above the refractive
index of water (n 1.3330) for every one percent (w/v)
increase in dry mass. A one percent increase in dry mass
represents an increase of 1 g/100 ml of solution. Table 6-1
lists the specific refractive increments of representative
biological substances.
Most biological molecules have a specific refractive
increment between 0.0017 and 0.0019, with an average of
0.0018. Tryptophan is the notable exception in that it has
a somewhat higher than average specific refractive increment, due to the preponderance of double bonds. Lipids
and carbohydrates, with their somewhat higher proportion
of hydrogen atoms, have a somewhat lower than average
specific refractive increment. For practical purposes, the
living cell can be considered to be composed of protein.
The specific refractive index of proteins is approximately
0.0018. Therefore a 5-percent solution of protein (in water)
has a refractive index of 1.3330 5(0.0018) , which is
similar to the refractive index of a typical mammalian cell.
Understanding optical path difference (OPD) is the
key to understanding phase-contrast microscopy. A region
of a specimen and the background, or two regions in a
TABLE 6-1 The Specific Refractive Indices of Biological Molecules
Substance
Specific refractive increment (100 ml/g)
Protein
bovine serum albumin (BSA)
0.001854–00187
horse serum albumin
0.001830–0.0018444
human serum albumin
0.00181–0.001860
egg albumin (chick)
0.001820
γ-globulin (human)
0.00186
serum globulin (horse)
0.00186
lactoglobulin (bovine)
0.001818
β1 Lipoprotein
0.00171
hemocyanine (Helix)
0.00179
hemocyanine (Carcinus)
0.00187
hemoglobin (human)
0.00194
glycine
0.00179
alanine
0.00171
tryptophan
0.0025
DNA
0.0016–0.0020
RNA
0.00168–0.00194
Amino acids
Nucleic acids
Lipids (average)
0.0014
Carbohydrates
0.0013–0.0014
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Light and Video Microscopy
specimen, will have an optical path difference if they have
different refractive indices or different thicknesses.
When light passes a homogeneous object that has a
different refractive index than the surround, its velocity is
altered, and its arrival at a given point is either advanced
or retarded, depending on whether the refractive index of
the object is less than or greater than, respectively, that of
its surroundings. A difference in phase arises because the
wave that goes through the specimen has a different optical path length than the wave that goes through the surround. If no is the refractive index of the object and ns is
the refractive index of the surround, the optical path difference (OPD) is given by:
OPD (n o n s )t
where t is the thickness of the specimen.
An OPD will also arise when the light passes through
an object that has the same refractive index as the surround
but has a different thickness. In this case:
OPD n(t o t s )
where n is the refractive index of the object and surround,
to is the thickness of the object and ts is the thickness of the
surround. In general, OPD OPLo OPLs, where OPLo
is the optical path length through the object and OPLs is
the optical path length of the surround.
By convention an optical path difference of one wavelength is equal to 360 degrees, and in circular coordinates,
the phase angle ϕ is given by:
OPD (360) (n o ns ) t [360/]
where λ is the wavelength of the illuminating light.
The relative phase and amplitude of light waves can
be represented by vectors, where the length of the vector
represents the amplitude of the wave and the angle of the
vector represents the relative phase of the wave (Zernike,
1942a, 1942b, 1946; Barer, 1952a, 1952b, 1953a, 1953b).
We can draw the vector in a circle, whose circumference
represents one wavelength of the incident light. We will
consider that the illuminating wave, incident on the specimen, has an amplitude of 1, and a phase angle of zero
degrees. With Köhler illumination, each point of the filament illuminates each and every point on the image plane,
and consequently, each wave vector represents the sum of
all the illuminating waves divided by the number of illuminating waves. The square of the amplitude of each vector gives the intensity of the image in the image plane. If
the specimen is transparent, the vector that represents the
waves that propagate through any given point in the specimen will also have an amplitude of one; but it will have a
phase angle equal to ϕ, which will be related to the optical path difference between the specimen and the surround
(Figure 6-8).
We will use this vector representation of light to predict with surprising accuracy the nature of the image that
will be obtained in the phase-contrast microscope. I would
like to emphasize, however, that although the mathematical models that describe phase-contrast microscopy are
quantitative and useful, they are only first approximations
to the truth, especially when dealing with complicated
biological specimens (Zernike, 1946; Bennett et al., 1951;
Barer, 1952a, 1952b, 1952c, 1955; Strong, 1958; Goldstein,
1990).
A light wave impinging on a given point in a transparent specimen will be diffracted by that point in the specimen, and the image of that point will be formed by the
interference of the diffracted and nondiffracted light at the
conjugate point in the image plane. The waves that contribute to the nondiffracted light at the image point originate
from every point on the filament. The waves that contribute to the diffracted light at the image point originate
only from the conjugate point of the specimen itself. I will
call the zeroth-order diffracted light that contributes to an
image point the undeviated light, and the sum of all the
nonzero diffracted orders, the deviated light. The undeviated light that makes up a given image point in the image
plane is represented by vector OA. The length of OA is
proportional to the amplitude of the wave and the intensity
is proportional to the square of the amplitude. The angle of
OA represents the phase of the incident wave. If we define
the phase of the undeviated light to be zero (ϕ 0), we
can represent the phase of other waves relative to OA.
The length of the vector (OP) that represents a point in
the image plane that is conjugate to a perfectly transparent
point in the specimen is equal in length to vector OA. Even
if the point in the specimen is not perfectly transparent,
the length of OP, in general, is indistinguishable from the
length of OA. However, the phase angle of the vector that
represents a point in the image plane conjugate to a point
in a transparent specimen is nonvanishing and depends on
the optical path difference between the point in the transparent specimen and the surround.
Vector OP is the sum of vector OA and vector AP.
Since vector OP represents the sum of the amplitudes of
the undeviated light and the deviated light and vector
OA represents the undeviated light, then vector AP must
represent the deviated light, which is the sum of the nonzero-order diffracted light (Figure 6-9).
ϕ
A
O
λ/4
P
FIGURE 6-8 Wave and vector representation of light that does not
interact with the specimen (A) and light that does interact with a point on
the specimen (P).
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Chapter | 6 Methods of Generating Contrast
In a typical transparent biological specimen, the phase
angle is small (say ϕ 12°), and the vector (AP) that
represents the deviated or higher-order diffracted light is
rotated about 90 degrees relative to vector OA that represents the zeroth-order diffracted light. A rotation of 90
degrees means that the higher-order diffracted light is
out-of-phase with the undiffracted light by 90 degrees.
As we learned in Chapter 3, the amplitude of the resultant
that represents the interference of two waves with similar
amplitudes but that are out-of-phase with each other by
90 degrees (λ/4) is equal to the sum of the amplitudes of
the two waves.
The light that makes up a point in the image plane
is represented by vector OP, where OP OA and
⬔AOP ϕ. Since the intensity of the light that makes
the conjugate image point is represented by (OP)2, and the
intensity of the surround ((OP)2) has the same value, the
specimen would be invisible in a bright-field microscope. The phase-contrast microscope, however, has the
ability to convert differences in phase into differences in
intensity.
In order to make a transparent object visible, vector
OP must differ in length from vector OA. This is accom-
O
A
ϕ
A
O
P
P
FIGURE 6-9 Vector representation OA represents the undiffracted light,
AP represents the diffracted light, and OP represents the vector sum of the
diffracted light and undiffracted light that makes up the image point.
A
plished by adding an additional phase of 90 degrees
(λ/4 π/2) to either the direct or the deviated light. In
positive phase-contrast microscopy, the direct wave is
advanced 90 degrees relative to the deviated wave (Figure
6-10). The advancement is depicted in the vector diagram by a counter-clockwise rotation of the OA vector by
90 degrees to make vector OA. The length and angle of the
deviated beam remains unchanged. The image point now is
represented by the vector sum of OA and AP. In order to
add the two vectors together, we translate vector AP to its
new position at the terminus of vector OA, while keeping
it parallel to vector AP. Because we keep the length and
angle of the vector constant, vector AP equals vector AP.
Then by summing vector OA and vector AP, we get vector OP, whose length differs from the length of OA in a
manner that depends on the optical path difference between
the specimen and the surround. Depending on ϕ, the intensity of the image point may now be greater or less than the
intensity of the background.
In negative phase-contrast microscopy, the direct wave
is retarded 90 degrees relative to the deviated wave (Figure
6-11). The retardation is depicted in the vector diagram
by a clockwise rotation of the OA vector by 90 degrees
to make vector OA. The length and angle of the deviated
beam remains unchanged. The image point is now represented by the vector sum of OA and AP. In order to add
the two vectors together, we translate vector AP to its
new position at the terminus of vector OA, while keeping
it parallel to vector AP. Because we keep the length and
angle of the vector constant, vector AP equals vector AP.
Then by summing vector OA and vector AP, we get vector OP, whose length differs from the length of OA in a
manner that depends on the optical path difference between
the specimen and the surround. Depending on ϕ, the intensity of the image point may now be greater or less than the
intensity of the background.
Using the vector method, we can predict qualitatively how various specimens will appear in a positive
A
A
P
P
O
ϕ
A
P
O ϕ
A
P
Oϕ
P
P
ϕ 45
ϕ 90
FIGURE 6-10 Vector representations of specimens observed with positive phase-contrast microscopy.
ϕ 180
A
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Light and Video Microscopy
O
ϕ
O
ϕ
A
A
O
ϕ
P
A
P
A
P, A
A
P'
P
ϕ 45
ϕ 90
ϕ 180
P'
FIGURE 6-11 Vector representations of specimens observed with negative phase-contrast microscopy.
6.0
5.0
Intensity
4.0
3.0
2.0
1.0
0
(360)
90
(270)
180
(180)
270
(90)
360
(0)
FIGURE 6-12 The relationship between intensity of an image point and
phase angle. The phase angles for negative phase-contrast microscopy are
given in parentheses.
phase-contrast microscope and a negative phase-contrast
microscope. The relative lengths of vectors OP compared
to the lengths of the background vectors OA for specimens
with phase angles (ϕ) of 45, 90, or 180 degrees viewed in
a positive phase-contrast microscope are given in Figure
6-10, and the relative lengths of vectors OP compared to
the lengths of the background vectors OA for specimens
with phase angles (ϕ) of 45, 90, or 180 degrees viewed in
a negative phase-contrast microscope are given in Figure
6-11. The intensities of the specimen point and the background are given by the squares of OP and OA, respectively. Figure 6-12 summarizes the intensity of the image
point compared with the background with respect to phase
angles. The relative intensities or the ratio of the intensities
of the specimen point compared to the surround are on the
ordinate. The phase angles are presented on the abscissa.
The phase angles without parentheses are used for specimens viewed with a positive phase-contrast microscope
and the phase angles in parentheses are used for specimens
viewed with a negative phase-contrast microscope.
The intensity of the image point is not linearly related to
the phase angle, and contrast reversals do occur. In fact, the
image points with phase angles of 0, 90, and 360 degrees
will be invisible when viewed with a positive phasecontrast microscope and image points with phase angles of
0, 270, and 360 degrees will be invisible when viewed with
a negative phase-contrast microscope. In a positive phasecontrast microscope, maximum darkness occurs when the
specimen has a phase change of 45 degrees and maximum
brightness occurs when the object has a phase change of
235 degrees. In a negative phase-contrast microscope,
maximum brightness occurs when the phase angle is
135 degrees and maximum darkness occurs when the phase
angle is 315 degrees. Figure 6-12 shows graphically the
relative intensity (I) of the image point compared to the
background. The relative intensities can also be computed
analytically using the following equation:
I 3 2 sin 2 cos We can put ourselves in Zernike’s shoes and put our
knowledge to work to design a phase-contrast microscope.
Zernike’s first phase-contrast microscope used axial illumination, where all the direct light is focused to a spot on
the optical axis in the back focal plane of the objective.
Zernike (1958) suggests doing an experiment that would
help us realize that an image of a phase object is composed
of the addition of the direct and diffracted light. Using a
microscope in which the sub-stage condenser has been
removed so as to ensure the specimen is illuminated with
105
Chapter | 6 Methods of Generating Contrast
Objective
Source
Specimen
FIGURE 6-13
Phase plate
Image
Phase-contrast microscope based on axial illumination.
parallel light, observe a specimen of India ink with brightfield illumination. Then place a piece of aluminum foil that
contains a 0.5 mm pinhole in it on top of the last lens of
a 10x objective. No matter what the relatively transparent
specimen is, the image observed through 10x eyepieces
will be that of a uniformly illuminated field, as if there
were no specimen. This is the image of the direct light.
Then, replace the pinhole with a glass disk with a 1 mm
black dot in the center and look at the specimen through
the eyepieces. The India ink will appear as white dots on
a black field, indicating the reality of the diffracted light.
The vector sum of the direct light and the diffracted light
gives rise to a bright-field image.
To make a phase-contrast microscope, which converts
differences in phase into differences in intensity, Zernike
put a glass phase plate that is thinner in the region through
which the direct light passes in the back focal plane of the
objective. The region through which the direct light passes
is called the conjugate region. Zernike made the conjugate
area thin by etching the glass in the conjugate region with
dilute hydrofluoric acid. Since the conjugate area is thinner
than the rest of the phase plate known as the complementary area, the direct light is advanced relative to the deviated light. Zernike etched the conjugate area of the positive
phase plate so that the direct light would be advanced λ/4
or 90 degrees relative to the deviated light, and he etched
the complementary area of the negative phase plate so that
the direct light would be retarded λ/4 or 90 degrees relative
to the deviated light (Figure 6-13).
Since the resolving power of the light microscope
depends on the obliquity of the light that enters the objective lens, Zernike opted for increased resolving power by
inserting an annulus, also known as a phase ring, in the front
focal plane of the sub-stage condenser and making the conjugate area in the phase plate an annulus too (Figure 6-14).
To turn a bright-field microscope into a phase-contrast
microscope, we must add a phase ring at the front focal
plane of the sub-stage condenser that allows a hollow
cylinder of light to pass into the sub-stage condenser. A hollow
cone of light illuminates the specimen. An inverted hollow cone
of direct light is captured by the objective lens and is focused
into a ring that coincides with the conjugate area of the phase
plate at the back focal plane of the objective.
The contrast of the image formed in a phase-contrast
microscope can be increased by coating the conjugate
Objective
Specimen
Phase
ring
Phase
plate
Image
plane
FIGURE 6-14 Phase-contrast microscope based on annular illumination.
region of the phase plate with MgF2. The MgF2 absorbs a
portion of the direct light, thus decreasing its amplitude. In
terms of the vector diagram, the MgF2 coating results in a
shorter vector OA while the vector AP remains unchanged.
Consequently vector OP becomes shorter relative to vector OA. Thus the difference in the intensity of a point
in the specimen to the intensity of the surround becomes
greater as a result of the MgF2 coating. The coating also
increases the slope of the curve depicted in Figure 6-12 for
specimens with small phase angles so that the reversal in
phase occurs at smaller phase angles. The reversal of contrast takes place at 90, 54, and 12 degrees, for a conjugate
area with 0, 75, and 99 percent absorption, respectively. At
100 percent absorption, the contrast reversal takes place
at 0 degrees, and we end up with dark-field illumination
(Figure 6-15).
Although the phase-contrast microscope is fundamentally a qualitative instrument for observing transparent cells (Huxley and Hanson, 1954), it can also be used
quantitatively. It has been used quantitatively to measure
the refractive index, density, and dry mass of cells. It has
also been used to measure changes in the refractive index
of cells during cell division, to measure hemoglobin and
nucleic acid concentrations, to study the action of X-rays
and drugs on lymphocytes, and to study the osmotic behavior of cells (Barer, 1952c, 1953c; Barer et al., 1953; Barer
and Dick, 1957; Barer and Joseph, 1954, 1955, 1958;
James and Dessens, 1962; Ruthmann, 1966; Ross, 1988;
Wayne and Staves, 1991).
In order to measure the refractive index of a cell using
a phase-contrast microscope, we observe cells that have
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Light and Video Microscopy
A
A
P
A
O
P
A
O
P
0% absorption of OA'
P
50% absorption of OA'
A
O
P
A
P
100% absorption of OA'
FIGURE 6-15 Vector representation of the influence of putting an absorbing layer on the annulus of the phase plate on the contrast of the image.
been placed in solutions that contain varying concentrations of a solute (e.g., bovine serum albumin) that is nontoxic and does not significantly influence the osmolarity
of the solution. Bovine serum albumin (BSA) is nontoxic
and has little influence on the osmolarity of a solution as
a consequence of its large molecular mass. The specific
refractive increment of bovine serum albumin is 0.0018 for
every 1 percent increase in dry mass. When we immerse
cells in various concentrations of BSA, we change the
phase angle. As we decrease the phase angle, the contrast
will typically decrease (we must known which portion of
the phase change-intensity curve we are on) and will eventually disappear when the refractive index of the BSA
solution equals the refractive index of the bulk of the cell.
While doing this experiment we can see that if the cell is
not homogeneous, certain organelles will disappear and
reappear before others as a result of the fact that different
organelles have different refractive indices.
The refractive index of a cell (no), obtained by finding
the refractive index of the medium in which the cells disappear, is given by the following formula:
n o 1.3330 Cdm
where 1.3330 is the refractive index of water, α is the specific refractive increment, and Cdm is the concentration of
dry mass (in % w/v) in a cell. Since protein makes up the
majority of the dry mass of a typical cell, Cdm could be
used as an estimate of the concentration of protein in the
cell. The concentrations of other macromolecules have been
determined with quantitative phase-contrast microscopy. For
example, the amount of DNA in a cell has been determined
by measuring the refractive index before and after treatment
with DNase. In Chapter 8, I will discuss how an interference microscope can be used more elegantly to quantitatively determine the dry mass of the cell or its parts.
It is a good exercise to observe your specimen in
media of different refractive indices if you are going to
use phase-contrast microscopy routinely. This is because
the image of a given cellular structure may be obscured in
one medium but made visible in another. In the old days, a
phase microscopist had a battery of phase-contrast objectives available, each with a different retardation, advance,
and absorption to give optimal contrast when used with a
certain specimen in a given medium. Now that we can buy
only a couple of different kinds of phase-contrast objectives, we must be cleverer and vary the medium in order
to vary the contrast. Remember each specimen exists in an
environment, and usually, it is the relationship between the
two that influences the image. This is a specific instance of
the nature-nurture debate.
Phase-contrast microscopy allows us to observe transparent, living cells at high resolution, but it also generates
some artifacts of its own. It is important to be able to recognize these artifacts and to minimize them if possible.
Phase-contrast microscopy is limited to thin specimens.
In thick specimens, the areas below and above the object
plane will provide unwanted phase changes that cause outof-focus images that are superimposed upon and obscure
the focused image. Optimal phase-contrast is obtained with
specimens, whose optical path differences do not exceed
the depth of field of the objective. That means thick specimens must have low refractive indices and specimens with
high refractive indices must be thin. As a rule of thumb,
to obtain a good image in a phase-contrast microscope,
the optical path difference between the specimen and
the surround should be less than the depth of field of the
objective.
Halos and shading-off are two artifacts that typically are
introduced by a phase-contrast microscopes (Figure 6-16).
Both of these artifacts result from the incomplete separation of the direct and deviated light at the phase plate.
Since the deviated light is diffracted by the object in all
directions, some of it passes through the conjugate area
of the phase plate. Most of the light diffracted by objects
with low spatial angular wave numbers is almost parallel to the undeviated light and consequently also goes
through the conjugate region of the phase plate. Thus
the diffracted light from coarse structures constructively
interferes with the undeviated light and produces a bright
spot in the image plane. In a positive phase-contrast
107
Chapter | 6 Methods of Generating Contrast
Image in
phase-contrast
microscope
Optical
density
Image in
brightfield
microscope
Distance along object
FIGURE 6-16
Shading-off effect in a phase-contrast microscope.
microscope, this results in bright halo around the image.
The halo is an unresolved image with reversed contrast
that is superimposed on the principle image (Ross, 1967).
The darker the image, the brighter the halo and vice versa.
Remember with a transparent specimen in a phase-contrast
microscope, the dark images appear dark, not because of
a decrease in the energy of the light due to absorption, but
due to a redistribution of the energy in the image plane. If
the energy in the reversed image and the principal image
could be completely superimposed in register, the images
would disappear completely.
A uniform object may not produce a uniform image
in a phase-contrast microscope as a result of shading-off.
Shading-off is when the contrast of the image decreases
from the edge toward the center until at the center of the
image, the intensity is the same as that of the background.
Shading-off happens because objects with low spatial
angular wave numbers send the majority of their deviated rays through the conjugate area of the phase plate.
Thus the deviated light from these regions are advanced or
retarded in the same manner as the direct light. Thus, there
is no increase in contrast, and these regions have the same
brightness as the background. In red blood cells, the biconcave shape enhances the shading-off effect, and the cells
look like donuts in a phase-contrast microscope (Goldstein,
1990).
The halo effect and the shading-off effect can be
reduced by decreasing the size of the annulus on the phase
ring and the phase plate. Although reducing the nondiffracted light reduces the brightness of the image, this
is no longer a problem when we use bright light sources
and cameras with sensitive imaging chips. The unwanted
introduction of halos can be minimized by surrounding both sides of the annular ring on the phase plate with
neutral density filters in a process known as apodization,
which literally means “removing the foot.” By reducing the intensity of light diffracted at small angles, apodized lenses increase the contrast of small details at the
expense of losing the contrast of large details. The halo
and shading-off effects can be completely eliminated by
using an interference microscope in which the nondiffracted and diffracted beams are completely separated (see
Chapter 8).
When given information about the specimen, the illuminating light, and the type of phase-contrast microscope,
we can determine the nature of the image produced by the
phase-contrast microscope using the following recipe:
1. Read the problem.
2. Identify the important pieces of information in the
problem.
3. Convert the information into mathematical symbols
(e.g., vectors).
a. Determine the optical path length of the object
(OPLo).
b. Determine optical path length of the surround
(OPLs).
c. Determine the optical path difference (OPD OPLo OPLo).
Since OPLi niti, A, B, and C require knowledge
of the thicknesses and refractive indices.
d. Determine the phase angle (ϕ). This requires
knowledge of the OPD and the wavelength of
light (λ).
e. Plot the vector (OA) that represents the direct
light (ϕ 0o, length 1 by convention).
f. Plot the image vector that represents the
interference of the direct and deviated light (OP).
g. By subtraction, determine the vector that
represents the deviated light (AP).
h. Determine the type of phase-contrast microscope.
Is the direct light advanced or retarded? By how
much? Is it reduced in amplitude? Plot vector
OA to represent these changes.
i. Since the deviated light represented by AP is
unchanged, move the vector AP so that its tail is
attached to the head of vector OA and the angle
(relative to the horizontal) is unchanged. This
new vector is called AP.
j. Now find the vector sum of OA, which represents
the direct light and AP, which represents the
deviated light. The sum of these two vectors gives
the vector that represents the image.
For example: Describe the image of a 10,000 nm thick
cell that contains 5 percent protein when it is immersed in
water and viewed with 500 nm light in a positive phasecontrast microscope.
OPD OPL o OPLs
OPLs (1.333) 10,000 nm
OPL o [1.333 5(0.0018)] 10,0000 nm
OPD 5(0.0018) 10,000 nm 90 nm
(360 500 nm) 90 nm 64.8
108
Light and Video Microscopy
the waves that experience a higher refractive index will be
shorter than the waves that experience a lower refractive
index (Fresnel, 1827–1829). This can be easily visualized
by using Huygens Principle.
We can take advantage of the fact that the deviated
light is the sum of two component vectors by illuminating the specimen with oblique illumination and capturing either the positive orders or the negative orders from
each side of a given detail, but not both diffraction orders.
Consequently, the image of one side of a detail will be
constructed from the interference of the positive orders
and the undeviated light and the image of the other side of
the detail will be formed from the interference of the negative orders and the undeviated light. The image from the
middle of the detail will be constructed from some of
the positive orders, some of the negative orders, and the
undeviated light. Consequently, one side of the detail will
be bright, the other side will be dark, and the middle will be
invisible. Such an image will appear three-dimensional,
but the pseudo-relief image does not represent the actual
three-dimensional structure. The pseudo-relief image
results from the fact that the gradient in optical path length
is positive on one side of a detail and negative on the other
side. In Chapters 9 and 10, I will discuss differential interference microscopy and modulation contrast microscopy,
two other optical ways to obtain a pseudo-relief image. In
The image is dark on a bright background. How would
the image look if we observed it with 360 nm light?
There are many elegant and creative ways to design
phase-contrast microscopes that let you visualize invisible
specimens. Some of these designs utilize polarized light
and some utilize interferometers (Pluta, 1989).
OBLIQUE ILLUMINATION RECONSIDERED
Details in a transparent biological specimen typically
retard the deviated light by λ/4 relative to the undeviated
light and consequently are invisible in a bright-field microscope (Zernike, 1955, 1958; Francon, 1961; Ellis, 1978;
Kalchar, 1985). The vector that represents the λ/4 retardation, however, can be resolved into two component vectors,
one that represents the light diffracted into the positive
orders and one that represents the light diffracted into the
negative orders (Figure 6-17).
The diffraction spectra of the positive and negative
orders are not symmetrical because on one side of a vesicle, for example, the waves emitted by a particle will go
through a medium with higher refractive index than the
waves that go through the other side. Because the velocity of light is inversely proportional to the refractive index,
Bright Dark
A
A
O
c
P
Image
a
b
P
P
P
Objective
a
b
O
A
P
O
c
A
P
O
1
2
3
0 0 12 3
1
0
1
b
A
P
a
c
Specimen
Sub-stage
Condenser
Oblique stop
FIGURE 6-17 Vector representation of the generation of a pseudo-relief image by oblique illumination. Notice that the negative diffracted orders
produce a dark image and the positive diffracted orders produce a bright image. The difference in refractive index between an object and the surround
leads to a difference in the wavelength of Huygens wavelets passing through the object and the surround. Consequently, the diffraction pattern created
by the interface of the object and surround is tilted left or right, depending on the direction of the difference in the refractive indices of the object and
the surround. When using oblique illumination, the objective lens preferentially captures the positive diffraction orders from one side of the object and
the negative diffraction orders from the other side of the object to produce a pseudo-relief image.
Chapter | 6 Methods of Generating Contrast
Chapter 14, I will discuss how a pseudo-relief image can
be produced electronically and numerically.
ANNULAR ILLUMINATION
Another casualty of the great sub-stage condenser wars of
the nineteenth century was the use of annular illumination.
With this method, an annulus that allows only the most
oblique rays to enter the objective is placed in the front focal
plane of the sub-stage condenser (Shadbolt, 1850, 1851;
Carpenter, 1883; Gordon, 1907; Spitta, 1907; Hallimond,
1947; Mathews, 1953). When using annular illumination,
the numerical apertures of the sub-stage condenser and the
objective lens should be identical. When using annular illumination, as opposed to Köhler illumination, the resulting
image is formed only from the oblique light that produces
109
images with the greatest resolution, and is not formed from
the axial light that forms low resolution images.
Annular illumination lost out to Köhler illumination,
in part, because the introduction of photomicrography and
its slow films required the brightest possible light sources.
However, by using annular illumination combined with
monochromatic polarized light, the “mixture of a multitude
of partial images” is further reduced, and the resolution of
the final image is astonishing, although the image is somewhat low in contrast. With bright light sources, sensitive
imaging chips, and contrast-enhancing digital image
processors, there is no reason why all microscopes should
not be equipped with annular illumination as a standard
feature in order to maximize the resolving power of the
light microscope. For a short time, the Unitron Corporation
produced a phase microscope that had an annular illuminator and no phase plate.
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Chapter 7
Polarization Microscopy
When we draw a picture of a light wave without thinking
deeply, we usually draw a linearly polarized light wave
because a linearly polarized wave is the simplest form of
a wave. Because linearly polarized light is so simple compared with common nonpolarized light, it acts as a convenient and unencumbered tool to probe the physicochemical
properties of matter. Polarized light microscopy has been
used to determine the identity of molecules, their spatial
orientation in biological specimens, and even their thermodynamic properties. Although polarized light is simpler
than common light, there are many things to keep straight
before we become comfortable with polarized light. For
that reason, I present the information in the following
chapter to my students in four 65-minute lectures, replete
with hands-on demonstrations that give virtual witness to
the experiments done by the masters who discovered the
properties of polarized light and birefringent crystals. The
purpose of the first lecture is to help the students become
comfortable with linearly polarized light. The second lecture helps the students become comfortable with specimens that are able to convert linearly polarized light into
elliptically polarized light as a consequence of having two
indices of refraction. The third lecture helps students learn
the elegant ways to quantify the degree of ellipticity of
the light so they can make inferences about the chemical
nature of the specimen and the orientation of the birefringent molecules. In the fourth lecture, I provide examples of
how polarized light microscopy has been used thoughtfully
and creatively to peek into the world of nanometer dimensions in living cells.
WHAT IS POLARIZED LIGHT?
Common or natural light is composed of sinusoidal waves
of equal amplitude where all azimuths of the vibration of the
electric field are represented equally. In end-view, the propagating light would look like Figures 7-1A and 7-1B. By
contrast, when the light is polarized, all the azimuths of the
vibration of the electric field are not represented equally. In
partially polarized light, some azimuths are underrepresented
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
compared with others, or put another way, the amplitude of
the electric field of some of the waves is less than the amplitude of the electric field of other waves. In end-view, the propagating partially polarized light may look like Figure 7-1C.
In fully polarized light, coherent, sinusoidal oscillations
propagate with a helical motion that appears as an ellipse in
end-view. Polarized light propagating helically is known as
elliptically polarized light (Figure 7-1E). In the special case,
where the minor and major axes of the ellipse are equal,
elliptically polarized light is called circularly polarized light
(Figure 7-1E). In another special case where the minor axis of
the ellipse vanishes, the light is known as linearly polarized
light (Figure 7-1F, G). This is the form of polarized light
we usually use to illuminate an object when doing polarized
light microscopy
A linearly polarized light wave with an angular wave
number kx (2π/λ, in 1/m), an angular frequency ω
(2πν, in rad/s), and a phase angle ϕ (in radians) propagates along the x-axis with the electric field (E) vibrating
in the xy plane or the xz plane, perpendicular to the propagation vector, is described by the following equations:
E y (x,t) E oy cos θ y (sin (k x x ωt ϕ))
E z (x,t) E oz sin θ y (sin (k x x ωt ϕ))
where θy is the angle that the electric field makes in the
yz plane with respect to the y-axis. The angles are positive for a counterclockwise rotation. These angles specify
the azimuth of the linearly polarized light. When θy 0°,
the plane of vibration is along the xy plane and the light
wave is said to be linearly polarized in the y direction.
When θy 90°, the plane of vibration is along the xz plane
and the light wave is said to be linearly polarized in the z
direction. Light that vibrates along any arbitrary plane at
an angle relative to the xy plane can be formed by combining two orthogonal waves that are in-phase (ϕ 0). When
a wave linearly polarized along the xy plane combines
with a wave with the same amplitude, but linearly polarized along the xz plane, a linearly polarized resultant wave
whose plane of vibration is in a plane 45 degrees relative
to the xy-plane results.
111
112
A
E
Light and Video Microscopy
FIGURE 7-1 Common (A,B), partially-polarized (C) and elliptically(D), circularly- (E) and linearly(F,G) polarized light.
B
C
D
F
When the two orthogonal component waves have
unequal amplitudes, the azimuth of the resultant will be at
an angle relative to the xy plane, closer to the wave with
the greatest amplitude. The azimuth of the resultant linearly
polarized wave can be easily determined by adding vectors
that represent the maximal amplitude of the two linearly
polarized component waves. Here is a good time to stress
that not only does the vector sum of two component waves
give rise to the resultant, but every resultant can be viewed
as being composed of two orthogonal components. This
is the “double reality” of vectors and light (Figure 7-2).
In order to help us understand the various kinds of
polarized light we can use a rope or long skinny spring.
One person holds the rope or spring still and the other person moves his or her hand up and down in a straight vertical
line (Figure 7-3). The wave generated in the rope or spring
moves from one person’s hand to the other person’s hand.
The energy in the wave causes each point of the rope or
spring to move up and down. While the wave moves from
one person to the other, the rope or spring does not move
sideways, but moves only up and down, forming a linearly
polarized wave whose azimuth of polarization is vertical.
If the second person moves his or her hand back and
forth horizontally while the first person holds his or her
hand still, the energy in the wave will cause each point
of the rope or spring to move from side-to-side, forming
a linearly polarized wave whose azimuth of polarization is
horizontal or orthogonal to the vertically polarized wave.
If both people move their hands with equal amplitude
at the same time, one vertically, and the other horizontally,
a spiraling motion will move down the rope or spring, and
each point of the rope or spring will move in a circular
motion, forming a circularly polarized wave with two axes
of equal length. We can decompose this wave by looking
at the shadow of this circularly polarized rope or spring
wave on the vertical wall. It will look just like the vertically polarized wave. Now look at the shadow on the horizontal floor. It will look just like the horizontally polarized
wave. We can consider the circularly polarized waves to be
a combination of two linearly polarized waves. Elliptically
polarized light is also a combination of two linearly polarized waves, except that the amplitude of the up-and-down
motion differs from the amplitude of the side-to-side
G
y
AxA cos A
Ay
Ay = A Sin Ax
x
FIGURE 7-2 The resultant of two coherent waves is determined by
finding the vector sum of the components. Moreover, any single wave can
be viewed as being composed of two orthogonal components. This is the
“double reality” of vectors and light.
FIGURE 7-3 Demonstration of transverse waves with a rope or long
spring.
motion. Professor Wheatstone designed a mechanical
apparatus to demonstrate the interaction of two orthogonal
linearly polarized waves (Pereira, 1854).
In biological polarization microscopy, elliptically
polarized light usually is not produced by the combination
of two orthogonal linearly polarized waves with different
amplitudes, but by the combination of two orthogonal linearly polarized waves with different phases.
E θ (x,t) E y (x,t) E z (x,t) y E oy (sin (k x x
ωt ϕ1 )) z E oz (si n (k x x ωt ϕ 2 ))
Letting Δϕ ϕ2 ϕ1
E θ (x,t) y E oy (sin (k x x ωt))
z E oz (sin (k x x ωt Δϕ))
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Chapter | 7 Polarization Microscopy
E θ (x,t) E o ((sin (k x x ωt))
(sin (k x x ωt Δϕ )))
Since sin (A B) sin A cos B cos A sin B
E θ (x,t) E o [(sin (k x x ωt))
(sin(k x x ω t) cos (Δϕ ))
sinθ y (cos(k x x ϕt) sin (Δϕ))]
When the phases of two orthogonal linearly polarized
waves of equal amplitude differ by an even integral multiple (m) of mπ, the resultant will be linearly polarized.
When the phases of two orthogonal linearly polarized
waves of equal magnitude differ by an odd integral multiple
(m) of mπ, the resultant will also be linearly polarized,
but the vibrations of the electric field will be orthogonal to
the vibrations produced by the result formed by two waves
an even integral multiple of π. When the phases of two
orthogonal linearly polarized waves of equal amplitude
differ by π/2 (90°), the resultant will be circularly
polarized. As we will discuss in detail later, any other difference in phase angle gives rise to elliptically polarized
light that describes a helix as the light propagates.
Sound waves, which are composed of longitudinal
waves that vibrate parallel to the axis of propagation,
cannot be linearly polarized. Since the concept of light
waves developed out of the concept of sound waves (see
Chapter 3), it was reasonable to assume prima facie that
light waves were also longitudinally polarized. However,
Thomas Young and Augustin Fresnel realized that light
must be composed, at least in part, of transverse waves that
vibrate perpendicular to the axis of propagation, because
light, unlike sound, could be linearly polarized. Young’s
and Fresnel’s radical proposal of the transverse nature of
light was difficult for many to accept because of the implications it had for the mechanical nature of the luminous
ether though which transverse were thought to propagate
(Peacock, 1855; Cajori, 1916; Whittaker, 1951; Shurcliff
and Ballard, 1964). Maxwell (1891) concluded that electromagnetic light waves were exclusively transversely
polarized, when he obtained a solution for the propagation
of electromagnetic waves in free space that had only transverse components. Maxwell’s elimination of the longitudinal component of electromagnetic waves resulted from his
assumption that the electromagnetic waves in free space
had neither a source nor a sink.
FitzGerald (1896) and Roentgen (1899) tried to revive
the idea that electromagnetic radiation might have a longitudinal component, but to a scientific community that had
finally accepted the transverse nature of light, the reintroduction of a longitudinal component of electromagnetic
waves was just too radical. The nature of the polarization
of light is still mysterious. Quantum mechanics is unable
to say whether a single photon is linearly polarized or circularly polarized (Dirac, 1958).
USE AN ANALYZER TO TEST
FOR POLARIZED LIGHT
We can test whether or not light is linearly polarized by
using an analyzer. One such analyzer is tourmaline, a colorful precious gem made out of various combinations of
boron silicate. Tourmaline is considered dichroic, since
it absorbs certain wavelengths of light vibrating in one
direction but not in the orthogonal direction (Brewster,
1833b). Consequently, the color of tourmaline, like the
colors of sapphires and rubies, depends on the azimuth of
the incoming light (Pye, 2001). In one azimuth of polarization, sapphires and rubies pass only blue light and red
light, respectively, while they pass white light in all other
azimuths.
Edwin Land developed a synthetic crystal, known as a
Polaroid, which has the ability to absorb all wavelengths of
visible light that are vibrating in a certain azimuth. Light
that is vibrating orthogonally to the azimuth of maximal
absorption is transmitted by the Polaroid. Light that is
vibrating at any other angle is transmitted according to the
following relation, known as the Law of Malus:
I I o cos2 θ
where I is the transmitted intensity, Io is the incident intensity, and θ is the angle between the azimuth of transmission
of the analyzer and the azimuth of the incident light. Thus,
if the intensity of light transmitted through the analyzer
varies according to this relation as one turns the analyzer,
then the incident light can be said to be linearly polarized.
When the axis of maximal transmission of the analyzer
is parallel to the azimuth of polarization (cos2 θ = 1), the
interaction with the analyzer is minimal and light passes
through the analyzer. When the axis of maximal transmission of the analyzer is orthogonal to the azimuth of polarization (cos2 θ = 0), the interaction is maximal, and no light
passes through the analyzer.
Edwin Land originally made Polaroids (of the J type) out
of sulphate of iodo-quinine crystals or herapthite embedded
in cellulose acetate. Herapathite was serendipitously discovered by the physician William Bird Herapath. Herapath
and his student, Mr. Phelps, fed a dog quinine, which is a
drug isolated from the bark of the fever-bark tree and is used
to treat malaria. When they added iodine to the dog’s urine
as part of a microchemical test for quinine (Gage, 1891;
Hogg, 1898), they noticed little scintillating green crystals.
Herapath looked at the crystals in a microscope and noticed
they were light or dark in some places where they overlapped and realized that they had discovered a new semisynthetic dichroic material (Figure 7-4; Herapath, 1852;
Herschel, 1876; Grabau, 1938; Land, 1951).
Land, while a nineteen-year-old undergraduate student
at Harvard University, read the second edition of David
Brewster’s (1858) book on the kaleidoscope. Brewster
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Light and Video Microscopy
PRODUCTION OF POLARIZED LIGHT
FIGURE 7-4 Herapath discovered that the crystals that formed in the
iodine-stained urine of a dog that had been fed quinine were either bright
or dark in the places where they overlapped. Since their transparency or
opacity of the thin crystals depended on their mutual orientation, he realized that they produced polarized light and he had discovered that “the
most powerful polarizing substance known … proved to be a new salt of
a vegetable alkaloid.”
wrote in this book that he dreamed of making plates of herapathite that were large enough and strong enough to use in
kaleidoscopes because such kaleidoscopes would produce
beautiful and intense interference colors from transparent
crystals (see later), instead of the less-brilliant absorption
colors produced by colored glass. Large flat herapathite
crystals were too brittle to be used in the kaleidoscopes.
Land had the idea of making large, stable, dichroic sheets
by embedding millions of tiny crystals of herapathite
in a gelatin medium. The medium was then subjected to
mechanical stress in order to align the crystals so that their
axes of maximal absorption were all coaligned. The H-type
Polaroid sheets that are used today are made totally from
synthetic crystals that are aligned by mechanical stress.
Land (1951) wrote about his motivation:
Herapath’s work caught the attention of Sir David Brewster, who
was working in those happy days on the kaleidoscope. Brewster
thought that it would be more interesting to have interference
colors in his kaleidoscope than it would to have just differentcolored pieces of glass. The kaleidoscope was the television of
the 1850’s and no respectable home would be without a kaleidoscope in the middle of the library. Brewster, who invented the
kaleidoscope, wrote a book about it and in that book he mentioned that he would like to use the herapathite crystals for the
eye piece. When I was reading this book back in 1926 and 1927,
I came across his reference to these remarkable crystals and that
started my interest in herapathite.
Edwin Land left Harvard University after his freshman
year so that he could spend his time developing his polarizer, and founded the Polaroid Corporation (Wensberg,
1987; McElheny, 1999).
Any material that can analyze polarized light can also be
used to produce polarized light. Thus a Polaroid will convert nonpolarized light into linearly polarized light by
absorbing light of all but one azimuth. Any device that
converts nonpolarized light into polarized light is called
a polarizer. In microscopy, Polaroids typically are used to
polarize light and to analyze it.
Crystals beside those found in Polaroids can be used to
polarize light, and historically, calcite was the first crystal
that was found to have the ability to polarize light. Before
the discovery of calcite, there was not any reason to think
that there were any hidden asymmetries in light that would
allow it to be polarized, be it a corpuscle or a longitudinal
wave. The discovery of calcite changed our view of light.
When nonpolarized light strikes a piece of calcite,
it is resolved into two beams of light—the ordinary and
the extraordinary light. The ordinary light experiences an
index of refraction of 1.658 and the extraordinary light
experiences an index of refraction from 1.486 to 1.658,
depending on the relative orientation of the light wave and
the crystal. Since calcite has two indices of refraction, it is
known as a birefringent material. A birefringent material,
if it is thick enough, has the ability to doubly refract light,
causing a single beam of light to diverge into two beams.
According to Newton (1730), “If a piece of this crystalline
stone be laid upon a book, every letter of the book seen
through it will appear double, by means of a double
refraction.”
The amazing properties of calcite were first discovered by Erasmus Bartholinus (1669). While playing with
a piece of the newly discovered Iceland Spar (now called
calcite), Bartholinus noticed that the transmitted light produced two images as if the incident light beam were split
into two transmitted beams (Figure 7-5). One of the images
precessed around the other image as he turned the crystal of calcite. The plane of the crystal that contains both
the ordinary ray and the extraordinary ray is known as
the principal section. Bartholinus named the rays that
formed the stationary image, the ordinary rays since they
acted like they passed though an ordinary piece of glass
and obeyed the ordinary laws of refraction. He called the
rays that made the precessing image, the extraordinary
rays, since they behaved in an extraordinary manner.
Bartholinus wrote,
Everyone praises the beauty of the diamond, and indeed jewels,
gems, and pearls can give many pleasures. Yet they serve only in
idle display on finger and neck. I hope that those of my readers for
whom knowledge is more important than mere diversion will derive
at least as much pleasure from learning about a new substance,
lately brought back to us from Iceland as transparent crystals.
Huygens (1690) explained the double refraction discovered by Bartholinus in terms of wave theory. He proposed that the atoms in the calcite acted asymmetrically
115
Chapter | 7 Polarization Microscopy
Calcite Rhomb
FIGURE 7-5
Bartholinus noticed that the light transmitted through a piece of calcite formed two images and must therefore be split into two beams.
o
e
o
e
FIGURE 7-6 Huygens explained double refraction in terms of wave theory. He proposed that the atoms in the calcite acted asymmetrically upon the
incoming light so that the waves that made up the ordinary beam were spherical and passed straight through the crystal, whereas the waves that made
up the extraordinary beam were elliptical and traveled diagonally through the crystal. If he rotated the crystal while he viewed the double image through
the top of crystal, the image produced by the ordinary ray (o) would remain stationary while the image produced by the extraordinary ray would precess
around the ordinary image.
upon the incoming light so that the waves that made up the
ordinary beam were spherical and the waves that made up
the extraordinary beam were elliptical (Figure 7-6). This
would result in an ordinary beam that was circular in outline when viewed end-on and an extraordinary beam that
was elliptical when viewed end-on. Huygens, however, was
at a loss to come up with anything more mechanistic and
wrote, “But to tell how this occurs, I have hitherto found
nothing which satisfies me.” Newton (1730) explained
the double refraction in terms of corpuscular theory, and
concluded that the asymmetries in the atoms of the calcite
acted upon corpuscles that had sides of various lengths and
therefore were accelerated through the calcite in a manner
that depended on which side of the corpuscle interacted
with the calcite.
Huygens (1690) and Newton (1730) performed experiments with two pieces of calcite that clearly demonstrated
that a crystal of calcite could resolve common light into two
components that differ in their polarity and that a second
prism could recombine the two components to form common light. These experiments are analogous to those that
were done by Newton, where he showed that one prism can
resolve white light into its chromatic components and a second prism can recombine the chromatic components to form
white light, and have become a classic way to experience the
marvels and mysteries of polarized light (Brewster, 1933).
116
The description given here is lengthy so that anyone and
everyone can personally repeat these illustrative experiments that demonstrate the conversion of common light to
polarized light. These experiments can be done using a light
source and two inexpensive pieces of optical calcite that can
be obtained from the gift shop at a local science museum.
Make a pinhole in a piece of black poster board and
place the pinhole on a convenient light source like a flashlight or a light table. The light coming through the aperture
is common light. Place a piece of calcite on the aperture.
The beam of common light is split into two beams, the distance between the two depending on the thickness of the
calcite. We can tell the extraordinary beam from the ordinary beam by the way the extraordinary beam precesses
around the ordinary beam. When the ordinary and extraordinary beams are aligned in a line that extends to the two
obtuse angles of the crystal, the two beams are in a principal section that contains the optic axis of the crystal.
Place a second piece of calcite with a similar thickness
on top of the first so that the two crystals have the same
orientation. In this orientation, the principal sections are
parallel, and each beam produced by the first crystal is not
divided into two, but rather the two beams produced by
the first crystal are further separated by the second crystal.
The beam that underwent an ordinary refraction in the first
crystal undergoes an ordinary refraction in the second crystal and the beam that underwent an extraordinary refraction
in the first crystal undergoes an extraordinary refraction in
the second crystal. The distance between the ordinary and
extraordinary beams emerging from the second crystal is
equal to the sum of the distances that would be produced
by each crystal separately. Huygens (1690) felt “it is marvelous” why the beams incident from the air on the second
crystal do not divide themselves the same as the beam that
enters the first crystal. He first hypothesized that, in passing through the first crystal, the ordinary beam “lost something which is necessary to move the matter which serves
for the irregular refraction …” and the extraordinary beam
“lost that which was necessary to move the matter which
serves for regular refraction.”
When the top crystal is turned 90 degrees so that the
principal sections of the two crystals are perpendicular, the
two beams that emerged from the second crystal disappear
and two new beams appear that are oriented diagonally with
respect to the original beams and are closer together. This
can be explained if the ordinary beam from the first crystal
becomes the extraordinary beam in the second crystal and
the extraordinary beam from the first crystal becomes the
ordinary beam in the second crystal. Thus Huygens’ first
hypothesis was wrong; the ordinary beam that exits the first
crystal is still able to undergo an extraordinary refraction
and the extraordinary beam that exits the first crystal is still
able to undergo an ordinary refraction.
When the top crystal is rotated from 0 to 90 degrees,
the brightness of the beams decreases with the square of
Light and Video Microscopy
the cosine of the angle between the two principal sections.
By contrast, the brightness of the newly emergent beams
increases with the square of the sine of the angle between
the two principal sections. The two beams that emerge
when the principal sections of the crystals are perpendicular to each other are equally bright and have the same
brightness as the two beams had when the principal sections were parallel to each other. Each of the four beams
produced at 45 degrees is half as bright as each of the two
beams produced at 0 and 90 degrees.
When the top crystal is rotated from 90 to 135 degrees,
the brightness of the two beams present at 90 degrees
decreases as the brightness of two new beams oriented
diagonally relative to the two beams present at 90 degrees
increases. The four beams present at 135 degrees are mirror images to the four beams present at 45 degrees.
When the top crystal is rotated a total of 180 degrees so
that the principal sections of the two crystals are again parallel, the two original rays merge into a single beam. The
single beam is twice as bright as each of the two beams
present at 0 and 90 degrees and four times as bright as
each beam present at 45 and 135 degrees. The single beam
emerging from the two crystals oriented with their principal sections 180 degrees relative to each other has all the
characteristics of common light.
Huygens concluded that the “waves of light, after having passed through the first crystal, acquire a certain form
or disposition in virtue of which, when meeting the texture
of the second crystal, in certain positions, they can move the
two different kinds of matter which serve for the two species
of refraction and when meeting the second crystal in another
position are able to move only one of these kinds of matter.”
Huygens realized that the waves had become polarized
after passing through the first medium, but since he had no
conception of the possibility of transverse waves, he was at
a loss to explain how they became polarized. Huygens also
realized that the calcite crystal itself had “two different
kinds of matter which serve for the two species of refraction,” but since he had no conception of the existence of
electrons and their electrical polarization, he “left to others
this research….”
According to David Brewster (1833b),
The method of producing polarized light by double refraction is
of all others the best, as we can procure by this means from a
given pencil of light a stronger polarized beam than in any other
way. Through a thickness of three inches of Iceland spar we can
obtain two separate beams of polarized light one third of an inch
in diameter; and each of these beams contain half the light of
the original beam, excepting the small quantity of light lost by
reflexion and absorption. By sticking a black wafer on the spar
opposite either of these beams, we can procure a polarized beam
with its plane of polarization either in the principal section or at
right angles to it. In all experiments on this subject, the reader
should recollect that every beam of polarized light, whether it is
produced by the ordinary or the extraordinary refraction, or by
positive or negative crystals, has always the same properties, provided the plane of its polarization has the same direction.
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Chapter | 7 Polarization Microscopy
These experiments indicated that common light is
composed of two types of polarized light with orthogonal
planes of polarization. Calcite splits common light into two
orthogonal beams, one that is polarized parallel to the principal section and one that is polarized perpendicular to the
principal section. The plane of polarization in the minds
of Huygens, Newton, and Brewster was not related to the
plane of vibration in our minds, because they did not know
of and/or accept the idea of transverse waves.
Until 1808, it seemed that double refraction was the only
means by which transparent substances could polarize light.
Then Ethienne Louis Malus, a proponent of the corpuscular
theory of light, discovered that polarized light can also be
produced by reflection from common transparent substances
such as glass and water. While in his home in the Rue
d’Enfer looking through a calcite crystal at the light from
the sunset reflected from a window in Luxembourg Palace,
Malus discovered that the light that was reflected from the
castle windows was polarized. That is, instead of seeing two
images of the reflected light when he looked through a calcite crystal, he saw only one. Depending on how he rotated
the crystal, the image was made from the ordinary or the
extraordinary beam. Before going to sleep that night, Malus
showed that although candle light viewed directly through
calcite produces two images, candle light viewed through
calcite after it was reflected from a plate of glass or a pan
of water produces only one (Arago, 1859a; Towne, 1988).
Malus (in Whittaker, 1951) found that
… light reflected by the surface of water at an angle of 52° 45’ has
all the characteristics of one of the beams produced by the double
refraction of Iceland spar, whose principal section is parallel to the
plane which passes through the incident ray and the reflected ray.
If we receive this reflected ray on any doubly refracting crystal,
whose principle section is parallel to the plane of reflection, it will
not be divided into two beams as a ray of ordinary light would be,
but will be refracted according to the ordinary law.
When Malus held the calcite crystal so that its principal
section was parallel to the plane of incidence (which is the
plane that includes the incident ray and the reflected ray), he
saw only the ordinary ray and concluded that the ordinary
ray was polarized parallel to the principal section. When
he held the calcite crystal so that its principal section was
perpendicular to the plane that passes through the incident
ray and the reflected ray, he saw only the extraordinary ray
and concluded that the extraordinary beam was polarized
perpendicular to the principal section. Malus (in Herschel,
1876) concluded, “that light acquires properties which are
relative only to the sides of the ray—which are the same
for the north and south sides of the ray” (i.e., of a vertical
ray), “using the points of a compass for description’s sake
only….” Malus defined the plane of polarization of the ordinary ray as being parallel to the principal section of calcite
and the plane of polarization of the extraordinary ray as
being perpendicular to the principal section (Knight, 1867).
Pereira (1853) confirmed that the azimuths of polarization
of the ordinary and extraordinary beams are orthogonally
polarized by using a plate of tourmaline to analyze the ordinary and extraordinary beam. He found that as he rotated the
analyzer, the two beams were alternately extinguished, indicating that the two beams were linearly polarized perpendicularly to each other (Tyndall, 1873, 1887). By 1821, Fresnel,
a proponent of the wave theory of light, was questioning the
arbitrariness of the “plane of polarization” and wondered
what the relationship was between the plane of vibration and
the plane of polarization (Whittaker, 1951).
Although the experiments done by Brewster and Malus
illustrate the differences between common light and polarized light, they are tricky to follow in the twenty-first century because the definition of the plane of polarization
they used differs from our current definition (Brewster,
1833b; Stokes, 1852; Arago, 1859a, 1859b, 1859c; Preston,
1895; Schuster, 1909; Jenkins and White, 1937; Strong,
1959; Hecht and Zajac, 1974; Born and Wolf, 1980; Collett,
1993; Niedrig, 1999; Goldstein 2003). Malus arbitrarily
defined the plane of polarization of light as the “plane
which passes through the incident ray and the reflected
ray.” However, in the mid-to-late nineteenth century, after
Maxwell showed that the refractive index depended on the
electrical permittivity of a substance, it became clear that
optical phenomena resulted from the action of matter on the
vibrating electric field of light, and consequently the plane
of polarization became redefined to mean the plane of vibration of the electric field. Arago (1859a; p. 153) wrote “…
it was long a disputed question whether the vibrations of
which they [light waves] consist, according to the wave theory, are actually performed in those planes or perpendicular
to them; the later has now been shown to be the fact.”
Using the current definitions, the electric field of the
extraordinary wave vibrates parallel to the principal section of calcite and the electric field of the ordinary wave
vibrates perpendicular to the principal section. Since the
principal section contains the optic axis of the crystal, the
electric field of the extraordinary wave vibrates parallel to
the optic axis and the electric field of the ordinary wave
vibrates perpendicular to the optic axis. Moreover, when
light is reflected from a dielectric, the reflected wave is linearly polarized parallel to the surface of the dielectric.
David Brewster (1815a) quantified Malus’ observations
on the polarization of light by reflection. Brewster found
that the degree of polarization in the reflected light is maximal when the angle of incidence (relative to the normal)
is equal to the arc tangent of the refractive index of the
reflecting surface:
θ Brewster arc tan (n)
This angle is known as Brewster’s angle (Figure 7-7).
For glass, where the refractive index is 1.515, θBrewster is
56.57 degrees. Reflection is not a really useful way of
118
Light and Video Microscopy
E
Reflected ray
Incident ray
Sunlight
E
57
Scattering molecule
57
Glass plate
E
FIGURE 7-7 Production of polarized light by reflection at Brewster’s
angle. According to Malus, the “plane of polarization” was the plane that
included the incident ray and the reflected ray.
Eye
obtaining polarized light for polarized light microscopy,
but it is a useful way to determine the orientation of a laboratory polarizer. When we look through an analyzer at the
glare reflected off a desktop or floor, and turn the analyzer
to the position where the glare is maximal, we know that the
azimuth of maximal transmission is parallel to the reflective surface. When we rotate the analyzer to the position
that gives maximal extinction, we know that the azimuth
of maximal transmission is perpendicular to the surface of
the reflector. This is how Polaroid sunglasses work!
Polarized light can also be produced by scattering
(Figure 7-8). When nonpolarized light interacts with atoms
or small molecules compared with the wavelength of
light, the atoms or molecules scatter the light in all directions (Rayleigh, 1870). This includes the molecules in the
atmosphere. When one looks at the sky in a direction perpendicular to the sun’s rays, the light coming toward one’s
eyes is linearly polarized (Können, 1985). The vibration
is perpendicular to the plane made by the ray of the sun
to the radiating molecule and the ray from the molecule
to the eye. We can also use the polarization of skylight to
tell the orientation of a laboratory analyzer. When the analyzer is rotated to the position where the sky appears maximally dark, the analyzer is oriented with it axis of maximal
absorption vertical, and its axis of maximal transmittance
horizontal.
We can detect polarized light with the rods in our eyes
only under very specialized conditions, but typically we
cannot detect the azimuth of polarized light (Minnaert,
1954). On the other hand, fish and bees can see and use
the polarization of light to gather information about their
world (Hawryshyn, 1992; Horváth and Varjú, 2004). Karl
von Frisch (1950) showed that bees use the polarization of
skylight to guide their flight and dances. Typically, when
FIGURE 7-8 Production of polarized light by scattering sunlight from
the molecules in the atmosphere.
bees return home after finding a good source of honey, they
perform a dance that points in the direction of the honey to
show the other bees in the hive where the honey is. When
von Frisch experimentally altered the polarization of the
skylight by using Polaroids, the dance, too, was altered and
the bees no longer pointed in the direction of the honey.
As an aside on skylight, the intensity of the scattered
light, compared to the light that passes straight through the
atoms, molecules or particles is inversely proportional to
the fourth power of the wavelength. Therefore, when we
look at the sky anywhere except directly in the direction
of the overhead sun, it appears blue (Rayleigh, 1870). This
was first appreciated by Leonardo da Vinci in the 1500s.
When we look directly at the sun at sunrise or sunset, it
appears red since all the shorter wavelengths have been
scattered away by the dust and/or water drops in the atmosphere by the time the light reaches our eyes.
Typically, there is little dust in the air in the morning, so
the sky will be red only if there are enough water droplets
in the air to scatter the light. Consequently, a red sky in the
morning indicates rain. At the end of a typical day, there is
a lot of dust in the air, so the sunset appears red. However,
if it is raining in the west, the rain will have washed away
most of the dust, which contributes to most of the scatter.
Consequently, the shorter wavelengths will have not been
scattered away and the sky will appear pale yellow, and
there will not be a “red sky at night” (Minnaert, 1954).
We have discussed what linearly polarized light is, how
to determine if light is linearly polarized, and how to produce linearly polarized light, as a result of dichroism, double
119
Chapter | 7 Polarization Microscopy
Polarizing axes
parallel
a
t
s
h
l r
Light
extinguished
Unpolarized
light
Polarizing axes
crossed
FIGURE 7-9 Extinguishing polarized light using a polarizer whose azimuth of maximal transmission is perpendicular to the azimuth of the linearly polarized light formed by the polarizer.
refraction, reflection, and scattering. Now we are ready to
see how molecules that can produce linearly polarized light
can influence the light that passes through crossed polars.
INFLUENCING LIGHT
All dichroic and birefringent materials that are able to
polarize and analyze light also are able to influence the
light that passes through crossed polars.
Two pieces of dichroic or birefringent material can
be set up such that the first element, called the polarizer,
produces linearly polarized light, and the second element,
known as the analyzer, can block the passage of the linearly polarized light (Figure 7-9). The equation that
describes the intensity of the light that passes through two
polars is known as the Law of Malus:
I I o cos2 θ
where θ is the angle made by the axes of maximal transmission of both polars.
In 1811, Francois Arago invented a polariscope to visualize the effect of a given substance on the polarization of
light. A polariscope is a tube with a polarizer on one end
and an analyzer at the other. (A polarimeter, by contrast, is
a polariscope in which the analyzer can be turned in a graduated and calibrated manner.) In a polariscope, the polarizer and the analyzer are set orthogonally to each other so
that no light exits the analyzer. Tongs, consisting of two
pieces of tourmaline oriented orthogonally to each other,
were designed by Biot to investigate the ability of a substance to influence polarized light. When a sample of tourmaline or calcite that is able to influence polarized light is
inserted in the polariscope or in the tongs, light exits the
p
FIGURE 7-10 A polarimeter.
analyzer, even when in the crossed position. It turns out
that tourmaline and calcite are able to influence the linearly polarized light. In fact, any dichroic or birefringent
material that is capable of polarizing light and analyzing
polarized light, when placed in a certain position between
crossed polars, is capable of influencing linearly polarized
light, so that light exits the analyzer. Thus crossed polars
can be used to test whether or not a material is dichroic or
birefringent.
Unlike thick crystals of calcite, thin crystals of calcite do not visibly separate laterally the extraordinary ray
from the ordinary ray. The two rays are still orthogonally
polarized and show another spectacular phenomenon that
occurs when the rays partially overlap. Arago noticed that
some transparent crystals appeared colored when viewed
between crossed polars. Jean-Baptiste Biot discovered that,
for a given crystal, there was a relationship between the
thickness of the crystal and the colors produced. Moreover,
different types of crystals (e.g., gypsum, quartz, and mica)
with the same thickness produced different colors. Using
the polarimeter, Biot also discovered that liquids, including turpentine, oil of lemon, and oil of laurel were able of
influence linearly polarized light (Figure 7-10).
Biot proposed that the ability to influence polarized
light was a property of the molecules that constituted the
sample. In 1833, Biot showed that sucrose rotated the linearly polarized light to the right, but after it was heated
with dilute sulfuric acid, the sugar solution rotated the
linearly polarized light to the left—that is, the direction
was inverted. Biot also studied the breakdown of starch
into a compound he called dextrine, since it rotated the
linearly polarized light to the right. Biot made the initial
observations on the ability of tartaric acid to influence linearly polarized light. This set the foundation for the work
of Pasteur (1860), Le Bel, and van’t Hoff (1874, 1967) on
stereochemistry (Pereira, 1854; Freund, 1906; Jones, 1913;
Pye, 2001).
Louis Pasteur noticed that when he put tartar of wine,
which is composed of tartaric acid, in his polarimeter, it
rotated linear polarized light to the right. Oddly enough,
racemic acid, which had the same chemical formula
(C4H6O6), was unable to rotate the azimuth of polarized
light. Pasteur noticed that the sodium ammonium racemate
was composed of two kinds of crystals that were mirror
images of each other. One kind of crystal had right-sided
tetrahedral faces and the other kind had left-handed tetrahedral faces. He separated the two kinds of crystals with
120
tweezers and a magnifying glass. He then dissolved the
two groups separately and determined that the class with
the right-handed tetrahedral face rotated the linearly polarized light to the right and was like tartaric acid, and the
class with a left-handed tetrahedral face rotated the linearly polarized light to the left. When he mixed the two in
equal quantities, he reformed racemic acid, which no longer rotated the azimuth of linearly polarized light. Pasteur
concluded that racemic acid was a mixture of tartaric acid
and another chemical that was its mirror image. Le Bel and
van’t Hoff deduced that molecules that contained a carbon
atom that bound four different atoms were asymmetrical
and existed in a three-dimensional structure that could exist
in two forms that were related by mirror symmetry.
If mineral and biological specimens are able to influence linearly polarized light; and, if the manner in which
they influence linearly polarized light is a property of their
molecular constituents, wouldn’t it be reasonable to construct a polarizing light microscope to understand better,
the molecular constituents of nature?
DESIGN OF A POLARIZING MICROSCOPE
Images of specimens taken with a polarized light microscope are shown in color plates 7 through 11. Henry Fox
Talbot designed the first polarizing microscope, in which
he could detect a change in the azimuth of polarization
brought about by each point in the specimen. The polarizing microscope converts a change in the azimuth of polarization into a change in color and/or intensity. In designing
the first polarizing light microscope, Talbot (1834a) wrote,
Among the very numerous attempts which have been made of
late years to improve the microscope, I am not aware that it has
yet been proposed to illuminate the objects with polarized light.
But as such an idea is sufficiently simple and obvious, it is possible that some experiments of this kind may have been published,
although I am not acquainted with them. I have lately made this
branch of optics a subject of inquiry, and I have found it so rich
in beautiful results as entirely to surpass my expectations.
As little else is requisite to repeat the experiments which I am
about to mention than the possession of a good microscope,
I think that in describing them I shall render a service to that
numerous class of inquirers into nature, who are desirous of witnessing some of the most brilliant of optical phaenomena without
the embarrassment of having to manage any large or complicated
apparatus. And it cannot be without interest for the physiologist
and natural historian to present him with a method of microscopic inquiry, which exhibits objects in so peculiar a manner
that nothing resembling it can be produced by any arrangements
of the ordinary kind.
In order to view objects by polarized light, I place upon the stage
of the microscope a plate of tourmaline, through which the light
of the large concave mirror is transmitted before it reaches the
object lens. Another plate of tourmaline is placed between the
eyeglass and the eye; and this plate is capable of being turned
round in its own plane, so that the light always traverses both the
tourmalines perpendicularly.
Light and Video Microscopy
The goal of a well set-up polarizing microscope is to
generate contrast and to provide a bright image of an
anisotropic substance against a black background at high
resolution and high magnification. The degree to which the
background can be darkened is expressed quantitatively as
the extinction factor (EF):
EF I p /I c
where Ip and Ic is the intensity of light that comes through
the analyzer when the polarizer and analyzer are parallel and crossed, respectively. A typical polarizing microscope has an extinction factor of 1000. A good polarizing
microscope, like the one designed by Shinya Inoué, has
an extinction factor 10,000 or more (Inoué and Hyde,
1957; Inoué, 1986; Pluta, 1993). By convention, the azimuth of maximal transmission of the polarizer is oriented
in the east-west direction on the microscope (which, by
convention (ISO 8576), is left to right when facing the
microscope; Pluta, 1993; Figure 7-11) and the azimuth of
maximal transmission of the analyzer is oriented in the
north-south orientation (which, by convention, is front to
back. East, north, west, and south are considered to be 0,
90, 180, and 270 degrees, respectively, and when the polars
are crossed, the polarizer is at 0 degrees and the analyzer is
at 90 degrees.
In order to obtain maximal extinction, Talbot (1834a,
1834b) switched from using tourmaline for the polarizer
and analyzer to using calcite prisms designed by William
Nicol. According to Brewster (1833b), a single piece of calcite must be approximately three inches tall in order to separate the ordinary and extraordinary rays sufficiently to be
practical to use as a polarizer and analyzer. William Nicol
(1828, 1834, 1839) found an ingenious way to construct a
prism that could separate the ordinary ray from the extraordinary using a minimal length of calcite. He constructed
the prism out of a rhomboidal piece of calcite that he cut
into two pieces. He cemented the two pieces together with
Canada balsam, which has a refractive index intermediate
between the refractive index experienced by the ordinary
ray and the refractive index experienced by the extraordinary ray as they propagate through the calcite (Figure 7-12).
Nonpolarized light striking the first part of the prism is
resolved into the ordinary and extraordinary rays. When
the ordinary ray, which had been experiencing a refractive
index of 1.658, strikes the cement (n 1.55), it is reflected
away from the optical axis by total internal reflection. The
extraordinary ray, which had been experiencing a refractive
index of 1.486, is refracted through the cement interface and
emerges through the far end of the prism, yielding linearly
polarized light (Talbot, 1834b).
The Nicol prism gives extremely high extinction.
Moreover, since it is transparent and thus does not absorb
visible light, it is almost a perfect polarizer since it passes
50 percent of the incident light. Tourmaline and Polaroids,
121
Chapter | 7 Polarization Microscopy
Rotating
analyzer
Analyzer
N, 90
Position of
compensator
NW
135
90
NE
45
Objective
W,180
E,0 Polarizer
45
Specimen Calibrated
rotating stage
SW
135
90
SE
S,270
Sub-stage
condenser
Rotating
polarizer
Source
FIGURE 7-11 The design of and conventions used in a polarized light microscope.
Extraordinary ray (ne1.486)
A
e
e
71
Ordinary ray (no 1.658)
Calcite
o
FIGURE 7-12 (A) Common light
being split by calcite and (B) by a
Nicol prism formed from two pieces
of calcite cemented together with
Canada balsam.
o
Extraordinary ray (ne 1.486)
B
e
Ordinary ray (no 1.658)
68
e
90
Nicol prism
o
by contrast, pass less than 50 percent of the light because
a small portion of the light that passes through the axis
of maximal transmittance is absorbed. On the down side,
Nicol prisms are very expensive, sometimes need recementing, and they have limited angular apertures because
the maximal angle of incident light is determined by the
critical angle that gives total internal reflection.
Many experimenters have designed polarizing prisms,
made out of different materials that are cut and cemented
in various ways in order to obtain the widest possible
angular aperture (Thompson, 1905). The wide angular
apertures are necessary in order to optimize resolution and
extinction. Unfortunately, all the prisms pass the extraordinary beam, instead of the ordinary beam. Thus, the specimen is illuminated with spheroidal waves as opposed to
spherical waves. This results in some astigmatism that can
be corrected with cylindrical lenses.
The mechanical stress put on glass during the grinding
process can introduce birefringence into the glass. Such
“strain birefringence” reduces the extinction factor of the
122
microscope and the contrast of the image by introducing
elliptically polarized light in the absence of a specimen.
The loss in extinction due to strain birefringence can be
prevented by using strain-free sub-stage condenser and
objective lenses. Often, a matched pair of strain-free objectives is used for the sub-stage condenser and objective
lenses (Taylor, 1976).
The extinction factor in a polarizing microscope is
much better with low numerical aperture objective lenses
compared with high numerical aperture objective lenses.
The reduced extinction factor is due to the rotation of the
azimuth of polarization when polarized light strikes a surface
at a large angle of incidence (Inoué, 1952b). An increase in
the numerical aperture of 0.2 results in a tenfold increase in
stray light. At one time the only way to get high extinction
was to decrease the numerical aperture of both the sub-stage
condenser and the objective lens to mitigate the decrease
in contrast introduced by the depolarization of light as it
strikes lenses at a large angle. In fact, it was suggested that
only parallel light be used for illumination. Such a solution
would compromise the resolving power of the light microscope. However we can get both a high extinction factor and
good resolving power by using rectified optics, a method
developed by Inoué and Hyde (1957; Inoué, 1961, 1986). It
is also possible to obtain a high extinction factor and good
resolving power using image processing techniques, including background subtraction (see Chapter 14).
The influence of a specimen on linearly polarized light
depends on the orientation of the specimen with respect to
the azimuth of polarization. Consequently, we should use
a rotating stage in a polarizing microscope to accurately
align the specimen relative to the azimuth of polarization.
Talbot (1834a) describes the influence of specimen orientation on its appearance:
The crystals, which were highly luminous in one position, when
their axes were in the proper direction for depolarizing the light,
became entirely dark in the opposite position, thus, as they rapidly moved onwards, appearing by turns luminous and obscure,
and resembling in miniature the coruscations of a firefly. It was
impossible to view this without admiring the infinite perfection
of nature, that such almost imperceptible atoms should be found
to have a regular structure capable of acting upon light in the
same manner as the largest masses, and that the element of light
itself should obey in such trivial particulars the same laws which
regulate its course throughout the universe.
Talbot (1834a) noticed that the addition of a mica plate
between the polarizer and the analyzer caused crystalline
objects that were nearly invisible to become brightly colored. This formed the basis for the development of compensators. Compensators typically are inserted in a slot in
the microscope body between the polarizer and the object
or between the object and the analyzer. The concept of
“compensation” was invented by Biot in order to get a hint
Light and Video Microscopy
at the molecular architecture of a specimen. Talbot (1834a)
describes the first use of a compensator in a microscope:
When these miniature crystals [copper sulphate] are placed on
the stage of the microscope, the field of view remaining dark as
before, we see a most interesting phenomenon; for as every crystal differs from the rest in thickness, it displays in consequence
a different tint, and the field of view appears scattered with the
most brilliant assemblage of rubies, topazes, emeralds, and other
highly coloured gems, affording one of the most pleasing sights
that can be imagined. The darkness of the ground upon which
they display themselves greatly enhances the effect. Each crystal
is uniform in colour over all its surface, but if the plate of glass
upon which they lie is turned round in its own plane, the colour
of each crystal is seen to change and gradually assume the complementary tint. Many other salts may be substituted for the sulphate of copper in this experiment, and each of them offers some
peculiarity, worthy of attention, but difficult to describe. Some
salts, however, crystallize in such thin plates that they have not
sufficient depolarizing power to become visible upon the dark
ground of the microscope. For instance, the little crystals of sulphate of potash, precipitated by aether, appear only faintly visible. In these circumstances a contrivance may be employed to
render evident their action upon light. It must be obvious that if
a thin uniform plate of mica is viewed with the microscope, it
will appear coloured (the tint depending on the thickness it may
happen to have), and its appearance will be everywhere alike, in
other words it will produce a coloured field of view. Now if such
a plate of mica is laid beneath the crystals, or beneath the glass
which supports them, these crystals, although incapable of producing any colour themselves, are yet frequently able to alter the
colour which the mica produces; for instance, if the mica has produced a blue, they will, perhaps, alter it to purple, and thus will
have the appearance of purple crystals lying on a blue ground.
Following the invention of the polarizing microscope
by Talbot (1834a, 1834b, 1836a, 1836b, 1837, 1839a),
chemists, physicists, geologists, engineers, and biologists
(Brewster, 1837; Quekett, 1852; Pereira, 1854; Valentin,
1861; Carpenter, 1883; Naegeli and Schwendener, 1892;
Hogg, 1898; Spitta, 1907; Reichert, 1913; Chamot, 1921;
Schaeffer, 1953; Chamot and Mason, 1958; Bartels, 1966;
Goldstein, 1969; see Inoué, 1986 for many references) have
been able to study birefringent or dichroic specimens with
this elegant tool. The polarizing microscope can do far
more than introduce color and contrast to make transparent birefringent specimens visible. But before I describe
the other miracles a polarizing microscope is capable of
performing, I must first describe the molecular basis of
birefringence.
WHAT IS THE MOLECULAR BASIS
OF BIREFRINGENCE?
In order to understand the interaction of light with matter, we must understand both the nature of matter and
the nature of light. While Malus, Arago, Biot, Wollaston,
Talbot, and Brewster were experimenting with the interaction of polarized light with matter, it was not clear whether
123
Chapter | 7 Polarization Microscopy
light was a particle or a wave. Therefore it was difficult
to come up with a general theory of polarization. Newton
(1730) wrote “for both must be understood, before the reason of their Actions upon one another can be known.” In
Chapter 3, I described what was known about the nature
of light at the turn of the nineteenth century. Here, I will
briefly describe a little bit about what was known about the
nature of crystalline matter at the same time.
Christiaan Huygens (1690) knew that two crystals,
Iceland spar and quartz, were birefringent. He proposed that
the corpuscles in matter that had one refractive index were
spherical; and these spherical corpuscles radiated spherical
wavelets of light. Then he went on to say that the corpuscles that constituted birefringent crystals were spheroidal,
and they gave rise to spheroidal wavelets of light. Charles
François Dufay, who discovered the two types of electricity,
known as vitreous and resinous, proposed that all crystals,
except those that were cubic, may end up being birefringent.
Rene-Just Haüy (1807) accidentally dropped a beautiful specimen of Iceland spar on the floor and noticed that
it broke into tiny pieces with a regular rhomboidal shape.
He found that other crystals could be broken, with a sharp
tool, into pieces with regular and characteristic shapes,
including rhomboids, hexagonal prisms, tetrahedrons,
and such. He believed that characteristic shapes of the
“integrant particles” were related to the arrangement of
the moleculae that that made up the crystal. The hardness
of a crystal depended on the cohesive force between the
moleculae, and if the hardness was not symmetrical, then
the cleavage planes were not symmetrical. This meant
that the cohesive forces between moleculae in asymmetric
crystals like Iceland spar were asymmetric. The cleavage
planes represent the planes in which the bonding between
the moleculae is relatively weak.
If the asymmetry of the constituent moleculae of
Iceland spar were the reason behind the birefringence, then
it should be possible to reduce the asymmetry by heating
up the Iceland spar and randomizing the constituent parts.
Indeed Mitscherlich found that heating a crystal of Iceland
spar differentially affects the sides of the rhomb and causes
the rhomb to approach a cube. Pari passu, the double
refraction diminishes (Brewster, 1833b).
David Brewster (1815b) and Thomas Seebeck independently showed that they could induce birefringence in glass,
a substance that usually is not birefringent, by heating the
glass and cooling it rapidly. Similarly, Brewster (1815c) and
Fresnel independently found that they could induce birefringence in glass and other substances by compressing or
stretching it. These experiments support the contention that
birefringence is a result of the asymmetry of attractive forces
between the particles that make up a given crystal (Brewster,
1833b). Stress-induced strain-birefringence is particularly
spectacular in molded transparent plastics, including Plexiglas and clear plastic tableware.
The refractive index is a measure of the ability of a transparent substance to decrease the speed of light as a result of
interactions between the substance and the light. Based on
the dynamic wave theory of light, the smaller the ratio of
the elasticity to the density of the aether within a transparent
substance, the slower light propagates through the substance.
Elasticity characterizes the ability to resist deformation
or to restore a deformed object so that it takes up its original
position. In terms of the electromagnetic theory, electrons
held tightly in place by the electromagnetic forces of the
nucleus or nuclei would not be easily polarized; whereas
electrons held in place less tightly by the electromagnetic
forces of the nucleus or nuclei would be easily polarized.
Substances that have readily polarizable, deformable electron clouds have a higher refractive index than substances
that have tightly held rigid electron clouds. Thus, according to the dynamical electromagnetic theory of light, the
speed of light though a substance depends on the elasticity
of the spring that holds an electron in the substance. The
less deformable the spring, the faster the light propagates
through the substance, the more deformable the spring, the
slower the light propagates through the substance.
The electrons are not held in place by a restoring force
transmitted through mechanical springs, but by analogous
electromagnetic forces that depend on the electric permittivity and magnetic permeability. According to Maxwell’s
(1865) electromagnetic wave theory of light, the square of
the index of refraction is approximately equal to the dielectric constant or relative permittivity (Ke) according to the following equation:
n 2 K e ε / εo
where ε is the frequency-dependent electric permittivity
of the substance and εo is the electric permittivity of the
vacuum. The relative permittivity thus must be a measure
of the deformability
of a substance. The ability of external
electric fields (E), including the oscillating electric fields of
light, to deform or separate positive and negative chargesin
a substance is characterized by the electric polarization (P).
P (ε εo )E
If we divide both sides of the equation by εo, we get
P/ εo (ε / εo εo / εo )E (ε / εo 1)E
and since ε/εo n2, then
n 2 1 P/ εo E 1 P/D
where the product of εo and E is equal to the electric
flux density (D, in N/Vm). In general, an electron vibrating in a bond can be displaced, deformed, or polarized parallel to the bond, more than it can be displaced, deformed,
or polarized perpendicular to the bond. Consequently, the
refractive index along the bond will be greater than the
refractive index perpendicular to the bond.
124
Light and Video Microscopy
If such bonds are randomly distributed throughout the
molecule, light will be slowed down in a manner that is
independent of the azimuth of polarization. Such a substance is called isotropic, and it will be invisible in a polarizing light microscope. Gases, liquids, most solids, and
glasses are isotropic because the bonds are arranged randomly in these substances. However some cubic crystals,
like NaCl, are isotropic because the electrons are arranged
symmetrically with respect to every azimuth. If a biological
specimen is isotropic, we can assume that the bonds in the
substance are distributed randomly with respect to all axes
since cubic crystals are rarely found in biological material.
If the bonds in a substance are not random, but
coaligned, the substance is said to be anisotropic. Since the
electron clouds can be deformed more readily by electric
fields vibrating parallel to a bond than electric fields vibrating perpendicular to a bond, light whose electric fields are
linearly polarized parallel to the bond will be slowed down
more than light whose electric fields are linearly polarized
perpendicular to the bond. Such a birefringent specimen
will be visible in a polarized light microscope.
The interaction of polarized light with electrons can
be studied very effectively using microwave radiation
(Figure 7-13). As opposed to visible light that has wavelengths in the nanometers or micrometer range, microwave
radiation has wavelengths in the centimeter range. The
microwaves are produced and received by a diode and are
measured with an electrical field meter. A wire grating is
used as a polarizer. Microwave radiation linearly polarized
perpendicular to the slits of the wire grating pass through
the grating, but microwave radiation linearly polarized
parallel to the wire grating interacts with the grating. The
radiation linearly polarized parallel to the wires interacts
with the electrons in the wire grating because the electrons
can be readily moved back and forth through a conductor.
Consequently, the radiant microwave energy is converted
into kinetic energy, which eventually is converted to heat by
the electrons moving along the length of the wire. The wire
grating has a large cross-section for the microwave radiation linearly polarized parallel to the wires, and removes
it from the radiation that passes through the grating.
Microwave receiver
Wire grating polarizer/analyzer
Microwave transmitter
FIGURE 7-13 Studying the interaction of polarized light with electrons
using microwave radiation.
On the other hand, the electrons cannot move across the air
gaps between the wires of the grating, so the microwave
radiation linearly polarized perpendicular to the wires
interacts minimally with the electrons and consequently
propagates right through the grating.
The interaction between electromagnetic radiation and
a material can be characterized by the refractive index and
the extinction coefficient of the material for electromagnetic
radiation with a given angular frequency. Refraction takes
place when the natural characteristic angular frequency
of the vibrating electrons is much greater than the angular
frequency of the incident light (Jenkins and White, 1950;
Wood, 1961; Hecht and Zajac, 1974). The natural angular frequencies of glasses for example are in the ultraviolet
range. When the angular frequency of light approaches the
natural angular frequency of a substance, the substance no
longer refracts the light, but absorbs it, which is why ordinary glass cannot be used to transmit ultraviolet light. The
extinction coefficient, given in units of area/amount of substance, characterizes the ability of the substance to reduce
the output light captured by an axial detector by converting the incident light into chemical energy or heat, while
the refractive index characterizes the ability of a substance
to reduce the direct output light captured by an axial detector by bending the incident light away from the detector.
Anisotropic substances have two refractive indices or two
extinction coefficients for light with a given angular frequency. Some anisotropic crystals, including calcite and
quartz are birefringent and some, including tourmaline, sapphires, and rubies, are dichroic.
In general, there are two kinds of birefringence, positive and negative—quartz is an example of a positively
birefringent substance and calcite is an example of a negatively birefringent substance. The two classes of birefringence are distinguished geometrically. In positively
birefringent substances, the axis with the greater refractive index is parallel to the optic axis whereas in negatively
birefringent substances the axis with the greater refractive
index is perpendicular to the optic axis.
When we view an aperture illuminated with common
light through a birefringent crystal like calcite, we will
typically see two images of the aperture, and the separation of the two images will depend on the orientation of
the crystal. There is one particular orientation that will
produce only a single image. In this orientation, we are
looking down the optic axis. The optic axis of the calcite is
coparallel with the imaginary line through the crystal that
connects the aperture to the eye.
The propagation of linearly polarized light through
a birefringent crystal will depend on the sign of birefringence, the angle that the propagation vector makes with the
optic axis, and the azimuth of polarization. In general,
1. Nonpolarized light composed of electric fields
vibrating in all azimuths, propagating through a positively
125
Chapter | 7 Polarization Microscopy
birefringent or a negatively birefringent crystal with its
propagation vector parallel to the optic axis, will experience only one index of refraction, and thus will form only
one image. The light will travel through the crystal as a
spherical wave (Figure 7-14). In this case, the electric vectors experience the ordinary index of refraction (no).
2. Nonpolarized light composed of electric fields
vibrating in all azimuths, propagating through a negatively
birefringent crystal perpendicular to the optic axis will
experience two indices of refraction. The components of
the electric field whose azimuths are perpendicular to the
optic axis will form the ordinary wave and the components
of the electric field whose azimuths are parallel to the optic
axis will form the extraordinary wave. In negatively birefringent substances, the extraordinary wave experiences a
smaller index of refraction (ne) than the ordinary wave (no),
and thus two images will be formed on top of each other:
the image formed by the ordinary wave, which experiences
a larger index of refraction than the extraordinary wave
will be closer to us than the image formed by the extraordinary wave. This is because the difference in refractive
index between the negatively birefringent crystal and air
is greater for the ordinary wave than for the extraordinary
wave. When we trace back the rays refracted from the
crystal-air interface, the ordinary waves appear to originate
from a spot closer to us than the extraordinary waves. The
ordinary wave propagates through the crystal as a spherical
wave and the extraordinary wave propagates as a spheroidal wave.
3. Nonpolarized light composed of electric fields
vibrating in all azimuths, propagating through a positively
birefringent crystal perpendicular to the optic axis will
experience two indices of refraction. The components of
the electric field whose azimuths are perpendicular to the
optic axis will form the ordinary wave and the components
of the electric field whose azimuths are parallel to the
optic axis will form the extraordinary wave. The extraordinary wave will experience a larger index of refraction
(ne) than the ordinary wave (no), and thus two images
will be formed on top of each other: the image formed by
the ordinary wave, which experiences a smaller index of
refraction than the extraordinary wave, will appear farther
from us than the image formed by the extraordinary wave.
This is because the difference in refractive index between
the positively birefringent crystal and air is greater for the
extraordinary wave than for the ordinary wave. When we
trace back the rays refracted from the crystal-air interface,
the ordinary rays appear to originate from a spot farther
from to us than the extraordinary rays. The ordinary wave
propagates through the crystal as a spherical wave and the
extraordinary wave propagates as a spheroidal wave.
4. Nonpolarized light composed of electric fields
vibrating in all azimuths, propagating through a positively
birefringent crystal at any angle between 0 and 90 degrees
relative to the optic axis will experience two indices of
refraction. Whereas the ordinary wave will be constituted
only from the components of the electric field whose azimuths are perpendicular to the optic axis, the extraordinary
o
o, e
e
OA
e
o
OA
BR
OA
BR
o, e
e
o
OA
o, e
o
e
BR
OA
BR
BR
FIGURE 7-14 Propagation of waves through negatively and positively birefringent materials when the incident light strikes parallel, perpendicular,
and oblique to the optic axis. Ordinary waves (——), extraordinary waves (- - - -).
126
wave will be constituted from the components of the electric field that are perpendicular and parallel to the optic
axis. Consequently, the extraordinary wave will be spheroidal and will produce an astigmatic image that is laterally
displaced from the image made by the ordinary ray. An
astigmatic image is one where a circle in the object is represented as a spheroid in the image. The image made by the
extraordinary wave will tend away from the optic axis. The
distance between the two images will depend on the thickness of the crystal. The ordinary wave propagates through
the crystal as a spherical wave and the extraordinary wave
propagates through the crystal as a spheroidal wave.
5. Nonpolarized light composed of electric fields
vibrating in all azimuths, propagating through a positively
birefringent crystal at any angle between 0 and 90 degrees
relative to the optic axis will experience two indices of
refraction. Whereas the ordinary wave will be constituted
only from the components of the electric field whose azimuths are perpendicular to the optic axis, the extraordinary wave will be constituted from the components of
the electric field that are perpendicular and parallel to the
optic axis. Consequently, the extraordinary wave will produce an astigmatic image that is laterally displaced from
the image made by the ordinary ray. The image made by
the extraordinary wave will tend toward the optic axis. The
distance between the two images will depend on the thickness of the crystal. The ordinary wave propagates through
the crystal as a spherical wave and the extraordinary wave
propagates through the crystal as a spheroidal wave.
Light vibrating perpendicular to the optic axis is always
refracted ordinarily and consequently, the refractive index
perpendicular to the optic axis is known as no. By contrast,
light vibrating parallel to the optic axis can be refracted in
an extraordinary manner and thus the refractive index parallel to the optic axis is called ne. Birefringence is defined
as ne – no. Thus when ne no, the specimen is positively
birefringent and when ne no, the specimen is negatively
birefringent. Birefringence (BR) is an intrinsic or state
quantity, which can be used to identify a given substance
because it is independent of the amount of substance. That
is birefringence, like density is an intrinsic or state quantity
in contrast to mass and volume, which are extrinsic qualities that vary with the amount of the substance.
Birefringence in a specimen can be detected with
polarization microscopy, by placing the specimen between
crossed polars and rotating the stage 360 degrees. Upon
rotation, a birefringent specimen will alternate between
being bright and dark. The brightness depends on the
orientation of the optic axis of the specimen relative to
the crossed polars. If the azimuth of the axis of maximal
transmission of the polarizer is defined as 0 degrees, then
the brightness increases as the optic axis of the specimen is rotated from 0 to 45 degrees, then decreases from
45 to 90 degrees, then increases from 90 to 135 degrees,
Light and Video Microscopy
then decreases from 135 to 180 degrees, and so on. If
we determine that the substance is birefringent, we can
deduce that the bonds in that substance are anisotropic or
asymmetrical.
INTERFERENCE OF POLARIZED LIGHT
When nonpolarized light strikes a relatively thick piece of
calcite or quartz, the image is duplicated since the incident
light is split into two laterally displaced beams of polarized
light that vibrate perpendicularly to each other. Since one
of the beams travels faster than the other one, the phases
are also different. When the crystals are placed on the stage
of a polarizing microscope so that the optic axis is parallel
to the stage and oriented 45° relative to the polarizer, the
incident linearly polarized light is split laterally into two
beams that are linearly polarized perpendicular to and outof-phase with each other.
In the case of a very thin crystal or a birefringent biological specimen, the incident light is divided into two
beams that vibrate orthogonally to and out-of-phase with
each other. However, when the specimen is thin enough,
there is almost no lateral separation, and both beams,
which originate from the same point in the specimen and
are coherent, are close enough to interfere with each other
after they pass through the analyzer. The difference in
phase, which is known as the retardation (Γ) in the polarization literature, depends on two things:
● The difference in the refractive indices between the
extraordinary beam and the ordinary beam (ne–no)
● The thickness of the specimen (t).
The retardation (in nm) is given by the following
equation:
Γ (n e n o )t (BR)t
The retardation, which is reminiscent of the optical
path difference, can also be expressed in terms of a phase
angle. The phase angle (in degrees and radians) is given by
the following equation:
ϕ Γ (360 / λ ) [(n e n o )t] (360 / λ )
[(n e n o )t] (2π/ λ )
and the phase change in terms of the wavelength of the
incident light λ i is given by:
Phase change [(n e n o )t)] (λ λ i )
In order to understand how an image is formed in a
polarized light microscope, I am going to give several
examples of imaginary specimens and a method that can be
used to determine the nature of their images. Then I will
present a general method to understand the nature of any
image obtained with a polarized light microscope. Imagine
putting a positively birefringent specimen (ne 1.4805,
127
Chapter | 7 Polarization Microscopy
no 1.4555, t 5,000 nm) on a rotating stage in a polarized light microscope and orienting it so its optic axis is
45 degrees (NE-SW) relative to the azimuth of maximal transmission of the polarizer (0°, E-W). Illuminate the
specimen with linearly polarized light with a wavelength of
500 nm (λ 500 nm). The birefringent specimen resolves
the incident linearly polarized light into two orthogonal linearly polarized waves, the ordinary wave and the extraordinary wave. The extraordinary wave vibrates linearly along
the NE-SW axis and the ordinary wave vibrates linearly
along the SE-NW axis. The ordinary wave will be ahead
of the extraordinary wave by 125 nm, and the extraordinary wave will be retarded relative to the ordinary wave by
125 nm. This is equivalent to the extraordinary wave being
retarded by 90 degrees, π/2 radians or λ/4 of 500 nm light.
Because the extraordinary wave propagates slower than
the ordinary wave, the axis of electron polarization that
gives rise to the extraordinary wave is called the slow axis,
and the axis of electron polarization that gives rise to the
ordinary wave is known as the fast axis. The optic axis of a
positively birefringent specimen is the slow axis and the axis
perpendicular to the optic axis is known as the fast axis.
Only coherent waves whose electric fields are coplanar
or whose electric fields have components that are coplanar can interfere with each other. Thus orthogonal waves,
whose electric fields are perpendicular to each other, cannot interfere with each other. However, if we allow the
coherent, orthogonal, linearly polarized waves leaving the
birefringent specimen to pass through an analyzer, whose
azimuth of maximal transmission is oriented at a 90-degree
(N-S) angle relative to the azimuth of maximal transmission of the polarizer, a component of each of the two
orthogonal waves can pass through the analyzer. The outof-phase components of the ordinary wave and the extraordinary wave that pass through the analyzer are coherent,
linearly polarized, and coplanar. Consequently they will
interfere with each other.
We can use a vector method to model the interaction
of light with a point in an anisotropic specimen, and to predict how bright the image of that point will be. Consider the
specimen just described. First, draw the relative phases of
the ordinary wave and the extraordinary wave (Figure 7-15).
Second, make a table of the amplitudes of each wave at
various convenient times during the period (Table 7-1).
Third, create a Cartesian coordinate system where the
azimuth of polarization of the incident light goes from E
to W, and the azimuth of light passed by the analyzer goes
from N to S (Figure 7-16). The linearly polarized light
that strikes the specimen, whose optic axis is oriented at
45 degrees (NE to SW) will be converted into two linearly polarized waves that vibrate perpendicularly to each
other. The extraordinary wave vibrates parallel to the optic
axis (NE to SW); the ordinary wave vibrates perpendicular
to the optic axis (SE to NW). Draw the vectors that represent the extraordinary waves on the NE-SW axis and the
Remember the two waves are orthogonal, and since
ne no, the o-wave travels faster than the e-wave.
Direction of travel
o
e
Amplitude
Distance
1 2 3 4
o, R
o
R
e
e, R
e
R
(1)
(2)
(3)
o
(4)
FIGURE 7-15 Determination of the resultant (R) of two orthogonal linearly polarized waves that propagate through a point in the specimen 90°
out-of-phase with each other.
TABLE 7-1 The Amplitudes of the Extraordinary
(e) Wave and the Ordinary (o) Wave at Various Time
Points for a Birefringent Specimen (ne 1.4805, no
1.4555, t 5,000 nm) Illuminated with 500 nm Light
Time
Position (in
degrees)
Relative
amplitude
of e wave
Relative
amplitude
of o wave
1
0
0
1
2
45
0.707
0.707
3
90
1
0
4
135
0.707
0.707
5
180
0
1
6
225
0.707
7
270
1
0
8
315
0.707
0.707
9
360
0
0.707
1
vectors that represent the ordinary waves on the SE-NW
axis.
Plot the amplitudes of the ordinary wave and the
extraordinary wave at each convenient time. The resultant
wave is obtained by adding the vectors that represent the
electric fields of the ordinary and the extraordinary waves.
The amplitude of the resultant wave at a given time point is
represented by the length of the vector and the azimuth of
the wave is represented by the angle of the vector. In this
128
Light and Video Microscopy
AN
AN
AN
ne
1 1
ne
ne
POL
POL
1
POL
2
3
1
1
no
no
AN
no
AN
AN
ne
ne
POL
POL
ne
6
POL
5
4
no
AN
no
no
AN
AN
ne
7
1
8
POL
ne
ne
FIGURE 7-16
1
POL
POL
1
no
9
no
1
no
Determination of the resultant wave from its components at individual points in time.
case, the resultant wave is circularly polarized and going
in a counterclockwise direction (Figure 7-17). Circularly
polarized light can be considered to be composed of two
orthogonal, linearly polarized waves of equal amplitude, 90
degrees out-of-phase with each other: one vibrating parallel
to the azimuth of maximal transmission of the polarizer and
one vibrating parallel to the axis of maximal transmission
of the analyzer. Consequently, half of the intensity of the
incident light will pass through the analyzer and the specimen will appear bright on a black background.
If the same specimen were placed so that its optic axis
were 45 degrees (SE-NW) relative to the polarizer, the
resultant wave would also be circularly polarized, but in
the clockwise direction (Figure 7-18). The specimen would
still appear bright on a dark background.
Imagine putting a positively birefringent specimen
(ne 1.4805, no 1.4555, t 10,000 nm) on a rotating
stage in a polarized light microscope and orienting it so
its optic axis is 45 degrees (NE-SW) relative to the azimuth of maximal transmission of the polarizer (0°, E-W).
Illuminate the specimen with linearly polarized light with a
wavelength of 500 nm (λ 500 nm). The birefringent specimen resolves the incident linearly polarized light into two
orthogonal linearly polarized waves, the ordinary wave and
129
Chapter | 7 Polarization Microscopy
the extraordinary wave. The extraordinary wave vibrates linearly along the NE-SW axis and the ordinary wave vibrates
linearly along the SE-NW axis. The ordinary wave will be
ahead of the extraordinary wave by 250 nm, and the extraordinary wave will be retarded relative to the ordinary wave by
250 nm. This is equivalent to the extraordinary wave being
retarded by 180 degrees, π radians or λ/2 of 500 nm light.
Again we can use the vector method to model the interaction
of light with a point in an anisotropic specimen, and to predict how bright the image of that point will be. Repeat the
process described earlier. First, draw the relative phases of
the ordinary wave and the extraordinary wave (Figure 7-19).
Second, make a table of the amplitudes of each wave at various convenient times during the period (Table 7-2).
Third, create a Cartesian coordinate system where the
azimuth of polarization of the incident light goes from E
to W, and the azimuth of light passed by the analyzer goes
from N to S ( Figure 7-20 ). The linearly polarized light
that strikes the specimen, whose optic axis is oriented at
45 degrees (NE to SW), will be converted into two linearly polarized waves that vibrate perpendicularly to each
other. The extraordinary wave vibrates parallel to the optic
axis (NE to SW); the ordinary wave vibrates perpendicular
to the optic axis (SE to NW).
AN
8
7
1
POL
5
3
4
TABLE 7-2 The Amplitudes of the Extraordinary
(e) Wave and the (o) Ordinary Wave at Various Time
Points for a Birefringent Specimen (ne 1.4805, no
1.4555, t 10,000 nm) Illuminated with 500 nm Light
POL
6
3
5
no
4
FIGURE 7-17 A single Cartesian coordinate system showing the propagation of a counterclockwise circularly polarized wave.
o wave
Relative
amplitude
of e wave
Relative
amplitude
of o wave
Time
Position (in
degrees)
1
0
0
2
45
0.707
0.707
3
90
1
1
4
135
0.707
0.707
5
180
0
6
225
0.707
0.707
7
270
1
1
8
315
0.707
0.707
9
360
ne
7
2
ne
FIGURE 7-18 A single Cartesian coordinate system showing the propagation of a clockwise circularly polarized wave.
8
9
2
6
AN
1
no
0
0
0
0
e wave
Remember that the
two waves
are orthogonal
Wave
travelling
this way
1
2
3
4
5
FIGURE 7-19 Determination of the resultant of two orthogonal linearly polarized waves that propagate through a point in the specimen 180° out-ofphase with each other.
130
Light and Video Microscopy
AN
AN
3
no
3
no
ne
4
4
ne
2
2
1
1
9
1
POL
5
POL
9
5
1
1
1
6
8
7
6
8
7
FIGURE 7-20 Determination of the resultant wave from its components
at individual points in time.
FIGURE 7-21 Linearly polarized light parallel to the azimuth of maximal transmission of the analyzer.
Next, plot the amplitudes of the ordinary wave and the
extraordinary wave at each convenient time. The resultant
wave is obtained by adding the vectors that represent the
electric fields of the ordinary and the extraordinary waves.
The amplitude of the wave is represented by the length of the
vector and the azimuth of the wave is represented by the
angle of the vector. In this case, the resultant wave is
linearly polarized in the N-S direction, along the axis
of maximal transmission of the analyzer. The specimen
will appear bright on a black background (Figure 7-21).
In this case, the image would look the same if its optic axis
were placed 45 degrees relative to the polarizer.
Imagine putting a negatively birefringent specimen
(ne 1.4555, no 1.4805, t 5,000 nm) on a rotating
stage in a polarized light microscope and orienting it so
its optic axis is 45 degrees (NE-SW) relative to the azimuth of maximal transmission of the polarizer (0°, N-S).
Illuminate the specimen with linearly polarized light with
a wavelength of 500 nm (λ 500 nm). The birefringent
specimen resolves the incident linearly polarized light
into two orthogonal linearly polarized waves, the ordinary wave and the extraordinary wave. The extraordinary
wave vibrates linearly along the NE-SW axis and the ordinary wave vibrates linearly along the SE-NW axis. The
extraordinary wave will be ahead of the ordinary wave by
125 nm, and the ordinary wave will be retarded relative
to the extraordinary wave by 125 nm.This is equivalent to
the ordinary wave being retarded by 90 degrees, π/2
radians or λ/4 of 500 nm light. Because the ordinary
wave propagates slower than the extraordinary wave, the
axis of electron polarization that gives rise to the ordinary
wave is called the slow axis, and the axis of electron polarization that gives rise to the extraordinary wave is known
as the fast axis. The optic axis of a negatively birefringent
specimen that produces the extraordinary wave is the fast
axis and the axis perpendicular to the optic axis is known
as the slow axis.
We can use the vector method to model the interaction of
light with a point in an anisotropic specimen, and to predict
how bright the image of that point will be. First, draw the
relative phases of the ordinary wave and the extraordinary
wave (Figure 7-22). Then make a table of the amplitudes
of each wave at various convenient times during the period
(Table 7-3).
Third, create a Cartesian coordinate system where the
azimuth of polarization of the incident light goes from
E to W, and the azimuth of light passed by the analyzer
goes from N to S. The linearly polarized light that strikes
the specimen, whose optic axis is placed at 45 degrees
(NE to SW), will be converted into two linearly polarized beams that vibrate perpendicularly to each other. The
extraordinary wave vibrates parallel to the optic axis (NE
to SW), which is the fast axis; the ordinary wave vibrates
perpendicular to the optic axis (SE to NW), which is the
slow axis. The amplitude of the wave is represented by the
length of the vector and the azimuth of the wave is represented by the angle of the vector. Plot the amplitudes of the
ordinary wave and the extraordinary wave at each convenient time on a Cartesian coordinate system as I explained
above.
The specimen produces circularly polarized light that
travels in the clockwise direction. The specimen appears
bright on a black background. If the specimen were placed
so that its optic axis was 45° relative to the polarizer, the
specimen would produce circularly polarized light that
travels in the counterclockwise direction.
Imagine putting a negatively birefringent specimen
(ne 1.402, no 1.452, t 10,000 nm) on a rotating
stage in a polarized light microscope and orienting it so
its optic axis is 45° (NE-SW) relative to the azimuth of
131
Chapter | 7 Polarization Microscopy
e wave
o wave
Remember
that the
two waves
are orthogonal
Waves travel
in this direction
2
1
3
4
5
FIGURE 7-22 Determination of the resultant of two orthogonal linearly polarized waves that propagate through a point in the specimen 90° out-of-phase
with each other.
TABLE 7-3 The Amplitudes of the Extraordinary
(e) Wave and the Ordinary (o) Wave at Various Time
Points for a Birefringent Specimen (ne 1.4555, no
1.4805, t 5,000 nm) Illuminated with 500 nm Light
Time
Position (in
degrees)
Relative
amplitude
of e wave
Relative
amplitude
of o wave
1
0
1
0
2
3
45
0.707
0.707
90
0
1
4
135
0.707
0.707
5
180
1
0
6
225
0.707
7
270
0
1
8
315
0.707
0.707
9
360
1
0.707
0
maximal transmission of the polarizer (0°, N-S). Illuminate
the specimen with linearly polarized light with a wavelength of 500 nm (λ 500 nm). The birefringent specimen resolves the incident linearly polarized light into two
orthogonal linearly polarized waves, the ordinary wave and
the extraordinary wave. The extraordinary wave vibrates
linearly along the NE-SW axis and the ordinary wave
vibrates linearly along the SE-NW axis. The extraordinary
wave will be ahead of the ordinary wave by 500 nm, and
the ordinary wave will be retarded relative to the extraordinary wave by 500 nm.This is equivalent to the ordinary
wave being retarded by 360 degrees, 2π radians or λ
of 500 nm light.
We can use the vector method again to model the interaction of light with a point in a birefringent specimen, and to
predict how bright the image of that point will be. First, draw
the relative phases of the ordinary wave and the extraordinary
wave (Figure 7-23). Second, make a table of the amplitudes
of each wave at various convenient times during the period
(Table 7-4).
Third, create a Cartesian coordinate system where the
azimuth of polarization of the incident light goes from E
to S, and the azimuth of light passed by the analyzer goes
from N to S. The linearly polarized light that strikes the
specimen, whose optic axis is placed at 45 degrees (NE
to SW), will be converted into two linearly polarized beams
that vibrate perpendicularly to each other. The extraordinary wave vibrates parallel to the optic axis (NE to SW);
the ordinary wave vibrates perpendicular to the optic axis
(SE to NW). Next, plot the amplitudes of the ordinary
wave and the extraordinary wave at each convenient time.
The resultant wave is linearly polarized along the azimuth
of maximal transmission of the polarizer and perpendicular
to the azimuth of maximal transmission of the analyzer, and
consequently the specimen is invisible on a black background
(Figure 7-24). Although a birefringent specimen whose retardation is equal to the wavelength of the monochromatic illuminating light is invisible, it can be made visible by using
white light, since for all other colors, the retardation will not
equal an integral number of wavelengths.
Birefringent specimens influence the incident linearly
polarized light and form two linearly polarized waves that
are out-of-phase and orthogonal to each other. The direction and ellipticity of the resultant wave depends on the
magnitude and sign of birefringence and the thickness of
the specimen. It also depends on the position of the specimen with respect to the polarizer and the wavelength of
light used to illuminate the specimen. When using monochromatic light, a birefringent specimen that introduces
a phase angle greater than 0 degrees and less than 90
degrees produces elliptically polarized light whose major
axis is parallel to the azimuth of maximal transmission
of the polarizer. When the phase angle is between 90 and
180 degrees, the specimen produces elliptically polarized
light whose major axis is parallel to azimuth of maximal
transmission of the analyzer. The greater the component of
132
Light and Video Microscopy
o wave and e wave
Waves travel
in this direction
Remember
that the
two waves
are orthogonal
1
2
3
4
5
FIGURE 7-23 Determination of the resultant of two orthogonal linearly polarized waves that propagate through a point in the specimen 0° out-ofphase with each other and through the azimuth of maximal transmission of the analyzer.
TABLE 7-4 The Amplitudes of the Extraordinary
(e) Wave and the Ordinary (o) Wave at Various Time
Points for a Birefringent Specimen (ne 1.402, no
1.452, t 10,000 nm) Illuminated with 500 nm Light
TABLE 7-5 The Appearance of a Specimen with a
Given Phase Angle in a Polarized Light Microscope
Using Monochromatic Illumination
Phase change, degrees
Time
Position (in
degrees)
1
0
2
Relative
amplitude
of o wave
Relative
amplitude
of e wave
0
0
45
0.707
0.707
3
90
1
1
4
135
0.707
0.707
5
180
0
0
6
225
0.707
0.707
7
270
1
1
8
315
9
360
0.707
–0.707
0
2
4
1
Dark
45
Somewhat bright
90
Half of the light incident on the
specimen
135
Pretty bright
180
As bright as the light incident on
the specimen
225
Pretty bright
270
Half of the light incident on the
specimen
315
Somewhat bright
360
Dark
elliptically polarized light that is parallel to the azimuth of
transmission of the analyzer, the brighter the specimen will
be (Table 7-5).
We can determine how any point on any specimen will
appear in a polarizing light microscope by using the following rules.
ne
3
0
0
AN
1
Brightness
1
4
9
1
POL
5
8
7
1
no
FIGURE 7-24 Linearly polarized light parallel to the azimuth of maximal transmission of the polarizer.
1. Identify the important pieces of information in the
problem.
2. Determine the retardation: Γ (ne – no)t.
3. Determine the phase angle: ϕ Γ(360°/λ) [(ne–
no)t] (360°/λ). Plot the amplitudes of the ordinary and
extraordinary waves.
4. Make a table of the amplitudes of the ordinary wave
and the amplitude of the extraordinary wave at various convenient time points.
Chapter | 7 Polarization Microscopy
5. Draw a coordinate system and place the azimuth of
maximal transmission of the polarizer in the E-W direction
and the azimuth of maximal transmission of the analyzer
in the N-S position. Then orient the optic axis of the specimen in either a 45 or a 45 degree angle relative to the
azimuth of transmission of the polarizer. Label the optic
axis ne, since it represents the extraordinary refractive
index and the axis perpendicular to the optic axis no, since
it represents the ordinary refractive index. Draw a vector
representation of the extraordinary wave parallel with the
optic axis (ne) and a vector representation of the ordinary
wave perpendicular to the optic axis (no).
6. Add the amplitudes of the ordinary and extraordinary wave vectors at each convenient time point to get the
resultant. Label each time point.
7. Connect the dots (in order) and determine the direction of the resultant light as it moves in time from the paper
toward you.
8. If the resultant has any component along the azimuth of the analyzer, the object will be visible. The greater
the component along the azimuth of transmission of the
analyzer is, the brighter the image will be.
THE ORIGIN OF COLORS IN
BIREFRINGENT SPECIMENS
In the examples just given, I have assumed that the specimens were illuminated with monochromatic light. What
happens when the specimens are illuminated with white
light? The phase angle of the light that leaves a birefringent
specimen depends on the wavelength of light. A birefringent specimen with a given retardation will introduce a different phase for light of each wavelength. The wavelengths
that undergo a phase angle of 180 degrees (or m λ/2,
where m is an integer) will come through crossed polars as
the brightest. The wavelengths that undergo a phase angle
of 0 degrees (or mλ, where m is an integer) will not pass
through the analyzer in the crossed position. The wavelengths that undergo intermediate phase angles will come
through intermediately.
A birefringent specimen that introduces a phase angle
of 360 degrees for 530 nm light will appear lavender
because the greenish-yellow 530 nm light leaving the specimen will be linearly polarized parallel to the azimuth of
maximal transmission of the polarizer and perpendicular
to the azimuth of maximal transmission of the analyzer.
In the crossed position, no 530 nm light will pass through
the analyzer, but both reddish and bluish wavelengths will,
since they will not be linearly polarized, but elliptically
polarized. The specimen will appear lavender, which is a
mixture of blue and red, and which is the complementary
color to greenish-yellow (530 nm).
The color of a specimen viewed between crossed
polars will be the complementary color to the color whose
133
wavelength is retarded one whole wavelength by the specimen. Consequently, the color of a specimen in a polarizing microscope provides information about the retardation
introduced by the specimen. Since the retardation is equal
to the product of the birefringence and the thickness; the
birefringence can be estimated from the color of the specimen if the thickness is known. If the birefringence is
known, the thickness can be estimated from the color of
the image. A Michel-Lévy color chart, first presented by
Auguste Michel-Lévy in 1888 to identify minerals, is used
to simplify this identification. Many published MichelLévy color charts have been compiled by John Delly (2003)
and are available online at http://www.modernmicroscopy.
com/main.asp?article=15&page=1.
If the analyzer were turned so that it was parallel to
the polarizer, the specimen described earlier would appear
greenish-yellow, which is the complementary color of
lavender. A complementary color is defined as the color
of light, which when added to the test color, produces
white light. The color of a birefringent specimen placed
between parallel polars and illuminated with white light
is, in essence, the color of the wavelength that gives a 360
degree phase change. The color of a birefringent specimen
placed between crossed polars and illuminated with white
light is, in essence, the complementary color of the wavelength that gives a 360 degree phase change.
USE OF COMPENSATORS TO DETERMINE
THE MAGNITUDE AND SIGN OF
BIREFRINGENCE
We are now in a position to utilize the experimental observations and deep thinking of Bartholinus, Huygens, Newton,
Arago, Malus, Wollaston, Biot, Fresnel, Talbot, Herschel,
and Brewster to understand much about the material nature
of the specimens we observe with a polarizing microscope. We can use a polarizing microscope to determine
the birefringence of a specimen quantitatively. The magnitude of birefringence of a sample characterizes the asymmetry of its molecular bonds. The birefringence is also a
state quantity, so we can use it to identify the molecules in
the sample. In addition, if we already know the identity of
a birefringent substance, we can determine the orientation
of the birefringent molecules in the specimen. Lastly, we
can interpret any natural or induced changes in the birefringence of a cell to indicate physicochemical changes in
cellular organization and/or chemistry (Johannsen, 1918;
Bennett, 1950; Oster, 1955; Pluta, 1993).
As Talbot (1834a) noticed, many specimens do not
appear colored in a polarizing microscope, but appear bright
white on a black background. This is because these specimens do not introduce a retardation that is large enough
to eliminate any wavelengths of visible light that would
result in the specimen appearing as the complementary
134
Light and Video Microscopy
Max at
λλ/2
Ellipticity of
polarized light
leaving the
specimen
Max at
λλ/2
Intensity of light
passing through
crossed polars
400
600
500
wavelength (nm)
FIGURE 7-25 The intensity and ellipticity of the light passing through
a first-order wave plate is wavelength dependent.
color. Experience shows that specimens with retardations
between about 50 nm and 350 nm appear white.
Talbot (1834a) showed that specimens illuminated
with white light in a polarizing microscope appeared colored when he placed a piece of mica between the crossed
polars. Nowadays we insert a crystal known as a first-order
red plate (a.k.a. red I plate or full wave plate) between the
crossed polars in order to produce color contrast (Bennett,
1950; Pluta, 1993). The first-order red plate usually is
made from a sheet of birefringent gypsum. The first-order
red plate is inserted in a known orientation so that its slow
axis, usually marked with a γ or nγ, is fixed at 45 degrees
relative to the transmission azimuth of the polarizer.
Depending on the manufacturer, the first-order red plate
introduces a retardation of between 530 and 590 nm.Thus,
when the first-order red plate is inserted between crossed
polars, at an orientation 45 degrees relative to the polarizer, it retards greenish-yellow light one full wavelength.
The greenish-yellow light is linearly polarized parallel to
the maximal transmission azimuth of the polarizer and
will not pass the analyzer. Everything but greenish-yellow
light will be elliptically polarized and will have a component that will go through the analyzer (Figure 7-25).
Consequently, the background will appear lavender—a
mixture of reddish and bluish colors, between crossed
polars and greenish-yellow between parallel polars.
When the first-order wave plate is inserted in a polarizing microscope in the presence of a specimen, each point
in the image depends on two factors: the elliptically polarized light produced by each point in a birefringent specimen and the elliptically polarized light produced by the
compensator. Depending on the relative orientation of the
slow axis of the specimen and the slow axis of the compensator, the elliptically polarized light that reaches the
analyzer is either added together or subtracted from one
another.
When a birefringent specimen that introduces a retardation of approximately 100 nm is placed on the stage, it will
appear white between crossed polars. It will appear bluish,
yellow-orangish, or both when the first-order red plate is
inserted. I will call the first-order red plate, or any birefringent material we insert into the microscope, to determine
the magnitude and sign of birefringence, the compensator. The compensator can be made out of a positively or
negatively birefringent material. In order to explain this
miraculous production of color, let me review some conventions. For a compensator made from a positively birefringent crystal, ne and no are the slow axis and fast axis,
respectively. For a compensator made from negatively birefringent crystal, ne and no are the fast axis and slow axis,
respectively. For a positively birefringent specimen, ne and
no are the slow axis and fast axis, respectively. For a negatively birefringent specimen, ne and no are the fast axis and
slow axis, respectively.
Each point in the image depends on the elliptically
polarized light produced by each point in the specimen and
the elliptically polarized light produced by the compensator. The sum of or difference between these two contributions of elliptical polarized light will also be elliptically
polarized light. If the resultant light of a given wavelength
is linearly polarized in the azimuth of maximal transmission of the polarizer, none of that color will contribute to
the image point. If the resultant light of a given wavelength
is linearly polarized parallel to the azimuth of maximal
transmission of the analyzer, that color will contribute
greatly to the image point. The contribution of any other
wavelength to an image point will depend on the relative
ellipticity of the resultant.
When the slow axis of a region of the specimen is parallel to the slow axis of the compensator, the image of
this region will appear bluish. Blue is known as an “additive color” because the linearly polarized light that passes
through the slow axis of the specimen is additionally
retarded as it passes through the slow axis of the compensator. If the fast axis of a region of the specimen is parallel to the slow axis of the compensator, the object will
appear yellowish-orange. Yellowish-orange is known as a
“subtractive color” since the linearly polarized light that
passes through the slow axis of the specimen is advanced
as it passes through the fast axis of the compensator
(Figure 7-26).
Let us start from the beginning and assume that we
have a microscope equipped with crossed polars, in which
the azimuth of maximal transmission of the polarizer is
along the E-W axis and the azimuth of maximal transmission of the analyzer is along the N-S axis. The slow
axis of the first-order wave plate compensator is inserted
45 degrees (NE-SW) relative to the polarizer. Let’s further assume that light passing through the slow axis of
the compensator will be retarded 530 nm relative to the
light passing through the fast axis of the compensator.
The light bulb on the microscope produces nonpolarized white light, which becomes linearly polarized after it
passes through the polarizer. When the linearly polarized
white light passes through a specimen, which is oriented
45 degrees relative to the polarizer, the linearly polarized white light is resolved into two linear components that
135
Chapter | 7 Polarization Microscopy
Additive color
AN
AN
Subtractive color
AN
sp
POL
ec
im
Magenta
field
sp
en
im
Slow
axis of
object
w
POL
ec
Magenta
field
llo
ue
Ye
Bl
POL
Magenta
field
γo
Slow axis
of object
en
Slow
axis of
1st order
γc, or
γ
γc o
Slow axis
of 1st order
red plate
red plate
Slow axis
of Ist order
red plate
Positivelybirefringent object
γc
Negativelybirefringent object
FIGURE 7-26 The color of a birefringent object in a polarized light microscope with a first-order wave plate depends in part on the orientation of the
fast and slow axes of the specimen relative to the slow axis of the compensator.
Intensity
400
500
600
λ
400
Wavelength (nm)
(A)
Object when
slow axes are
crossed
Object when
slow axes are
parallel
Background
500
600
400
Wavelength (nm)
(B)
500
600
Wavelength (nm)
(C)
FIGURE 7-27 The colors produced by a first-order wave plate, in the absence (A) and presence of a specimen with its slow axis oriented parallel to
the slow axis of the compensator (B) and perpendicular to the slow axis of the compensator (C).
differ in phase and vibrate perpendicularly to each other.
Let’s assume that the light that passes through the slow
axis of the specimen is retarded 100 nm relative to the light
that passes through the fast axis of the specimen.
If the slow axis of the specimen is parallel to the slow
axis of the compensator, the light that passes through these
two slow axes will be retarded 630 nm. Therefore, 630 nm
light will be retarded one full wavelength. Since 630 nm
light is orange-ish, orange-ish light will be linearly polarized parallel to the azimuth of maximal transmission of the
polarizer and will not pass through the analyzer. Light of all
other wavelengths will be elliptically polarized. Elliptically
polarized light with wavelengths close to 630 nm will have
a very small minor axis parallel to the maximal transmission azimuth of the analyzer and wavelengths further away
from 630 nm will have a larger one. Wavelengths longer
than about 700 nm are invisible to us and therefore we will
see many more wavelengths shorter than 630 nm than wavelengths longer than 630 nm. Consequently, the specimen will
appear bluish, which is the complementary color of orangeish (Figure 7-27).
If the slow axis of the specimen is parallel to the fast
axis of the compensator, the light that passes through these
two axes will be advanced 430 nm. Therefore, 430 nm light
will be advanced one full wavelength. Since 430 nm light is
bluish, bluish light will be linearly polarized parallel to the
maximal transmission azimuth of the polarizer and will not
pass through the analyzer. Light of all other wavelengths
will be elliptically polarized. Wavelengths close to 430 nm
will have a very small minor axis parallel to the maximal
transmission azimuth of the analyzer and wavelengths
further away from 430 nm will have a larger one.
Wavelengths shorter than about 400 nm are invisible to us
and therefore we will see many more wavelengths longer than 430 nm than wavelengths shorter than 430 nm.
Consequently, the specimen will appear yellow-orange-ish,
which is the complementary color of bluish.
The color of individual specimens scattered in all orientations throughout the field of a polarized light microscope
depends on the orientation of its slow axis relative to the
orientation of the slow axis of the first-order red plate.
Many birefringent specimens are not linear, but spherical or cylindrical and thus may show both additive and subtractive colors in different regions of the specimen. In these
cases, it is helpful to think of the Cartesean coordinate system as being capable of translating over the specimen to
any desired point. We also have to make the assumption that
the slow axis is parallel to the physical axis in positively
136
Light and Video Microscopy
AN
AN
PO
PO
AN
Yellow
AN
Blue
gc
Blue
PO
PO
Blue
Yellow
Yellow
gc
Yellow
Blue
FIGURE 7-28 The colors of a specimen composed of positively birefringent molecules is a function of the orientation of the molecules. What colors
would we observe in the specimens above if they were composed of negatively birefringent molecules?
birefringent molecules and perpendicular to the physical
axis in negatively birefringent molecules.
When a specimen is composed of positively birefringent molecules that are radially arranged, the molecules
will appear bluish in the regions where the physical axes
of the positively birefringent molecules are parallel to the
slow axis of the compensator, and yellowish-orange in the
regions where the physical axes of the positively birefringent molecules are perpendicular to the slow axis of the
compensator.
When a specimen is composed of positively birefringent
molecules that are tangentially arranged, the molecules
will still appear bluish in the regions where the physical
axes of the positively birefringent molecules are parallel to
the slow axis of the compensator; and yellowish-orange in
the regions where the physical axes of the positively birefringent material are perpendicular to the slow axis of the
compensator. However, in this case the arrangement of
colors will be different than the arrangement of colors produced by a specimen in which the positively birefringent
material is radially arranged (Figure 7-28). We can then
distinguish radially arranged positively birefringent molecules from tangentially arranged positively birefringent
molecules from the color pattern.
When the specimen is composed of negatively birefringent molecules that are radially arranged, the specimen will appear yellowish-orange in the regions where
the physical axes of the negatively birefringent molecules
are parallel to the slow axis of the compensator; and
bluish in the regions where the physical axes of the negatively birefringent molecules are perpendicular to the slow
axis of the compensator. Such a specimen has the same
color pattern as a specimen composed of tangentially
arranged positively birefringent molecules. To distinguish
between the two, you must know beforehand whether you
are looking at a specimen composed of positively birefringent or negatively birefringent molecules.
When the specimen is composed of negatively birefringent molecules that are tangentially arranged, the specimen will appear yellowish-orange in the regions where
the physical axes of the negatively birefringent molecules
are parallel to the slow axis of the compensator; and bluish in the regions where the physical axes of the negatively
birefringent molecules are perpendicular to the slow axis
of the compensator. Such a specimen has the same color
pattern as a specimen composed of radially arranged positively birefringent molecules. To distinguish between the
two, you must know beforehand whether you are looking
at a specimen composed of positively birefringent or negatively birefringent molecules.
When we know the sign of birefringence of the molecules
that make up the specimen, we can determine the orientation
of those molecules in the specimen. On the other hand, when
we know the orientation of molecules from independent
experiments (e.g., electron microscopy), we can determine
the sign of birefringence of the molecules that make up the
137
Chapter | 7 Polarization Microscopy
Amylose
Maltose unit
O
4
O
1
H
H
4
CH2OH
O
O
H
HO
H
1
H
4
CH2OH
O
OH
H
H
α
HO
O
H
1
α
Cellobiose unit
HO
O
H
H
OH
H
4
1
O
H
O
H CH2OH
CH2OH
4
HO
␤ HO
O
H
1
H
OH
H
H
O
H
H
4
H CH2OH
H
OH
H
1
O
H
O ␤
4
HO
n
H
O
n
Amylose
H
O
4
O
OH
H
H
H
1
H
CH2OH
O
H
1
H
OH
H
O
H
Cellulose
NH2
O
HO
N
5
P O
CH2
OH
H
4'
N
O
A
1'
H
3'
Deoxyribonucleic acid DNA
H
N
T
NN
H
G
C
2'
HO
H
Deoxyadenosine-5-phosphate(A)
T
A
C
G
FIGURE 7-29 The structure of positively birefringent molecules (e.g., starch and cellulose) and a negatively birefringent molecule (DNA).
specimen from the pattern of colors that appear in a polarizing microscope equipped with a first order red plate.
In biological specimens, we often do not know where the
optic axis of a given specimen is. Thus we have to make an
operational definition of ne and no. We usually assume that
the molecule is uniaxial and that ne is parallel to the physical
axis of the specimen and no is perpendicular to the physical axis of the specimen. Biaxial crystals, which have two
138
Light and Video Microscopy
optic axes and three indices of refraction, typically are not
found in biological materials. Immobilized molecules, like
amylose (in starch), cellulose, or fatty acyl-containing lipids,
where the majority of the electrons vibrate parallel to the
physical axis of the molecule, are considered positively birefringent. Molecules, like DNA, where the majority of the
electrons vibrate perpendicular to the physical axis of the molecule, are considered negatively birefringent (Figure 7-29).
As I mentioned earlier, if a specimen placed on a microscope between crossed polars has a great enough retardation
to eliminate one visible wavelength, the specimen will
appear colored and we can determine its retardation directly
by comparing the color of the specimen with the Newton
colors that appear on a Michel-Lévy chart. If we know
the thickness of the specimen by independent means (e.g.,
interference microscopy), we can read the magnitude of
birefringence of the specimen from the Michel-Lévy chart.
However, the retardations caused by most biological specimens are too small to give interference colors without a
compensator. We can determine the retardation of these
specimens by comparing the color of the specimen viewed
with a first-order red plate, with the Newton colors that
appear on a Michel-Lévy chart. Where we find a match in
the colors, we can read the retardation due to the specimen
and the first-order red plate directly from the Michel-Lévy
chart and then subtract from this value the retardation due
to the compensator. The retardation of the specimen is
equal to the absolute value of this difference. Again, if we
know the thickness of the specimen by independent means,
we can determine the magnitude of birefringence (BR) of
the specimen from the following equation:
BR n e n o Γ/t.
The magnitude of retardation can also be rapidly estimated and the sign of birefringence determined with the aid
of another fixed azimuth compensator known as the quartz
wedge compensator (Bennett, 1950; Pluta, 1993). Quartz
is a positively birefringent crystal with ne 1.553 and
no 1.544 (BR 0.009). Since the retardation is equal
to the product of birefringence and thickness, and since the
thickness varies along the compensator, the retardation varies from zero to about 2000 nm.When the quartz wedge is
slid into the microscope so that the slow axis of the compensator, often denoted with a γ or nγ , is fixed at 45 degrees
relative to the crossed polars and illuminated with white
light, a series of interference fringes, identical in order to the
colors in the Michel-Lévy chart, appears in the field.
When using a quartz wedge, the specimen is placed on the
stage so its slow axis is 45 degrees relative to the azimuth
of maximal transmission of the polarizer and illuminated with
white light. In order to get complete extinction, the aperture
diaphragm must be closed all the way. When the slow axis
of the specimen and compensator are perpendicular, there
will be one position of the compensator where the retardation
of the compensator equals the retardation of the specimen
and the specimen will be extinguished. At this position, the
compensator introduces an ellipticity that is equal in magnitude but opposite in sense to the ellipticity introduced by the
birefringent specimen. If you cannot bring the specimen to
extinction, then its slow axis is coaligned with the slow axis
of the compensator or its retardation exceeds 2000 nm.
We find the position of extinction by gradually sliding
the quartz wedge into the compensator slot. As this is done
the color of the specimen changes from its initial color
toward the “subtractive colors” and eventually it turns
black. When the specimen is brought to extinction, look
at the adjacent background color produced solely by the
elliptical light introduced by the quartz wedge. Then match
this color with the identical color on the Michel-Lévy color
chart and read the retardation of the compensator directly
from the color chart.
The quartz wedge will bring the specimen to extinction
only if the slow axis of the compensator is perpendicular
to the slow axis of the specimen. Therefore, we can use the
quartz wedge compensator like the first-order wave plate to
determine the orientation of molecules as long as we know
the sign of birefringence of those molecules. Double wedge
or Babinet compensators work the same way as the quartz
wedge compensators, but are more accurate for estimating
smaller retardations (Bennett, 1950; Pluta, 1993).
There are many compensators that can introduce a range
of retardations by tilting or rotating the birefringent crystals
in the compensator (Pluta, 1993). The Berek or Ehringhaus
compensators are examples of tilting compensators—
that is, compensators whose ability to produce elliptically
polarized light is increased by tilting the compensator from
a position where its optic axis is parallel to the microscope
axis to an angle where the compensator’s optic axis is at
an angle relative to the microscope axis (Figure 7-30). The
Berek compensator consists of a MgF2 or calcite plate that
is cut with its plane surfaces perpendicular to its optic axis.
Therefore, when the Berek compensator is placed in the
microscope horizontally, it acts like an isotropic material and
cannot compensate a birefringent object. The MgF2 or calcite plate can then be tilted with respect to the optical axis of
Eye
Optic
axis of
compensator
Eye
Analyzer
Analyzer
Compensator
Compensator
Specimen
Specimen
Polarizer
Polarizer
FIGURE 7-30 Compensation with a Berek or Ehringhaus compensator.
The compensator is tilted from the horizontal position to the vertical position to compensate the specimen.
139
Chapter | 7 Polarization Microscopy
65
2400
60
2200
55
egree)
2600
1000
II
30
600
m
e)
15
I
10
gre
m/de
4n
3.03
400
200
λ 546
0
20
/4 de
nt (
rmo
5n
ler
46
λ5
éna
S
40 60 80 100 120 140 160 180
Angular reading in degrees
e)
re
g
/de
25
20
800
0
35
46
1200
40
λ5
1400
III
Retardation (nm)
1600
50
45
Berek (110
1800
Retardation (nm)
IV
–120 nm/d
2000
eS
éna
rmo
λ
nt (3
(1 546
.034
.78 /1
nm/
0
deg
nm Kö
ree)
/de hle
gr r
ee
)
where c is the constant of the individual compensator plate
for the wavelength of light used, i is the difference between
the two compensation readings and f(i) is the function of i
given in the manufacturer’s table. Since tilting compensators have a logarithmic calibration curve, they are able to
compensate specimens with a wide range of retardations.
However, although tilting compensators have a large range,
/4 d
log Γ log c log f(i)
their sensitivity is very low: on the order of 22 nm per
degree (Figure 7-31).
Although the first order wave plate, quartz wedge,
Babinet, Berek, and Ehringhaus compensators are useful for estimating the retardation of specimens with large
retardations, we have to use rotary compensators such as a
Brace-Köhler compensator or a de Sénarmont compensator in order to measure the small retardations introduced by
many biological specimens. In general, the greater the sensitivity of a compensator, the smaller the range in which it
is useful; therefore it is important to understand something
about both your specimen and the various compensators in
order to chose the best compensator.
A Brace-Köhler compensator is a rotary compensator made out of a mica plate (Bennett, 1950; Pluta, 1993).
The mica plate can be rotated 45 degrees around the
microscope axis to introduce elliptically polarized light.
Depending on the sensitivity of the compensator, the
45 degree rotation corresponds to a λ/30, λ/20, or λ/10
of retardation. Initially, the slow axis of the compensator
is parallel to the azimuth of maximal transmission of the
polarizer or the analyzer. At either of these positions, the
compensator introduces no ellipticity to the light. When
the slow axis of the compensator is rotated away from one
of these positions, the Brace-Köhler compensator produces elliptically polarized light. The ellipticity of the light
increases as the slow axis of the compensator is rotated
Berek (22 nm/degree)
the microscope. The MgF2 or calcite plate provides maximal
compensation when it is oriented in a vertical position.
Tilting compensators introduce maximal retardations
of 2000 to 3000 nm. At any intermediate tilt, the compensator retards the light from the specimen an intermediate
amount. The tilting angle of the compensator that brings
the specimen to extinction is read directly from the compensator tilting knob. We then look at a table supplied by
the compensator manufacturer that relates the retardation
to the compensator angle and the wavelength of illuminating light. In order to increase the accuracy of the measurement, the compensator is tilted in both directions and
the average of the two tilting angles is used to calculate
the retardation. Maximum accuracy is obtained by using
monochromatic light and by making several measurements
on a single sample and calculating the average. Retardation
is obtained from the following formula:
/20
λ 546
.8
(0
h
Kö
/30
0.6
er (
l
Köh
e)
gre
/de
m
1n
5
0
0
5
10 15 20 25 30 35
Angular reading in degrees
FIGURE 7-31 The ranges and sensitivies of various compensators used with polarized light microscopes.
40
45
140
Light and Video Microscopy
between 0 and 45 degrees, and it introduces maximum
ellipticity to the light when its slow axis is 45 degrees.
In order to determine the retardation of the birefringent
specimen, the compensator is rotated until the specimen is
brought to extinction. The specimen is brought to extinction, or compensated, at the position where the compensator produces elliptically polarized light that is equal in
magnitude, but opposite in sense to that of the object.
To use the Brace-Köhler compensator, center the stage
and the objectives on a polarizing microscope, and then
place the specimen on a rotating stage, focus and illuminate the specimen with Köhler illumination, using a green
interference filter of the appropriate wavelength (see later).
Then cross the polarizer and the analyzer to get maximum
extinction. Close down the field diaphragm as much as you
can to minimize stray light, and to get the highest extinction factor. To this end, also close down the aperture diaphragm as much as you need to optimize extinction and
resolution. Rotate the specimen so that it is maximally
bright. Or better yet, since our vision is more accurate in
determining the maximal darkness on a black background
than maximally bright on a black background, find the
position where the specimen is maximally dark and then
rotate the stage exactly 45 degrees. At this position, the
slow axis of the specimen will be 45 degrees relative to
the polarizer. Make sure that you are in a dark room and
your eyes are dark-adapted.
Next, insert the compensator and turn the knurled knob
until the background is maximally black. In this position,
the slow axis of the compensator, denoted with a γ or nγ,
will be parallel to the azimuth of maximal transmission of
the polarizer or the analyzer. The compensator should read
45 degrees. The initial angle, read off the compensator, is
called c1. Now rotate the compensator knob until the specimen is brought to extinction, and note c2, the new angle
of the compensator. Depending on whether the specimen
is positively or negatively birefringent, the Brace-Köhler
compensator will have to be turned clockwise or counterclockwise. As you turn the knob, the compensator will
move from a position where the slow axis of the compensator is parallel to the azimuth of maximal transmission of
the polarizer or analyzer to a position where there is maximal retardation and the slow axis is 45 degrees relative
to the polarizer, and the angle that the compensator was
rotated can be read directly from the compensator. A λ/10
Brace-Köhler compensator gives a maximum of λ/10 retardation; a λ/20 Brace-Köhler compensator gives a maximum
of λ/20 retardation; and a λ/30 Brace-Köhler compensator gives a maximum of λ/30 retardation. The wavelength
of the compensator should match the wavelength of the
interference filter used to illuminate the specimen. The
retardation of the specimen is obtained by inserting the angle
read from the compensator into the following formula:
Γspecimen (Γcompensator ) sin (2)
where θ c1 – c2 and Γcompensator is equal to 546 nm/30 18.2 nm for λ/30 Brace-Köhler compensator, 546 nm/20 27.3 nm for a λ/20 Brace-Köhler compensator, and 546 nm/
10 54.6 nm for a λ/10 Brace-Köhler compensator. The
minus sign indicates that the slow axis of the compensator and the slow axis of the specimen lie on opposite sides
of the azimuth of maximal transmission of the polarizer.
Notice, that when θ 45°, the sin 2θ 1 and Γspecimen –
( Γcompensator).
Let’s look at stress fibers in cheek epithelial cells for
an example. Insert the compensation in the SE-NW direction. When the λ/30 Brace-Köhler compensator is set
for 45 degrees, its slow axis is parallel with the analyzer.
The background is maximally dark and we are able to see
bright stress fibers going from NE to SW. The stress fibers
are brought to extinction when we rotate the compensator
to 59 degrees. The retardation of the specimen is 8.5 nm
according to the following calculation (Figure 7-32):
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
(Γcompensator ) sin (2)
18.2 nm (sin 2(45° 59°))
18.2 nm (sin 2(14))
18.2 nm (sin (28))
18.2 nm (0.4695)
8.5 nm
Consider the same sample that has stress fibers oriented from NE to SW. Our first reading, c1, will still be
45 degrees, but our second reading, c2, will be 31 degrees.
The retardation of the specimen is 8.5 nm according to
the following calculations:
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
(Γcompensator ) sin (2)
18.2 nm (sin 2(45° 31°))
18.2 nm (sin 2(14))
18.2 nm (sin (28))
18.2 nm (0.4695)
8.5 nm
The sign of the retardation is an indication of the relationship between the slow axis of the compensator and the
slow axis of the specimen. If you know the orientation of
the specimen, you can determine the sign of birefringence;
if you know the sign of birefringence, you can determine
the orientation of the birefringent molecules relative to the
orientation of the slow axis of the compensator.
When using this method of Brace-Köhler compensation, the background lightens as the object is brought
to extinction. Thus, it is a little tricky to determine the
absolute compensation angle that brings the specimen to
maximal extinction. In order to overcome this difficulty,
Bear and Schmitt introduced a new method in which they
determined the angle of the compensator when the object
and the isotropic background were equally gray (c3), and
141
Chapter | 7 Polarization Microscopy
AN
AN
POL
POL
C2 59°
C2 31°
C1 45°
Γspec Γcomp sin 2(C1 C2)
FIGURE 7-32
compensator.
C1 45°
Γspec Γcomp sin 2(C1 C2)
Positively birefringent stress fibers in cheek cells with two different orientations are brought to extinction with a Brace-Köhler
TABLE 7-6 Sensitivity and Maximal Compensation of Brace-Köhler Compensators Using Different Methods of
Compensation
Traditional method
Bear-Schmitt method
Compensator
Maximum comp*
Sensitivity**
Max comp*
Sensitivity**
λ/30
18.33 nm
0.41 nm/degee
36.6 nm
0.81 nm/degee
λ/20
27.5 nm
0.61 nm/degree
55 nm
1.22 nm/degee
λ/10
55 nm
1.22 nm/degree
110 nm
2.44 nm/degee
Assuming 550 nm.
Obtained by dividing the maximum compensation by 45°.
*
**
subtracted this angle from c1. The difference between these
two angles is α. The retardation of the specimen is given
by the following formula:
Γspecimen 2(Γcompensator ) sin (2)
This method is half as sensitive as the original method
but more accurate, and the gain in accuracy may more than
balance the loss of sensitivity. Using this method, we find
that the stress fibers in the SE-NW direction are just as
gray as the isotropic background when the compensator
is set at 52 degrees. The retardation of the specimen is
8.8 nm, according to the following calculations:
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
Γspecimen
2(Γcompensator ) sin (2)
2 (18.2 nm ) sin (2(c1 c3 ))
2 (18.2 nm) sin (2(45 52))
2 (18.2 nm) sin (2(7))
2 (18.2 nm) sin (14)
2 (18.2 nm) sin (0.2419)
8.8 nm
Identical values of retardation would have been
obtained by both methods if c3 could be read precisely to
51.786. The maximum compensation and sensitivity of the
various Brace-Köhler compensators are given in Table 7-6.
With the traditional method, Brace-Köhler compensators cannot be used to compensate objects with retardations greater than their maximum. However, using the
Bear-Schmitt method, the maximum retardation that can
be measured can be increased by a factor of two.
In general, we use compensators, including a firstorder wave plate, a quartz wedge, a Berek compensator, an
Ehringhaus compensator, and a Brace-Köhler compensator
to extinguish the specimen by introducing an ellipticity to
the linearly polarized light coming from the polarizer that
is equal in magnitude but opposite in sense to that introduced by the specimen. Upon extinguishing the birefringent specimen, the retardation introduced by the specimen
is obtained from either the Michel-Lévy chart or from formulas that relate the retardation to the angle the compensator was tilted or rotated.
The de Sénarmont compensation method is a little
different from the methods described earlier, in that the
142
Light and Video Microscopy
Eye
Analyzer
λ/4
plate
Optic axis
of λ/4 plate
Specimen
Polarizer
FIGURE 7-33 A de Sénarmont compensator typically utilizes a λ/4
plate and a rotating analyzer.
specimen is brought to extinction by rotating the analyzer (or polarizer) instead of moving the compensator
(Figure 7-33). de Sénarmont compensation requires a
polarizer and an analyzer, one of which can be rotated
accurately 180 degrees. The birefringent specimen is
placed with its slow axis at a 45-degree angle relative to
the polarizer. A λ/4 plate is then inserted into the compensator position with its slow axis, denoted with a γ or n,
parallel to the fixed polarizer (or if the analyzer is fixed
it must be parallel to the fixed analyzer). Monochromatic
light must be used, and the wavelength of the illuminating
light must match the wavelength of the λ/4 plate.
To do de Sénarmont compensation, set the rotating
polar so that the background is maximally black and make
a note of that angle, which is most likely, but not always,
0 degrees. Then turn the rotating polar until the birefringent specimen is brought to extinction and note this angle.
The difference between the two angles is called the compensation angle (ac). The retardation of the specimen is
given by the following formula:
Γspecimen (2a c )( / 360) m .
The sensitivity of the de Sénarmont compensator is
3.034 nm per degree and it normally is used for retardation
up to one wavelength. It can be used for objects that have
many wavelengths of retardation; however, it is capable of
giving only the fraction of the wavelength above one order.
The value of m can be deduced from a rough measurement
made with a quartz wedge compensator. The sign of birefringence can be obtained since the rotating polar must be
turned in opposing directions to extinguish positively or
negatively birefringent specimens oriented with their physical axes in the same direction.
Consider that the slow axis of a specimen is oriented 45 degrees (NE-SW) relative to the fixed polarizer (E-W) and the slow axis of the λ/4 plate (E-W). The
de Sénarmont compensator works because linearly polarized light passing through a specimen is resolved into two
orthogonal linearly polarized components that are out-ofphase with each other. Instead of considering the wave
emerging from the specimen as being elliptically polarized, as we did when discussing the other compensation
methods, consider the emerging light as consisting of two
orthogonal, linearly polarized waves of equal amplitude.
Each wave passes through the λ/4 plate after it emerges
from the specimen. The slow wave emanating from the
specimen passes through the λ/4 plate and makes an angle
of 45 degrees (NE-SW) relative to the slow axis of the
λ/4 plate. This is optically equivalent to the slow axis of
the λ/4 plate making an angle of 45 degrees relative to
the incoming linearly polarized light. Thus the slow linearly polarized wave is turned into circularly polarized
light with a clockwise rotation.
Now, consider the fast component that emerges from
the birefringent specimen as a linearly polarized wave that
transverses the λ/4 plate at an angle of 45 degrees (SENW) relative to the slow axis of the λ/4 plate. The fast
linearly polarized wave emanating from the specimen is
converted into circularly polarized light that travels with
a counterclockwise sense of direction. Thus two coherent
circularly polarized waves have equal amplitudes and frequencies, but opposite senses when they emerge from the
λ/4 plate. Each of these two waves has a component that is
coplanar with the azimuth of maximal transmission of the
analyzer, and consequently, they can interfere in that plane.
In order to determine the resultant azimuth of these
two circularly polarized waves we must add the amplitudes of each vector at various time intervals. Two coherent circularly polarized waves with equal magnitudes but
opposite senses recombine to give linearly polarized light.
The azimuth of the linearly polarized wave depends on the
phase angle between the two circularly polarized waves.
The azimuth of the resultant linearly polarized wave will
not be parallel to the azimuth of maximal transmission of
the rotating analyzer. The rotating analyzer is then turned
from its original position where the background was maximally dark, to a position where the specimen is brought to
extinction. The angle through which the rotating analyzer
is turned is known as the compensation angle.
I will describe another vector method for describing
the brightness of the specimen when the analyzer is rotated
through any angle (Figure 7-34). Consider a polarizing
microscope with a fixed polarizer and a rotating analyzer.
The slow axis of the λ/4 plate is parallel to the azimuth
of maximal transmittance of the polarizer. Consider a
birefringent specimen that causes a phase change of
45 degrees oriented so that its slow axis is 45 degrees
relative to the polarizer. The slow axis of the λ/4 plate is
45 degrees relative to the linearly polarized wave that
originates from the slow axis of the specimen. Thus this
light wave will be circularly polarized by the λ/4 plate and
will travel in the clockwise direction. The slow axis of the
λ/4 plate is 45 degrees relative to the linearly polarized
143
Chapter | 7 Polarization Microscopy
A
B
AN
C
AN
AN
2
1
POL, γc
POL, γc
D
3
POL, γc
AN
Summary of resultants
for all time points
1
2
3
4
POL, γc
ac
E
AN
F
AN
G
AN
Summary of resultants
for all time points
1
1
POL, γc
POL, γc
POL, γc
ac
2
2
FIGURE 7-34 The phase relations between the clockwise and counterclockwise circularly polarized waves that leave the quarter wave plate for a
specimen with a phase angle of 45 degrees (A-D) and a specimen with a phase angle of 90 degrees (E-G). When the counterclockwise circularly polarized wave is 45° ahead of the clockwise circularly polarized wave, the resultant linearly polarized wave is rotated 22.5° counterclockwise relative to
the axis of maximal transmission of the polarizer. To extinguish the resultant, the analyzer also has to be rotated 22.5° counterclockwise. When the
counterclockwise circularly polarized wave is 90° ahead of the clockwise circularly polarized wave, the resultant linearly polarized wave is rotated 45°
counterclockwise relative to the axis of maximal transmission of the polarizer. To extinguish the resultant, the analyzer also has to be rotated 45° counter
clockwise.
wave that originates from the fast axis of the specimen.
Thus this light wave will be circularly polarized by the λ/4
plate and will travel in the counterclockwise direction.
Draw a Cartesian coordinate system so that the abscissa
(E-W) represents the azimuth of maximal transmission
of the polarizer and the ordinate (N-S) represents the
azimuth of maximal transmission of the analyzer. Draw the
path of the two circularly polarized light beams on this
coordinate system. The wave originating from the fast axis
of the specimen will be ahead of the wave originating from
the slow axis of the specimen by an amount equal to the
phase angle. Here are two examples: In the first example
144
Light and Video Microscopy
AN
AN
POL
0°
1
AN
2
POL
2
1
POL
3
Summary of resultants
for all time points
FIGURE 7-35 When the counterclockwise circularly polarized wave is 0° ahead of the clockwise circularly polarized wave, the resultant linearly
polarized wave is rotated 0° clockwise relative to the axis of maximal transmission of the polarizer. To extinguish the resultant, the analyzer also has to
be rotated 0°.
(like the example earlier), the specimen introduces a
45-degree phase angle, linearly polarized light is produced by the λ/4 plate, and the analyzer must be rotated
22.5 degrees counterclockwise to extinguish the specimen.
In the second, the specimen introduces a 90-degree phase
angle, linearly polarized light is produced by the λ/4 plate,
and the analyzer must be rotated 45 degrees counterclockwise to extinguish the specimen. In both case, the analyzer
must be rotated through an angle that is equal to half the
fractional phase change of the specimen.
fractional phase change n (360 /) Γspecimen 2a c.
Following is an example of a specimen that introduces
no difference in phase or a phase angle equivalent to an
integral number of wavelengths of the monochromatic illuminating light (Figure 7-35).
A clever person can make his or her own de Sénarmont
compensator by attaching a Polaroid to a circular protractor to make a rotating polarizer and by making a λ/4 plate
by layering six to seven layers of Handi-Wrap together.
In order to eliminate any wrinkles, cut a hole in a piece of
cardboard and tape each layer of Handi-Wrap to the cardboard. A clever person can also make a λ/4 plate out of
mica (H2Mg3(SiO3)4) that is split into thinner and thinner
pieces with a fine needle. Make several of these pieces,
and then test them to find which ones are λ/4 plates for
the wavelength of interest. Mount the λ/4 plate in Canada
Balsam between two cover glasses (Spitta, 1907).
The retardations measured with all compensators are
based on trigometric functions and thus the retardation data
may need to be transformed when doing statistics in order
to meet the assumptions of linearity (Neter et al., 1990).
I have discussed a number of methods we may use
to measure the retardation of birefringent specimens.
However, to know the magnitude of birefringence, we must
be able to measure the thickness of the specimen. The best
way to measure the thickness is to use interference microscopy (see Chapter 8). There are two other methods that
may be acceptable.
With the focusing micrometer method, we use a lens
with a high numerical aperture and minimal depth of field.
First, calibrate the fine focusing knob (see Chapter 2; Clark,
1925; McCrone et al., 1984). Second, focus on the top surface of the specimen and read the measurement on the fine
focusing knob. Third, focus on the bottom of the object
and again read the measurement on the fine focusing knob.
Since the greater the refractive index of the specimen, the
thinner it appears, this method is accurate only when we
already know the average refractive index of the specimen.
We can also estimate the thickness of a spherical or
cubic specimen by using the ocular micrometer method, in
which we measure the length of the specimen in the horizontal dimension and assumes that it is the same as the
length of the specimen in the vertical dimension.
CRYSTALLINE VERSUS FORM
BIREFRINGENCE
Some molecules are not intrinsically birefringent themselves, but they can be aligned in such a way that linearly polarized light will be retarded more when it passes
through the specimen in one azimuth compared to another.
Such oriented molecules are visible when viewed between
crossed polars. This is known as form birefringence. Form
birefringence can result from natural biological processes
that align macromolecules (e.g., spindle formation during
mitosis). Form birefringence can also result from the alignment of molecules by cytoplasmic streaming (Ueda et al.,
1988). This is also known as flow birefringence.
Birefringence in solids, induced by mechanical stress, is
known as strain birefringence (Brewster, 1833b; Lintilhac
and Vesecky, 1984). The quality of glass used to make
lenses is monitored, in part, through measurements of
145
Chapter | 7 Polarization Microscopy
strain birefringence (Musikant, 1985). Photo-elastic studies use polarized light and polarized light microscopy to
determine the strain in materials by looking at the pattern
of polarization colors produced by a specimen under stress.
Form, but not intrinsic birefringence, disappears when
a permeable specimen is immersed in media of increasing
refractive indices and reappears when the refractive index
of the medium surpasses the refractive index of the specimen (Bennett, 1950; Frey-Wyssling, 1953, 1957; Colby,
1971; Taylor, 1976). Intrinsic birefringence is not affected
by immersion media because the molecules that make up
the immersion media are two big to penetrate the bonds
of the anisotropic molecules. When selecting immersion
fluids it is important to use fluids that will not change
the physicochemical nature of the specimen itself. Patzelt
(1985) compiled a useful list of immersion fluids with
refractive indices between 1.3288 (methanol) and 1.7424
(methyl iodide) that can be used to distinguish between
form and intrinsic birefringence.
ORTHOSCOPIC VERSUS CONOSCOPIC
OBSERVATIONS
Up until now I have been discussing orthoscopy, which
means that I have been discussing what the specimen looks
like at the image plane. Mineralogists also find it useful to
observe the diffraction pattern produced by the specimen in
the reciprocal space of the aperture plane. This is known as
conoscopy. When doing conoscopy, it is convenient to be
able to position the specimen in three dimensions by using
a goniometer, which is a rotating stage that can rotate the
specimen in the specimen plane as well as tilt the specimen
45 degrees relative to the optical axis of the microscope.
By observing the diffraction plane, conoscopy provides an
effective way of determining whether a mineral is uniaxial
or biaxial; that is, if it has one optic axis and two refractive indices or if it has two optic axes and three indices of
refraction (Patzelt, 1985).
REFLECTED LIGHT POLARIZATION
MICROSCOPY
Polarized light microscopes can be used in the reflected
light or epi-illumination mode. In epipolarization microscopy, the light passes through the objective before it strikes
the specimen and then the reflected light is captured by the
same objective lens. Epipolarization microscopes are used
for metallurical work and have also been used in biological
work to localize antibodies that are conjugated to colloidal
gold (Hughes, 1987; Hughes et al., 1991; Gao and Cardell,
1994; Gao et al., 1995; Stephenson et al., 1998; Ermert
et al., 1998, 2000, 2001).
USES OF POLARIZATION MICROSCOPY
Polarization microscopy is used in geology, petrology, and
metallurgy to identify minerals (McCrone et al., 1979,
1984). Polarization microscopy is also used in art identification in order to determine the age, and thus the authenticity of a painting (McCrone, 1992; Brouillette, 1990). Each
pigment used to make paint usually has a metallic base.
Throughout history new pigments have been invented. The
pigments can be identified in a “pinprick” of paint with a
polarizing microscope. White pigment made out of rutile
(TiO2/CaSO4) was not introduced until 1957, so if you find
them in a painting supposedly done in 1907, the painting is
probably a forgery. Walter McCrone (1990) estimates that
90 percent of paintings are fakes.
Polarization microscopy also has been used extensively
in biology to study the structure of DNA, membranes, the
microfibrils in cell walls, wood, cell walls, microtubules
in the mitotic apparatus and the phragmoplast, chloroplast structure, muscle fibers (the I band and the A band
stand for isotropic band and anisotropic band, respectively), starch grains and biological crystals composed of
calcium oxalate, calcium carbonate and silica (Quekett,
1848, 1852; Carpenter, 1883; Naegeli and Schwendener,
1892; Schmidt, 1924; Noll and Weber, 1934; Hughes and
Swann, 1948; Swann, 1951a, 1951b, 1952; Inoué, 1951,
1952a, 1953, 1959, 1964; Inoué and Dan, 1951; Preston,
1952; Frey-Wyssling, 1953, 1957, 1959, 1976; Inoué and
Bajer, 1961; Forer, 1965; Ruch, 1966; Salmon, 1975a,
1975b; Taylor, 1975; Frey-Wyssling, 1976; Palevitz and
Hepler, 1976; Hiramoto et al., 1981; Wolniak et al., 1981;
Inoué, 1986; Cachon et al., 1989; Schmitt, 1990; Inoué
and Salmon, 1995). Perhaps the most elegant use of the
polarized light microscope in biology was to determine
the entropy and enthalpy of the polymerization reaction of
the mitotic spindle fibers by Shinya Inoué.
The mitotic spindle is a dynamic structure that reversibly
breaks down when exposed to elevated hydrostatic pressures and microtubule-depolymerizing drugs, including colchicine (Inoué, 1952a). While observing the mitotic spindle
of Chaetopterus with polarization microscopy, Shinya Inoué
(1953, 1959, 1964) noticed a remarkable and completely
unexpected phenomenon. He observed that as he increased
the temperature of the stage, the amount of anisotropy of
the mitotic spindle increased (Figure 7-36). Since a completely random specimen is isotropic, and anisotropy typically indicates that the specimen is ordered—an increase in
the anisotropy of the specimen means an increase in order.
This was surprising because typically, increasing the temperature increases the disorder in a system.
This unusual effect of temperature on protein had
been observed before with muscle protein and the tobacco
mosaic virus protein. It turns out that protein monomers
have a shell of water around them, and this bound water
prevents the protein monomers from interacting among
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Light and Video Microscopy
standard free energy (Gstd) relative to the energy that
occurs at equilibrium (Geq 0) can be calculated from the
following equations:
Retardation (nm)
5
4
G eq Gstd RT ln K eq /K std
RT ln{([B]/[A o B])/(1/1)}
3
Gstd G eq RT ln K eq /K std
RT ln{([B]/[A o B])/(1/1)}
2
1
5
10
15
20
25
Temperature (°C)
30
35
At standard pressure, the standard free energy is composed of a standard enthalpy term (J/mol) and a standard
entropy term (in J mol1 K1) according to the following
equation:
FIGURE 7-36 The retardation of the mitotic spindle is temperaturedependent.
Gstd Hstd T Sstd
Therefore,
themselves and forming a polymer. The removal of the
bound water requires an input of energy, which comes
from raising the temperature. As the temperature increases,
the shell of water surrounding the protein monomers
is removed and hydrophobic interactions between the protein monomers themselves can take place. Inoué proposed
that the fibers in the spindle were made out of proteins, and
the fibers formed when the protein subunits polymerized.
Inoué quantified his work in the following way: He
assumed that the maximum anisotropy occurred when all
the subunits were polymerized. Inoué called the total concentration of the protein subunits Ao and the concentration of polymerized subunits B, where B is proportional
to the amount of anisotropy (Γ, in nm) measured with the
polarizing microscope. When all the subunits are polymerized B Ao, and when all the subunits are depolymerized, B 0. The free subunits can be calculated as Ao – B.
Inoué assumed that polymerization occurred according to
the following reaction:
kon
Ao B
B
koff
⇔
where the equilibrium constant Keq [B]/[Ao–B]
Inoué determined the concentration of polymerized
subunits at a given temperature by measuring the retardation of the spindle at that temperature. He assumed that
the maximal value of retardation was an estimate of
the total concentration of subunits. He calculated the
concentration of free subunits at a given temperature by
subtraction.
The degree of polymerization is determined by the
equilibrium constant (Keq), which represents the ratio of
polymerized to free subunits ([B]/[Ao–B]). The molar
Gstd Hstd T Sstd RTln([B]/[A o B])
This can be rewritten as a linear equation:
ln ([B]/[A o B]) (std /R)(1/T) Sstd /R
or
ln ([B]/[A o B]) ( Hstd /R)(1/T) Sstd / R
Inoué plotted ln ([B]/[AoB]) versus (1/T) to get a van’t
Hoff plot, where the slope is equal to (ΔHstd/R) and the
Y intercept is equal to ΔSstd/R (Figure 7-37). Thus at a
given temperature he could estimate ΔHstd/R and TΔSstd.
Inoué determined the standard enthalpy of polymerization at room temperature to be 34 kcal/mol and the
product of the standard entropy and the absolute temperature to be 36.2 kcal/mol. Since TΔSstd is greater than
ΔHstd, polymerization of the subunits is an entropy-driven
process. Thus Inoué concluded that the subunits of the
spindle fibers were surrounded by bound water and the
removal of the bound water caused an increase in entropy.
This increase in entropy provided the free energy necessary
to drive the polymerization reaction. Moreover, he proposed that the controlled depolymerization of the spindle
fibers provided the motive force that pulled the chromosomes to the poles during anaphase. These experiments are
remarkable in light of the fact that they were done approximately 20 years before the discovery of tubulin. After the
discovery of microtubules with the electron microscope,
Inoué and Sato (1967) recast the dynamic equilibrium
hypothesis in terms of microtubules (Sato et al., 1975;
Inoué, 1981).
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Chapter | 7 Polarization Microscopy
Temperature, C
30
25
20
15
10
5
20
10
8
6
[B] / [A0 B]
4
2
1
0.8
0.6
0.4
0.2
0.1
0.08
0.06
3.25
3.35
3.45
3.55
1/Temperature, 1/K 103
FIGURE 7-37 The entropy and enthalpy of polymerization of spindle fibers can be determined by drawing a van’t Hoff plot with ln ([B]/
[Ao–B]) vs 1/T.
OPTICAL ROTATORY (OR ROTARY)
POLARIZATION AND OPTICAL ROTATORY
(OR ROTARY) DISPERSION
E Pluribus Unum. E Unum Pluribus. It is a general truth
that, when all factors are accounted for, the whole is
equal to the sum of its parts. In explaining how polarized light interacts with birefringent specimens, I have
freely resolved vectors into their components and summed
the two components into a resultant. In order to emphasize
the “double reality” of vectors and their components, I will
end this chapter where I began, discussing the rotation of
linearly polarized light. Here we will discuss how linearly
polarized light can be resolved into two circularly polarized waves that rotate with opposite senses. We will use
this knowledge to understand how, in a molecule, electron
vibrations are not always linear but also helical. Polarized
light allows us to visualize the three-dimensional electronic
structure of molecules.
Francois Arago discovered in 1811 that quartz is
unusual. He passed linearly polarized yellow light
produced by a sodium flame and a Nicol prism polarizer
through a 1 mm section of quartz cut perpendicular to the
optic axis, and he discovered that the yellow light passed
right through the crossed Nicol prism that he used as an
analyzer. The light that passed through the analyzer was
still linearly polarized since he could extinguish the light
by rotating the analyzer 22 degrees. The quartz appeared to
rotate the azimuth of polarization in a process Arago named
optical rotatory polarization. Substances that are capable of
rotating linearly polarized light are called optically active.
In 1817, Jean-Baptiste Biot found that when he passed
white light through the quartz plate, the plate appeared colored, and the color changed as the analyzer was rotated.
That meant that the degree of rotation was wavelengthdependent. The wavelength-dependence of optical rotatory polarization is known as optical rotatory dispersion
(Wood, 1914; Slayter, 1970). Substances that rotate the
azimuth of polarization to the right are known as dextrorotatory and substances that rotate the azimuth of polarization to the left are known as laevo-rotatory. In 1822 John
Hershel found that quartz molecules are dextro-rotatory
and others are laevo-rotatory. Lenses used to transmit
ultraviolet light are made of quartz. These must have equal
contributions of dextro-rotatory and laevo-rotatory quartz
to the optical paths to ensure that the lens itself does not
introduce rotatory polarization (Wood, 1914).
Optical rotatory polarization was explained by
Augustin-Jean Fresnel (Wood, 1914; Robertson, 1941). He
proposed that the incident linearly polarized light can be
considered to be composed of two in-phase components
of circularly polarized light that propagate with opposite
senses with differing speeds. An optically active substance
can be considered to have circular birefringence.
By looking at the angle the light bends when it passes a
quartz-air interface, Fresnel showed that a circularly polarized wave with clockwise rotation experiences a different
refractive index than the circularly polarized wave with
counterclockwise rotation as they spiral though a substance
capable of optical rotatory polarization. Upon recombination in the azimuth of maximal transmission of the analyzer, the linearly polarized resultant passed through the
analyzer placed in the crossed position because the two
circularly polarized waves recombine to make linearly
polarized light whose azimuth of polarization was changed
as a consequence of the phase angle introduced by the
specimen. The analyzer is then turned either clockwise
or counterclockwise to find the position where the light
is again extinguished. This position, combined with the
direction of rotation, gives the value for the optical rotatory
polarization of a given thickness of a pure liquid or solid,
or at a given thickness, the concentration of a liquid.
Biot accidentally found that the oil of turpentine that he
used to mount crystals in also had the ability to rotate the
azimuth of polarization. Solutions of randomly arranged
molecules, including sugars, amino acids, and organic
acids, are also able to rotate the azimuth of linearly polarized light. In 1848 to 1851, Louis Pasteur found that when
a solution of laboratory-synthesized racemic acid, which
148
was identical to naturally occurring tartaric acid in every
way except for its inability to rotate linearly polarized light,
was allowed to crystallize, two types of crystals formed.
The two crystals were mirror images of each other. Using
a microscope, Pasteur separated the two types of crystals
into right-handed crystals and left-handed crystals. When
the right-handed crystals were dissolved in solution, they
rotated the linearly polarized light to the right. Solutions of
the left-handed crystals rotated polarized light to the left.
Thus racemic acid did not rotate polarized light because it
consisted of an equal mixture of two optical isomers of tartaric acid. Pasteur concluded that there must be a chemical
asymmetry in the two optical isomers, but he did not know
what caused the asymmetry (Jones, 1913).
By considering molecules to be three-dimensional
rather the two-dimensional structures that were drawn on
paper, Jacobus van’t Hoff and Joseph Le Bel independently
proposed in 1874 that the carbon atom was tetrahedral and
that the asymmetries in molecules were caused by a tetrahedral carbon atom that made bonds with four different
functional groups. Optical rotatory polarization and optical
rotatory dispersion can be used to identify molecules and
deduce their structure (Djerassi, 1960). Proteins with helical structures also tend to exhibit optical rotatory polarization. According to Paul Drude, electrons in substances that
show optical rotatory polarization vibrate in a helical manner instead of back and forth (Wood, 1914). In principle,
both optical rotation and optical rotatory dispersion can be
done through the microscope to identify small quantities of
material in a sample.
If the two circularly polarized components of the incident light are differentially absorbed, then the resultant
Light and Video Microscopy
will be elliptically polarized and will pass through
crossed polars. This is known as circular dichroism. The
Cotton Effect, named after A. Cotton, results from a combined effect of circular rotatory dispersion and circular
dichroism.
Optical rotation, or circular birefringence, is different than linear birefringence in that a solution that has no
preferred directionality associated with it can rotate the
plane of linearly polarized light as a consequence of threedimensional asymmetry in the structure of the solutes randomly arranged in the solution (Robertson, 1941). To visualize this, hold a slinky in your hand—no matter which way
you turn it, its sense of rotation will be the same to you.
WEB RESOURCES
Polarized Light
Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polarcon.
html#c1
Polarized Light Microscopy
Olympus Microscopy Resource Center: http://www.olympusmicro.com/
primer/techniques/polarized/polarizedhome.html
Nikon Microscopy U:http://www.microscopyu.com/articles/polarized/
polarizedintro.html
Molecular Expressions Optical Microscopy Primer: http://micro.magnet.
fsu.edu/primer/techniques/polarized/polarizedhome.html
Polarized light has been utilized by Austine Wood Comarow to make Polages,
which are “paintings without pigments.” http://www.austine.com/
Chapter 8
Interference Microscopy
Interference microscopy is similar to phase-contrast
microscopy in that both types of microscopes turn a difference in phase into a difference in intensity, and for this
reason, a chapter on interference microscopy would naturally follow Chapter 6. However, since many interference
microscopes utilize polarized light, I present interference
microscopy to my students after they become fully comfortable with polarized light. Color plates 12 and 13 provide
examples of images taken using image duplication-interference microcopy. Moreover, since interference microscopes
are not commonly found in laboratories, to make the process of interference more familiar to my students, I begin
by taking them outside to blow bubbles while we discuss
the optics of thin films. It also gives them a chance to picture Isaac Newton blowing bubbles, to realize the truth in
Albert Szent Györgyi’s words that, “Discovery consists in
seeing what everyone else has seen and thinking what no
one else has thought.”
GENERATION OF INTERFERENCE COLORS
Sometimes less is more, and it is really pretty amazing how
transparent objects such as a solution of soap or gasoline
become colored when they become thin enough. Newton
(1730) wrote, “It has been observed by others, that transparent Substances, as Glass, Water, Air, &c. when made very
thin by being blown into Bubbles, or otherwise formed into
Plates, do exhibit various Colours according to their various
thinness, altho’ at a greater thickness they appear very clear
and colourless.” The observation of colors produced by thin
plates was first observed by Robert Hooke (1665), and published in his book, Micrographia. Newton, however, quantitatively studied the generation of colors by thin plates, and
we usually speak of the colors generated by interference as
Newton’s colors. Newton (1730) wrote,
If a Bubble be blown with Water first made tenacious by dissolving a little Soap in it, ‘tis a common Observation, that after a
while it will appear tinged with a great variety of Colours.… As
soon as I had blown any of them I cover’d it with a clear Glass,
and by that means its Colours emerged in a very regular order,
like so many concentrick Rings encompassing the top of the
Bubble. And as the Bubble grew thinner by the continual subsiding of the Water, these Rings dilated slowly and overspread
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Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
the whole Bubble, descending in order to the bottom of it, where
they vanished successively. In the mean while, after all the
Colours were merged at the top, there grew in the center of the
Rings a small round black Spot.
Interference is not only responsible for the colors of
thin plates, but can also account for the iridescent colors
of some algae, the blue leaves of Selaginella (Fox and
Wells, 1971), as well as some insects, butterflies, and birds,
including peacocks (Fox, 1936). Newton (1730) wrote,
“The finely colour’d Feathers of some Birds, and particularly those of Peacocks Tails, do, in the very same part of
the Feather, appear of several Colours in several Positions
of the Eye, after the very same manner that thin Plates
were found to do.…”
Newton found that the colors produced by a thin film
formed by a given substance were dependent on the thickness of the thin film. He also found that the color of the
thin film depends on the angle of observation since the
length through which light propagates through the thin
film to get to our eyes changes when we look at it from
different angles. He also found that, for films of identical
thickness and viewed at identical angles, the color depends
on the refractive index of the substance that makes up the
thin film. All these observations can be summed up by the
following sentence: The color of a thin film depends on
the difference in the optical path lengths of the light waves
that reflect off the top surface of the thin film and the light
waves that reflect off the bottom surface of the thin film.
Newton tried to explain the generation of colors in
terms of the corpuscular theory of light, but he had to
introduce an ad hoc hypothesis that the aetherial medium
through which the corpuscles travel underwent “fits.”
Thomas Young (1801, 1807) thought that perhaps the light
itself underwent the fits and was thus wave-like. He then
suggested that light waves that were reflected from the bottom surface of the thin film combined with the light waves
that were reflected from the top surface and destroyed each
other in a process he called interference. By the 1820s,
Augustin Fresnel (Fresnel, 1827, 1828, 1829; Arago, 1857;
Mach, 1926) came up with a complete theory of the generation of interference colors for thin films of both isotropic
and birefringent material. I discussed the colors formed by
birefringent material in Chapter 7. Here I will discuss the
149
150
Light and Video Microscopy
Since tan β (AC/2)/d, AC 2d tan β and sin α AD/(2d tan β), solve for AD:
Eye
W
X
AD 2d tan β sin α
90°α
α
α
Since tan β sin β/cos β:
D
n1
F
A
β β β
E
FIGURE 8-1
AD 2d (sin β/cos β) sin α
2d (sin 2 β/cos β)(sin α / sin β)
C
d nn
n1
B
Interference of light reflected from a thin film in air.
generation of colors by isotropic substances that have only
one refractive index.
Consider the following situation: Light, traveling
through air, which has a refractive index of 1, strikes a thin
film with a refractive index n, at A, at an angle α relative
to the normal. The light then is refracted toward the normal
and travels to B. The light then is reflected in such a way
that the angle of reflection equals the angle of incidence
and thus both angles equal ⬔β. The reflected light then
strikes the film-air interface at C, where it is refracted away
from the normal, and travels parallel to wave W. Wave W
and wave X are able to interfere with each other because
they are coherent; i.e. generated from the same source, and
close together. The fact that waves that are close enough
together are able to interfere indicates that waves have a
wave width as well as a wave length. The optical path difference (OPD) between the two waves is given by the following formula (Figure 8-1):
OPD n(AB BC) AD
As written, this formula is not very useful to us.
However, a little geometry, a little trigonometry, and the
Snell-Descartes Law will make this equation more useful.
Since AE and BF are parallel, ⬔ABF ⬔EAB β.
From the definition of tangent and cosine, we get the following relations:
tan β AC/ 2d AC 2d tan β
Use the Snell-Descartes Law (for air). Since sin α/sin
β n, then
AD 2dn (sin 2 β/cos β)
Since the optical path length is the product of the refractive index and the distance, AD is the optical path that the
reflected light takes in air.
OPL1 2dn (sin 2 β /cos β)
Now we must determine the optical path length that the
wave takes to and from the second surface. Since cos
β d/(AB) 2d/2AB:
2 AB 2d/cos β
The optical path length of the wave reflected at the second
surface is the product of the refractive index and the distance traveled and is given by
OPL 2 2 ABn (2dn/cos β)
The optical path difference (OPD) is
OPD OPL 2 OPL1
(2dn/cos β) 2dn ( sin 2 β/cos β)
OPD (2dn/cos β)(1 sin 2 β)
Since, 1 – sin2 β cos2 β
OPD (2dn/cos β)(cos2 β)
and
OPD (2dn cos β)
This equation can also we written in terms of the angle of
incidence using the following form of the Snell-Descartes
Law: Since sin α /sin β n,
cos (90 α ) AD/AC
cos β d/AB d/BC AB BC d/cos β
n sin α /√(1 cos2 β)
and
cos β √(1 ((sin 2 α )/n 2 ))
The following is a trigonomic identity:
sin α cos (90 α )
or
cos (90 α ) AD/AC
OPD 2dn √(1 ((sin 2 α )/n 2 ))
2d √(n 2 (sin 2 α ))
sin α AD/AC
This equation, if it is true, suggests that when the thickness
of the thin film is zero, there is no optical path difference
Thus,
and
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Chapter | 8 Interference Microscopy
between the wave reflected from the top surface and the
wave reflected from the bottom surface, and consequently,
all the wavelengths of light should constructively interfere
to form a white light reflection. Unfortunately, experience
shows that this is not always true, and that often there is
no reflection when the thickness is zero and consequently
the thin film appears black. Both Young and Fresnel were
able to model reality better by postulating that the reflection that takes place at the surface between the rarer and
the denser medium introduces a λ/2 change in phase. In
Thomas Young’s (1802) words,
In applying the general law of interference to these colours, as
well as to those of thin plates already known, I must confess
that it is impossible to avoid another supposition, which is a part
of the undulatory theory, that is, that the velocity of light is the
greater, the rarer the medium; and that there is also a condition
annexed to the explanation of the colours of thin plates, which
involves another part of the same theory, that it, that where one
of the portions of light has been reflected at the surface of a
rarer medium, it must be supposed to be retarded one half of the
appropriate interval, for instance, in the central black spot of a
soap-bubble, where the actual lengths of the paths very nearly
coincide, but the effect is the same as if one of the portions
had been so retarded as to destroy the other. From considering
the nature of this circumstance, I ventured to predict, that if the
two reflections were of the same kind, made at the surfaces of a
thin plate, of a density intermediate between the densities of the
mediums containing it, the effect would be reversed, and the central spot, instead of black, would become white; and I now have
the pleasure of stating, that I have fully verified this prediction, in
interposing a drop of oil of sassafras [n 1.536] between a prism
of flint glass [n 1.583] and a lens of crown glass [n 1.52]; the
central spot seen by reflected light was white, and surrounded by
a dark ring.
Thus, according to Young, the colors of reflected
light seen at a given angle depend not only on the thickness and refractive index of the material that makes up the
thin film, but also on the difference in refractive indices at
both surfaces (Young, 1807; Fresnel, 1827, 1828, 1829;
Baden-Powell, 1833; Lloyd, 1873; Mach, 1926). Two
reflecting surfaces can also be made from three different
media.
According to Young’s and Fresnel’s rules, when the
difference between the refractive indices of the incident
medium and the transmitting medium is positive, there is
no change in the phase of the reflected light. When the difference is negative, there is a half-wavelength change in
phase in the reflected light. For example, for a thin film
soap bubble in air, n1–n2 is negative and n2–n3 is positive.
As a result, there is a half-wavelength change in phase for
all wavelengths introduced at the first surface.
OPD OPL1 OPL 2 2dn cos β λ/ 2
The optical path difference between the refracted and
reflected wave vanishes when 2dn cos β λ/2, and light
with a wavelength equal to 2dn cos β is not reflected.
n1
n2
n3
FIGURE 8-2 Interference of light reflected from a thin film when
n1 n2 n3. This is the case for the thin films of metal oxides that are
responsible for the iridescent colors of glass.
Wavelengths close to this wavelength are partially reflected.
By conservation of energy, the transmitted light represents
the portion of each wavelength that is not reflected and
the color of the transmitted light is complementary to the
color of the reflected light (Young, 1807; Dunitz, 1989).
The observed color depends on the refractive index of the
thin film, its thickness, and the angle of the observation
(which is related to β). When the thickness of the film (d)
approaches 0, the optical path differences for all wavelengths approach –λ/2. Consequently, all wavelengths
destructively interfere and there is no reflected light causing
the thin film to look black.
In the case described earlier, n1 n2 n3; however,
when the refractive indices are such that n1 n2 n3 such
as it would be at an air/oxide/glass interface of a air/metal
oxide/metal interface, then there is a λ/2 change in phase
of the reflected light at both interfaces and the optical path
difference is given by (Figure 8-2):
OPD (2dn cos β λ/ 2) λ / 2 2dn cos β λ
The optical path difference of a given wavelength vanishes
when 2dn cos β λ, and light with a wavelength equal to
2dn cos β is completely reflected and the complementary
color is transmitted. When the thickness approaches zero,
all wavelengths are reflected and the film appears white.
Thin films of metal oxides are responsible for the iridescent colors of glass made by Frederick Carder of Steuben
Glass and Louis Comfort Tiffany of the Tiffany Glass
Company and of some jewelry available today.
Lenses often are coated with thin films to minimize
reflections. The idea for antireflection coatings came to
Lord Rayleigh when he realized that the old optical glass
that had tarnished transmitted more light than an untarnished piece of glass. Thin films made of magnesium fluoride replace the tarnish in antireflection coatings used on
lenses today. The thin films act as antireflection coatings
when the unidirectional optical path length of the film is λ/4
and the light reflected from the two interfaces destructively
interferes. The antireflection coating reduce the percentage
of reflected light from 4 percent to 1 to 2 percent.
152
Light and Video Microscopy
Before I discuss how the knowledge of how interference
colors produced by thin films can be used to our advantage
in microscopy, I want to briefly discuss the generation of
interference colors by diffraction (see Chapter 3).
In 1611, Maurolico wrote:
If you view the light of a candle, placed not too far away, through
a white feather from a dove or from some other bird, when
placed opposite the eye you will see, between the lines on the
feather and those branches, a certain distinct cross with a wonderful variety of colors, such as are seen in the rainbow. This can
happen only through the light being received between the small
grooves of the feather tufts, and there multiplied, continually
incident and by turns reflected.
The colors of some bird feathers and of many brightly
colored beetles result from the process of diffraction. The
importance of diffraction in the coloration of beetles was
first suggested by Thomas Young (1802). In order to artificially produce colored spectra, David Rittenhouse (1786)
and Joseph Fraunhöfer (1821; see Meyer, 1949) independently discovered that gratings were able to separate light
into its constituent colors. Fraunhöfer etched extremely
precise gratings on glass and illuminated them with a slit
of white light. He found that in the center, a white image
of the slit is produced, only slightly darker than the image
would have been in the absence of a grating. Both sides
of the bright band were dark. On the outsides of the dark
bands were colored bands of violet, blue, green, yellow,
orange, and red, in that order. Fraunhöfer found that the
angular position of each color in the first spectrum could
be found with the following formula:
sin θ λ/d
where d is the distance between the etched lines.
Since each wavelength is diffracted to a different position, a colored spectrum is produced when white light
strikes a diffraction grating. John Barton decided to take
advantage of the production of colors by multiple slits and
developed a machine that was able to cut grooves 1/2000
to 1/10,000 of an inch apart in steel with a diamond knife.
Mr. Barton made colorful buttons and ornaments known as
“iris ornaments” (Brewster, 1833b; Baden-Powell, 1833).
Many animals and some plants produce vivid structural
colors as a result of thin film interference, diffraction, or a
combination of the two (Fox, 1936; Rossotti, 1983; Lee,
2007). In general, however, animal and plant colors result
from the differential absorption of light by chemical pigments, and the reflection of colors that are not absorbed.
The beauty of jewelry made from minerals results, in part,
from the optical properties of the minerals, including their
index of refraction, their dispersion, their transparency, and
the wavelength-dependent extinction coefficient of their
pigments (Boyle, 1664, 1672).
THE RELATIONSHIP OF INTERFERENCE
MICROSCOPY TO PHASE-CONTRAST
MICROSCOPY
A phase-contrast microscope turns a difference in phase
into a difference in intensity. In a phase-contrast microscope, contrast from a transparent object arises from the
constructive or destructive interference that takes place
at the image plane between the nondeviated and deviated waves that emerge from each point on the specimen.
The incomplete separation of the nondeviated and deviated waves going through the phase plate in the back focal
plane of the objective results in the introduction of undesirable artifacts, such as halos and shading-off, in the image
(Osterberg, 1955; Tolansky, 1968).
An interference microscope turns a difference in phase
into a difference in intensity, or more marvelously, into a
difference in color. In an interference microscope, contrast
is generated by the interference of the light wave, which
passes through each point of the specimen, and a reference
wave that is coherent with the light that passes through the
specimen. Since the reference wave does not pass through
the specimen, the separation of the two interfering waves
is complete, and, as a result, halos and shading-off are
prevented.
Consider a point on a transparent biological specimen,
with a refractive index (no) of 1.33925 and a thickness of
10,000 nm, mounted in water (ns 1.3330). When the
specimen is observed with green light (500 nm), it introduces an optical path difference (OPD) and phase angle
(ϕ) of 62.5 nm and 45 degrees, respectively, according to
the following formulas:
OPD (n o n s )t
ϕ OPD (360/ λ )
In a bright-field microscope, the image is formed from the
interference of the nondiffracted (U) and the diffracted (D)
waves. Using a vector method to illustrate the appearance
of an invisible, transparent specimen, we see that p, the
resultant of U and D, is the same length as U and thus the
object is equal in intensity to the background and is thus
invisible (Figure 8-3).
In a phase-contrast microscope, we either advance the
U wave (positive phase-contrast) or retard the U wave (negative phase-contrast) to transform a difference in phase into
a difference in intensity compared with the background
(Figure 8-4). In a positive phase-contrast microscope, such
a specimen will appear darker than the background; with
a negative phase-contrast microscope, this specimen will
appear brighter than the background.
Now consider what happens in an interference microscope when we introduce a reference wave R that is coherent
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Chapter | 8 Interference Microscopy
with, and capable of interfering with, both the U wave
and the p wave. Assume that the U wave and the p wave
are equal in amplitude so that the object is invisible (a).
Now introduce the R wave so that it is retarded 90 degrees
relative to the U wave. A new resultant (U) will occur
from the interference of the U wave and the R wave (b).
Furthermore, another new resultant (P) will occur from
the interference of the p wave and the R wave (c). Notice
that P is longer than U, thus the object will appear bright
against a less bright, but not dark, background (Figure 8-5).
Imagine that we can vary the phase of the reference wave
(R) until so that the background appears maximally dark.
That is, when the U wave and the R wave destructively interfere, the amplitude of the resultant wave (U) will be zero
(Figure 8-6).
U
O
Imagine that we can also vary the phase of reference
wave R, so that the specimen appears maximally dark. That
is, when the p wave and the R wave interfere, the amplitude
of the resultant P will be zero (Figure 8-7).
Imagine that we can introduce a phase change of 0 to
360 degrees to the reference wave. If, when we vary the
phase of the reference (R) wave we can find one place
where the reference wave is exactly 180 degrees out-ofphase with the nondeviated (U) wave, the background
will be maximally dark. If the interference microscope
is equipped with a compensator, we can then read the
angle (θ1) of compensator when the background is maximally dark. Next turn the compensator until the particle is
maximally dark. This is where the reference (R) wave is
exactly 180 degrees out of phase with the particle (p) wave.
A
O
R
D
p
U
U
A
U
R
U 0
P
FIGURE 8-3 Vector representation of an image point (P) produced
by the nondiffracted (U) and diffracted waves (D) in a bright-field
microscope.
FIGURE 8-6 By varying the phase of the reference beam (R), we can
bring the background to extinction.
A
P
O
U
A
U
O
D
p
A
P
R
D
p
p
P
P
A
PositivePhase
contrast
P'
p
U
A
P 0
P
FIGURE 8-4 Vector representations of an image point (P) produced by
the nondiffracted (U) and diffracted waves (D) in positive and negative
phase-contrast microscopes.
O
R
O
NegativePhase
contrast
O
FIGURE 8-7 By varying the phase of the reference beam (R), we can
bring a point in the image to extinction.
U
A
O
p
D
p
P
R
R
U
P
P
FIGURE 8-5 Vector representation of a background point (U) produced by the vector sum of the nondiffracted light (U) and the reference beam (R). Vector
representation of an image point (P) produced by the vector sum of the diffracted (D), nondiffracted (U), and the reference beam (R) in an interference
microscope. The vector sum of the diffracted (D) and nondiffracted (U) light is equal to the vector (p) that represents all the light that comes from a
point in the specimen.
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Light and Video Microscopy
R2
R1
(θ1 θ2)
O
U
A
p
P
FIGURE 8-8 The phase angle of a point in the image compared to the
background can be determined from the difference in the angles that bring
the image point and the background to extinction.
Then we read this angle (θ2). The difference in the compensation angles (θ1 – θ2) is equal to the phase angle (φ) introduced
by the specimen, since the phase angle is equal to the optical
path difference (OPD, in nm) times 360 degrees divided by
the wavelength of incident light (Figure 8-8). That is,
ϕ (OPD)(360/ λ) (θ1 θ 2 )
Implicit in this formula is the assumption that a 360-degree
turn of the compensator compensates 1 λ. However, when
we use an interference microscope with a de Sénarmont
compensator, a half-turn (180°) of the analyzer compensates 1 λ. Thus the following formula applies:
ϕ (OPD)(360 / λ ) 2(θ1 θ 2 )
Zeiss Jena produced a microscope that lets us do both
phase-contrast microscopy and interference microscopy
with the same apochromatic objectives of any magnification (Beyer, 1971; Schöppe et al., 1987; Pluta, 1989). In
this microscope, a focusable image transfer system projects the diffraction pattern from the back focal plane of the
objective lens onto an interferometer that splits the nondiffracted light from the diffracted light. In the phase-contrast
mode, a phase plate that advances the nondiffracted light
to produce positive phase-contrast images or a phase plate
that retards the nondiffracted light to produce negative
phase-contrast images is inserted into the interferometer.
To convert from phase-contrast microscopy to interference
microscopy, the phase-contrast insert is replaced with an
interference insert that includes a compensator.
Although the unification of Germany was a wonderful
event in the world, and it still brings tears to my eyes when
I think of the old men chipping away at the Berlin wall,
it also meant that all microscope manufacturers would be
driven by a market economy as opposed to being driven by
the craftsmanship that meant so much to Ernst Abbe. I realized that this meant that the elegant but complicated microscopes made by the East German Zeiss craftsmen would
no longer be made. I quickly bought a Jenalpol Interphako.
I love that microscope because it illustrates to my students how there are alternative ways to solve technological
problems. Moreover, we can look at the optics above the
objective lens as an analog image processor that serves as
an inspiration of what we can do with digital cameras and
image processors. I will discuss this microscope more in
Chapter 9. So before I describe various interference microscopes, I will describe how they can be used quantitatively.
QUANTITATIVE INTERFERENCE
MICROSCOPY: DETERMINATION OF
THE REFRACTIVE INDEX, MASS,
CONCENTRATION OF DRY MATTER,
CONCENTRATION OF WATER,
AND DENSITY
With a quantitative interference microscope, we can accurately measure the phase angle that we must introduce into
the reference wave to bring either the background or the
specimen to maximal extinction. Once we know the phase
angle, we can easily determine the optical path difference
with the following formula:
OPD ϕ (λ/ 360)
If we know the thickness of the specimen from independent measurements, and the refractive index of the medium
(ns), we can calculate the refractive index of the object (no)
from the following formula:
OPD (n o n s )t
or
n o [(OPD)/t] n s
or more explicitly:
n o (θ1 θ 2 )(λ/ 360)(1/t) n s
As I discussed in Chapter 6, the refractive index of a
biological specimen is related to the concentration of dry
mass in the specimen. The refractive index of an aqueous specimen is equal to the refractive index of water
(1.3330) plus the refractive index due to the concentration
of dry mass (Cdm, in g/100 ml). The refractive index due
to the concentration of dry mass is equal to the product of
the concentration of dry mass (Cdm, in g/100 ml) and the
specific refractive increment (α; in 100 ml/g). For most
macromolecules that make up biological specimens, the
refractive index increases by 0.0018 for every 1 percent
(w/v) increase in dry mass. The refractive index of an
aqueous specimen is given by the following formula:
n o 1.3330 αCdm
Once we know the refractive index of the specimen, we
can calculate its concentration of dry mass by rearranging
the formula above:
Cdm (n o 1.3330)/ α (n o 1.3330)/ 0.0018
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Chapter | 8 Interference Microscopy
We can combine the following two equations to find the
relationship between the optical path difference and
the concentration of dry mass (in g/100 ml) in the cell.
Assuming ns 1.3330,
OPD (n o 1.3330)t
and
Cdm (n o 1.3330)/ 0.0018
Solve both equations for (no – 1.3330):
OPD/t Cdm (0.0018)
aqueous solution of bovine serum albumin (OPDb). It is
important to select media that will not cause any osmotic
swelling or shrinkage, since any change in volume will
introduce an unwanted change in the concentration of dry
mass. As a consequence of the colligative properties of matter, which depend on the concentration of particles and not on
their individual chemical properties, the solute of choice must
have a high molecular mass. Solutions of high molecular mass
have high densities and refractive indices yet low osmotic pressures. Observing the specimen in two media allows us solve
two simultaneous equations with two unknowns, t and no
OPD w (n o n w )t
or
OPD Cdm (0.0018)t
or
Cdm OPD/[(0. 0018)t]
The optical path difference is equal to the concentration of
dry mass (Cdm) times the specific refractive increment (α)
times the thickness (t). The concentration of dry mass can
be conveniently calculated with the following equation:
Cdm OPD/(α t) (θ1 θ 2 )(λ/ 360)(1/ α t)
The thickness is usually difficult to measure accurately,
making it inaccurate to calculate the concentration of dry
mass, but we can accurately determine the mass per unit
area in the following manner:
Cdm (θ1 θ 2 )(λ/ 360)(1/ α t)
Cdm mass/volume
Cdm mass/(area t)
mass/(area t) (θ1 θ 2 )(λ/ 360)(1/ α t)
mass/area (θ1 θ 2 )(λ/ 360)(1/α )
The area can be measured accurately with a microscope,
particularly with the aid of an image processor (see Chapter
14). When we know the area of the specimen, (θ1 – θ2), λ
and α, we can then determine the dry mass of the specimen.
mass (area)(θ1 θ 2 )(λ/ 360)(1/α )
Although the area is relatively easy to measure accurately,
the thickness is more difficult to measure accurately, and the
percent error in measuring thickness is much greater than
the percent error in measuring area. We can measure the
concentration more precisely if we can measure it independently of the thickness.
This can be done by measuring the optical path difference twice, each time using a medium with a different
refractive index. For example, first measure the optical
path difference between the specimen and the surround
in water (OPDw) and then measure the optical path difference between the specimen and the surround in a 5 percent
and
OPD b (n o n b )t
where OPDw is the optical path difference when the cells
are in water, OPDb is the optical path difference when the
cells are in 5% BSA, nw is the refractive index of water
(1.333), nb is the refractive index of 5% BSA (1.333 5
(0.0018)) 1.3420, and no is the refractive index of the
object. Solving these equations for t, we get,
t OPD w /(n o n w ) OPD b /(n o n b )
After rearranging, we get:
OPD w (n o n b ) OPD b (n o n w )
OPD w n o OPD w n b OPD b n o OPD b n w
OPD w n o OPD b n o OPD w n b OPD b n w
n o (OPD w OPD b ) OPD w n b OPD b n w
n o (OPD w n b OPD b n w )/(OPD w OPD b )
The concentration of dry mass can then accurately be
determined with the following formula:
Cdm (n o n w )/ 0.0018
Furthermore, once we know no, we can accurately calculate
the thickness of the specimen with the following formula:
t OPD w /(n o n w ) OPD b /(n o n b )
If a cell is composed of a single substance, we can
determine the molarity of this substance by dividing its
concentration (in kg/m3) by its molecular mass (in kg/mol).
Even if a cell is composed of many substances, we can
determine the DNA content, for example, by measuring
the concentration before and after the specimen is treated
with DNase. Trypsin, lipase, and such can also be used to
measure the concentration of protein, lipid, and other macromolecules. (Davies et al., 1954, 1957).
We can also determine the percentage of water in a
cell by assuming that the specific volume of protoplasm is
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Light and Video Microscopy
the same as the specific volume of proteins (Vsp 75 ml/
100 g 0.75 ml/g). The concentration of water (Cw, in
g/100 ml or %) is obtained from the following formula:
Cw 100% Vsp Cdm
Thus, a solution composed of 10 percent (w/v) protein contains 92.5 percent (w/v) water. The molarity of water (Mw)
in a cell can be determined using the following formula:
M w [Cw (in percent)/100%] 55.55 M
where 55.55 M is the molarity of pure water. Thus a solution composed of 10 percent (w/v) protein will contain
51.34 M water.
The density of a cell or organelle (in kg/m3) can be
determined with the following formula:
Density (Cw /100%)D w Cdm
where Cw is the concentration of water (in %), Dw is the
temperature-dependent density of water (1000 kg/m3),
and Cdm is the concentration of dry matter in the specimen
(in kg/m3).
I have described how it is possible to measure refractive index, mass, concentration of dry mass, concentration of water, density, and thickness with an interference
microscope. In order to see how sensitive an instrument an
interference microscope is, I will calculate the minimum
amount of mass an interference microscope can measure.
With a good interference microscope it is easy to measure an optical path difference of about λ/100. This translates to about 5.5 nm if we illuminate the specimen with
550 nm light. By combining the following two formulas
derived earlier:
mass (area)(θ1 θ 2 )(λ/ 360)(1/α )
ϕ (OPD)(360/ λ ) (θ1 θ 2 )
we get:
mass (area)(OPD)(1/ α ) (area)
(5.5 109 m)(1/1.8 107 m 3 /g)
where 1.8 107 m3/g is the specific refractive increment
in units of m3/g. It is equal to 0.0018/g/100 ml.
Since we can resolve a unit area of about 0.2 106
m 0.2 106 m or 4 1014 m2 with an apochromatic
objective lens (NA 1.4), the limit of detection of mass
with an interference microscope is equal to 1.2 1015 g
(about a femtogram), which is approximately the mass of a
single band on a chromosome.
SOURCE OF ERRORS WHEN USING
AN INTERFERENCE MICROSCOPE
There are a number of possible sources of error when using
an interference microscope for quantitative measurements
(Davies and Wilkins, 1952; Barer, 1952a, 1952b, 1953c,
1966; Barer et al., 1953; Mitchison and Swann, 1953; Barer
and Joseph, 1955, 1958; Ross, 1954; Davies et al., 1954,
1957; Barer and Dick, 1957; Ingelstam, 1957; Hale, 1958,
1960; Francon, 1961; Ross and Galavazi, 1964; Beneke,
1966; Bartels, 1966; Chayen and Denby, 1968; Wayne and
Staves, 1991). These include errors due to geometry, errors
in the determination of optical path difference, errors due
to differences in the specific refractive index, errors due to
inhomogeneous specimens, and errors due to birefringence
of the specimen.
Sometimes we cannot exactly determine the shape of
the specimen, we can only approximate the area. However,
using image processors to determine the area of a specimen, errors in geometry can be virtually eliminated.
Since we cannot always determine what is optimally
dark, different observers may choose a different dark level
in order to obtain the different optical path differences.
This error in the determination of the optical path difference is typically between 0.5 and 3 percent, and can be
minimized by using an image processor to find the maximally dark position.
The specific refractive increment varies among various compounds and the specific refractive increment used
to determine the mass of a specimen may differ from the
actual specific refractive increment of the macromolecules
in the specimen. Errors due to differences in the specific
refractive increment can be as much as 5 percent.
Most specimens are inhomogeneous and thus one part
of the specimen is brought to extinction before another
part. Errors due to the inhomogeneity of the specimen can
be minimized by determining the maximal darkness of as
large an area as possible; that is, by integrating. However
when doing this, spatial resolution is sacrificed for a
decrease in the inhomogeneity error.
Many interference microscopes used polarized light
and consequently, the refractive index of the specimen will
vary with the orientation of the optic axes of the molecules
in the specimen. When measuring birefringent specimens,
use an interference microscope that is not based on polarized light.
I have described the theory behind how interference
microscopes can be used as a very sensitive balance to
weigh a cell or organelle. Although the first interference
microscope was built by J. L. Sirks in 1893, companies
were not interested in developing interference microscopes
until the 1950s when Barer (1952) and Davies and Wilkins
(1952) figured out how interference microscopes could
be used quantitatively. Companies then began to develop
interference microscopes based on a variety of interesting optical principles, and it was a dream of the interference microscopists of the 1950s to be able to put a cell in
a microscope, press a button, and read of the mass of the
cell directly. However, it is the winner-take-all nature of
science that the introduction of a newer technique with yet
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Chapter | 8 Interference Microscopy
Methods to form two coherent beams
Methods to recombine two coherent beams
FIGURE 8-9
Methods to form and to recombine two coherent beams.
unknown errors and limitations kills the development and
use of a technique with known errors and limitations. Thus,
in the 1950s, the introduction of the electron microscope,
with its potential for atomic resolution, brought a temporary stop to the development of light microscopes.
However, in the 1970’s, the resurgence of the light
microscope slowly began as several independent cell biologists, including Robert Allen, Andrew Bajer, Arthur Forer,
Paul Green, Peter Hepler, Shinya Inoué, Eiji Kamitsubo,
R. Bruce Nicklas, Barry Palevitz, Jeremy Pickett-Heaps, Ted
Salmon, and D. Lansing Taylor, among others, who were
both admired and emulated, showed that light microscopes
could be used to observe the molecular structure, motility,
and physicochemical properties of living cells without perturbing the natural state of the cell; whereas the electron
microscope was able to obtain its high resolving power
(Slayter, 1970) only at the expense of killing the cell.
The resurgence of light microscopy was helped by
some bio-organic chemists, including Alan Waggoner and
Roger Tsien, who developed probes that could be used to
visualize the physicochemical properties of living cells and
to localize macromolecules using fluorescence microscopy
(Tsien et al., 2006; Chapter 11). The microscope manufacturers began to redesign microscopes for the study of living
cells, and imaging centers in academia and industry have
a variety of microscopes that will perform many fantastic
tasks (Webb, 1986). Although the functions of the interference microscope have not been replaced by the other
techniques, the poor interference microscope is relatively
unknown and unused. Especially when combined with digital image processing, the interference microscopy is still a
very useful method to measure such fundamental quantities as mass and thickness in a living cell (Dunn, 1991).
MAKING A COHERENT REFERENCE BEAM
In a phase-contrast microscope, the two coherent waves that
interfere in the image plane arise from the same point in the
specimen. In an interference microscope, we must generate
two coherent waves (Svensson, 1957; Koester, 1961; Krug
et al., 1964). A single wave can be split into two coherent
waves with a variety of methods (Figure 8-9), including
reflection, refraction, diffraction, and by using two holes in
an opaque barrier. A wave can be split by reflection by passing it through a half-silvered mirror, where half of the amplitude of the wave is reflected and half of the amplitude of
the wave is transmitted. A wave can also be split by double
refraction where the incident wave is split into two orthogonal, in-phase, linearly polarized waves. A wave can also be
split by a diffraction grating where the incident wave is split
into the various orders, and the 1 and 1 orders (for example) can be used as the two coherent waves. A wave can also
be split into two waves by passing it through two holes in an
opaque surface. Optical processes are reversible and the same
four methods can be used to recombine two coherent waves
into one resultant. An interferometer consists of a beam
(or wave) splitter and a beam (or wave) combiner.
The closer two waves with finite widths are to each
other, the more likely they are to be coherent and interfere.
In describing how interference microscopes work, I will be
considering the interference of nearly parallel waves. The
amplitude of the resultant (Ψ(x)) of two interfering waves
with equal amplitude (Ψo), but that differ in phase by ϕ, is
given by the following time-independent version of a formula given in Chapter 6:
ψ(x) 2 ψ o cos (ϕ/ 2)
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Light and Video Microscopy
M
C
B
Eye
H
H
A
D
M
FIGURE 8-10 A diagram of a Mach-Zehnder interferometer composed of fully silvered mirrors and half-silvered mirrors in the absence of a
specimen.
The phase angle is equal to (360°/λ)(OPD), where OPD
is the optical path difference between the reference
wave and the specimen wave. The interference can occur
between two waves (or beams) or between multiple waves
(or beams).
DOUBLE-BEAM VERSUS MULTIPLE-BEAM
INTERFERENCE
When a specimen is placed on the stage between the wave
splitting and wave recombining portions of the interferometer so that only one set of waves propagates through
the specimen and the other set acts as a reference wave,
the interference pattern in the corresponding portion of the
image plane is altered in a specimen-dependent manner. In
white light, the image is spectacular!
Light passing through an interferometer consisting of
a wave (or beam) splitter and a wave (or beam) combiner
in a microscope interferes in the image plane (Michelson,
1907). If all the elements in the interferometer are parallel, the interference between two coherent waves produces
a homogeneous background color. The color will be the
complementary color to the one whose phase angle is
0 degrees. If one of the elements is tilted, then waves of different wavelengths will have a phase angle of 0 degrees at
different places in the field. As a result, colored fringes will
occur across the field, identical to those found in a MichelLévy color chart. When monochromatic light is used, the
pattern in the image plane consists of a uniformly monochromatic background, when the wave fronts are parallel
or a pattern of alternating dark and monochromatic light
bands when the wave fronts arrive at a small angle.
When the background is uniform, the difference
between the specimen and the surround is characterized
by a process known as double-beam interferometry. We
compensate the specimen by noting the color of the surround and then turning the compensator until the specimen
becomes the same color. At this point, we read the angle
from the compensator. We must remember the color of the
original surround since the background color also changes
as additional optical path length are introduced into the
reference wave in order for the specimen to attain the color
of the original background. Double-beam interferometry is
good for biological specimens (Pluta, 1989, 1993).
When a specimen is placed in a microscope whose field
has multiple fringes, the background fringes are displaced
laterally in the position the specimen occupies. This is
because, in the presence of the specimen, the optical path
length changes so that the position, where the phase angle
for a given wavelength is 0 degrees, is displaced laterally
to a position where the tilted element of the compensator
gives a phase angle of 0 degrees for that wavelength in the
presence of a specimen. Multiple-beam interferometry is
valuable for accurately characterizing linear elements like
fibers (Pluta, 1989, 1993; Barakat and Hamza, 1990).
INTERFERENCE MICROSCOPES
BASED ON A MACH-ZEHNDER TYPE
INTERFEROMETER
Interference microscopes, unlike bright-field microscopes,
include an interferometer. A Mach-Zehnder interferometer (Figure 8-10), independently designed in the 1890s
by Ludwig Mach, the son of Ernst Mach, and Lugwig
Zehnder, is a “round the square” interferometer. In this
interferometer, the incident light passes through a halfsilvered mirror (A). At the half-silvered mirror, half of
the light is reflected 90 degrees relative to the incoming
beam and half of the light passes straight through the halfsilvered mirror. Both waves propagate until they hit two different fully-silvered mirrors (B and D). Each wave is then
reflected by one of two fully-silvered mirrors so that the
wave that was perpendicular to the incident wave becomes
parallel to the incident wave and the wave that was parallel to the incident wave becomes perpendicular to it. Then
the two reflected waves travel to another half-silvered mirror
(C), where the wave from mirror B propagates straight
through it and the wave from mirror D is reflected
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Chapter | 8 Interference Microscopy
C
B
M
Eye
H
H
A
D
Typical specimen
M
FIGURE 8-11 A diagram of a Mach-Zehnder interferometer in the presence of a specimen whose phase angle is 180°. The specimen appears dark.
Fully-silvered mirror (M), half-silvered mirror (H).
Glass wedge
C
B
M
Eye
H
A
H
D
Typical specimen
M
FIGURE 8-12 Compensation of a specimen in a Mach-Zehnder interferometer. The specimen appears bright. Fully-silvered mirror (M), half-silvered
mirror (H).
perpendicular to the incident wave. The final half-silvered
mirror recombines the two waves. When the mirrors are
placed correctly, the distances the two waves travel are
equal and the two waves exit in phase and constructively
interfere to make a bright resultant wave.
The wave that takes the path ABC represents the reference wave, and the wave that takes the path ADC represents the specimen wave. Imagine placing a pure phase
specimen that introduced a phase change of λ/2 between
mirrors A and D. The two waves that exit mirror C would
then be 180 degrees out-of-phase and would destructively
interfere to create blackness (Figure 8-11).
Now imagine that we put a transparent glass wedge
compensator of a given refractive index between mirrors
B and C and slide it into the optical path until the specimen becomes maximally bright. Then we have introduced
an identical increase in optical path length to path ABC as
the specimen added to path ADC. At this point, the optical path difference (OPD) vanishes. If we could read the
increase in optical path length we introduced from a knob
on the compensator, then we would know the optical path
length introduced by the specimen (Figure 8-12).
In practice it is easier to discern differences between
variations in blackness than variations in brightness, so we
first find the position where the background is maximally
black (θ1) and then find the position where the specimen
is maximally black (θ2). The difference between these two
readings (θ1 – θ2) is equal to the phase angle introduced by
the specimen (ϕ). From the measured phase angle, we can
determine the refractive index, thickness, mass, density,
and percent water of the specimen using the equations
I discussed earlier.
The Leitz interference microscope uses a Mach-Zehnder
interferometer. It is really a double microscope. The illuminating light is split by a specially designed prism consisting of a half-silvered mirror following the principles of
reflection. The prism separates the two waves a distance of
6.2 cm. The two waves then pass through perfectly matched
condensers. Each wave then goes through separate objectives. The object is placed under one of the objectives. The
optical path length of the two light beams can be adjusted
with the aid of compensators. The light waves that pass
through the two matching objectives are then recombined
with a prism, similar to the one that separated the original
wave. This microscope can be used for almost any biological specimen since the two waves are separated by such a
large distance (Figure 8-13).
The Dyson (1961) interference microscope is another
commonly found microscope that is based on the MachZehnder interferometer, except that the “round the square”
is slightly distorted into a rhombus. The Dyson interference system is mounted in front of an ordinary objective.
The specimen (O) is mounted under a cover glass and on a
glass slide. The slide and cover glass are fully immersed in
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Light and Video Microscopy
Eye
Eye
Objective
Beam
recombing prism
M
Matching objectives
Matching sub-stage
condensers
H3
Beam
splitting prism
H2
Oil
Specimen
o
Oil
H1
FIGURE 8-13 Diagram of a Leitz interference microscope based on a
Mach-Zehnder interferometer.
M
immersion oil, which, on the bottom, comes in contact with
a half-silvered surface (H1) on the top of a slightly wedged
plate. The bottom of the wedge has a fully silvered mirrored
spot. The plate (H1) can be adjusted with two screws. Above
the object, there are two wedge-shaped plates with two halfsilvered surfaces (H2 and H3). Above the two halfsilvered
mirrors is a glass block with a fully-silvered concave surface
(C) that acts as a reflection lens with a magnification of 1.
The lens has a transparent hole at which the image of the
specimen appears. The ordinary objective lens of the microscope is used to view this image. In comparison to the Leitz
microscope, the object must be very small to allow the reference beam to go around it (Figure 8-14).
INTERFERENCE MICROSCOPES
BASED ON POLARIZED LIGHT
In the Jamin-Lebedeff interference microscope, the illuminating beam is linearly polarized with a Polaroid filter.
The linearly polarized light is then passed through either a
calcite or a quartz crystal that is oriented with its optic axis
45 degrees relative to the azimuth of maximal transmission
of the polarizer. This crystal functions as a wave (or beam)
splitter. The birefringent plate separates the linearly polarized
light into an ordinary wave and an orthogonally-polarized
extraordinary wave that are laterally separated. The degree
of lateral separation of the ordinary and extraordinary waves
depends on the birefringence and thickness of the crystal.
In the Jamin-Lebedeff microscope, the degree of separation
is 546 μm for the 10X objective-condenser pair; 175 μm for
the 40X condenser-objective pair; and 54 μm for the 100X
condenser-objective pair.
FIGURE 8-14 Diagram of a Dyson interference microscope based on a
modified Mach-Zehnder interferometer.
The ordinary wave and the extraordinary wave then pass
through a half-wave plate so that their azimuths of vibration
are rotated 180 degrees. Now the ordinary wave vibrates
in the same azimuth that the extraordinary wave vibrated
before it reached the halfwave plate and the extraordinary
wave vibrates in the same direction as the ordinary wave did
before it reached the half-wave plate. Thus, at the half-wave
plate, the ordinary wave and the extraordinary wave interchange their azimuth of polarization.
In the absence of a specimen the two waves enter a second birefringent crystal that is cut and oriented exactly the
same as the first wave splitting crystal.
In the case of the positively birefringent quartz prisms,
where the extraordinary wave is retarded relative to the ordinary wave, the extraordinary wave that exited the wave splitter enters the fast axis of the wave (or beam) combiner where
it experiences the refractive index of the ordinary wave (no)
and thus acts as the ordinary wave and passes straight through
the wave (or beam) combiner. The ordinary wave that exits
the wave splitter enters the slow axis of the beam combiner
where it experiences the refractive index of the extraordinary
wave (ne) and thus acts as the extraordinary wave and experiences the anomalous refraction. In this way, the two waves
are recombined into the same axial ray although they still are
vibrating perpendicularly to each other (Figure 8-15).
In the case of the negatively birefringent calcite, where
the ordinary wave is retarded relative to the extraordinary
wave, the ordinary wave enters the fast axis of the beam
combiner where it experiences the refractive index of the
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Chapter | 8 Interference Microscopy
Eye
Analyzer
λ/4 plate
A1
B1
Beam
recombiner
Beam
recombiner
Specimen
Specimen
λ/2 plate
e
Beam
splitter
o
Calcite 0A
Beam splitter
A
B
Quartz 0A
Polarizer
FIGURE 8-15 Diagram of a Zeiss interference microscope based on a Jamin-Lebedeff interferometer.
extraordinary wave (ne) and thus acts as the extraordinary wave
and experiences the anomalous refraction. The extraordinary
wave that enters the wave splitter enters the slow axis of the
wave combiner where it experiences the refractive index of
the ordinary wave (no) and thus acts as the ordinary wave and
goes straight through the wave combiner. In this way, the two
waves are recombined into the same axial ray although they
still are vibrating perpendicularly to each other.
The recombined ordinary and extraordinary waves
then strike a quarter wave plate whose slow axis is parallel
to the polarizer. The λ/4 plate then turns each of the two
orthogonal, linearly polarized waves into two circularly
polarized waves that rotate with opposite senses. The light
then travels to the analyzer, which is crossed relative to the
polarizer. In the absence of a specimen the background is
maximally dark since there is no optical path difference
introduced into the light path. The resultant of the extraordinary wave and the ordinary wave, in the absence of a
specimen, is linearly polarized in the azimuth of maximal
transmission of the polarizer.
When a specimen is inserted into the microscope it
introduces a retardation of the ordinary wave relative to the
extraordinary wave that leaves the wave splitter. This will
cause the two circularly polarized waves that leave the λ/4
plate to be out-of-phase. The two put-of-phase circularly
polarized waves produce linearly polarized light whose azimuth is determined by the phase angle between the ordinary
and extraordinary waves. The change in azimuth can then
be determined with the de Sénarmont compensator.
When using a de Sénarmont compensator, we must use
monochromatic light to measure the optical path difference
introduced by the specimen. First, bring the background to
extinction by turning the analyzer and read the angle on the
analyzer knob (θ1). Then rotate the analyzer until the part
of the specimen that is of interest is extinguished, and read
the angle on the analyzer knob (θ2). The optical path difference introduced by the specimen is then calculated from
the following formula:
OPD 2[(θ1 θ 2 )λ/ 360]
When we look at an image in an interference microscope
based on a Jamin-Lebedeff interferometer, we see two
images that are laterally displaced from each other. One
image is in focus and the other one is astigmatic and outof-focus. When I spoke about the operation of this microscope I talked as if only the ordinary waves go through the
specimen. However extraordinary waves that come from
other regions of the wave splitter may also pass through the
specimen. We obtain an image A1 from the ordinary waves
that pass through the specimen and an image B1 from the
extraordinary waves that pass through the specimen. The
image made by the extraordinary waves that pass through a
specimen is an astigmatic image since the refractive index
that these waves experience depends on the angle of incidence. The two images are of complementary colors.
One type of interference microscope designed by
Smith uses a Wollaston prism to produce two coherent
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Light and Video Microscopy
Calcite Wollaston prism
o
e
e
o
Eye
e
Calcite Wollaston prism
o
FIGURE 8-16 A Wollaston prism splits light into two coherent waves.
The waves that strike the interface between the two prisms at the midway
point in the prism leave the prism in phase. An optical path difference
between the ordinary wave and the extraordinary wave can be introduced
by sliding the Wollaston prism. The ordinary wave emerges ahead of the
extraordinary wave in the beam splitter when the prism is shifted to the
left, and the extraordinary wave emerges ahead of the ordinary wave in
the beam splitter when the prism is shifted to the right.
and orthogonal, linearly polarized waves. In these microscopes, the nonpolarized, monochromatic light from the
lamp is linearly polarized by passage through a Polaroid
below the sub-stage condenser. The linearly polarized light
is split into two orthogonal linearly polarized waves by a
Wollaston prism (Figure 8-16).
A Wollaston prism is made from two wedges of a birefringent material that are positioned so that their optic axes
are perpendicular to each other. Linearly polarized light that
is vibrating at an azimuth 45 degrees relative to the optic
axis of the first wedge is resolved into two linearly polarized
components by the lower wedge: the component vibrating
parallel to the optic axis experiences only ne, whereas the
component vibrating perpendicular to the optic axis experiences only no. For a negatively birefringent crystal like calcite, ne no and thus ve vo, and the ordinary wave that
vibrates perpendicular to the optic axis is retarded relative
to the extraordinary wave that vibrates parallel to the optic
axis. Since each wave experiences only one refractive index,
only spherical wavelets are formed and both the extraordinary wave and the ordinary wave pass through the lower
crystal without being bent.
Once the extraordinary wave and the ordinary wave
strike the interface, the ordinary wave enters a medium
o
e
e
o
FIGURE 8-17 A Wollaston prism can also recombine two coherent
waves. An optical path difference between the recombined ordinary wave
and the extraordinary wave can be introduced by sliding the Wollaston
prism of the recombining prism. The beam that enters the recombining
prism as the ordinary wave emerges ahead of the extraordinary wave
when the prism is shifted to the right and the beam that enters the recombining prism as the extraordinary wave emerges ahead of the ordinary
wave when the prism is shifted to the left.
with a lower index of refraction, so it is bent away from
the normal and becomes an extraordinary wave. By contrast, the extraordinary wave enters a medium with a
higher refractive index and is bent toward the normal and
becomes an ordinary wave. On entering air they both separate further by bending away from the normal. When the
Wollaston prism is inverted, it acts as a wave (or beam)
recombiner (Figure 8-17).
In a Smith interference microscope (Figure 8-18), the ordinary wave is the image forming wave that passes through the
specimen and the extraordinary wave passes beside the specimen. A second Wollaston prism recombines the two rays. The
second Wollaston prism is oriented opposite to the first one so
that in the absence of a specimen, the second prism exactly
cancels the phase angle introduced by the first prism.
The recombined beam then passes through a λ/4 plate
whose slow axis is parallel to the azimuth if maximal transmission of the polarizer. The λ/4 plate turns the ordinary
and extraordinary waves into circularly-polarized waves
with opposite senses of rotation. Together, the analyzer
and the λ/4 plate act as a de Sénarmont compensator and
the analyzer can then be rotated to bring the background
and then the specimen to extinction.
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Chapter | 8 Interference Microscopy
Eye
Analyser
λ/4 plate
Objective
e o
e o
Beam recombiner
Specimen
Wollaston
prism
(calcite)
Back focal
plane
of objective
o
e o
e
Beam splitter
Sub-stage condenser
Objective
Sub-stage
condenser
Wollaston
prism
(calcite)
Specimen
FIGURE 8-19 A diagram of a Smith-Baker interference microscope
based on polarized light.
Front focal
plane of
sub-stage
condenser
Polarizer
FIGURE 8-18 A Smith interference microscope. Note the antiparallel
orientation of the cement line of the two Wollaston prisms. In most publications, the cement lines in the two Wollaston prisms are shown with a
parallel orientation—an arrangement that could not work. I used to tell
my students that I thought that the orientation of the two prisms should
be antiparallel, even though the majority of publications, including the
technical report put out by Zeiss (Lang, 1968) show parallel Wollaston
prisms, and since I may be crazy, they were free to go with the majority
opinion. After many years of saying this, I finally called Zeiss and told
them that I think that their technical publication was incorrect and that the
Wollaston prisms must have an antiparallel orientation to split and recombine the beams. Ernst Keller of Zeiss graciously called me back, saying,
“You have the whole building upside down” and indeed “I was right.”
I use this as an example for my students, to base their conclusions on first
principles and not on what the majority says–the majority can be right,
but it is not always right.
Smith invented another kind of interference microscope,
produced by Baker and by American Optical (Richards,
1963, 1964, 1966), that has a sensitivity of λ/100 or about
5 nm. In this interference microscope, the birefringent
prisms that make up the wave splitter and wave combiner
are placed on the top lens of the sub-stage condenser and
bottom lens of the objective, respectively (Figure 8-19).
The Smith interference microscope is adjusted by setting
up Köhler illumination using white light. Then an ocular
is replaced with a centering telescope to view the colored
fringes in the back focal plane of the objective. The lower
birefringent prism is tilted and rotated until the first-order
red fringe is centered and then spread uniformly across
the rear focal plane of the objective. The iris diaphragm is
then closed enough to eliminate other interference colors
in the back focal plane of the objective but not so much as
to decrease resolution. The ocular is replaced and an image
appears in strikingly brilliant colors. The colors can be varied by rotating the analyzer.
The measurement of the optical path difference introduced by the specimen requires monochromatic light.
The green (546 nm) filter is inserted and the analyzer is
turned until the region of the surround near the specimen is
brought to extinction. Once the angle of the analyzer (θ1) is
read, the analyzer is rotated until the part of the specimen
that is of interest is brought to extinction. The angle of the
analyzer (θ2) is read again and the optical path difference
(OPD) is then calculated from the following formula:
OPD 2[(θ1 θ 2 )λ/ 360]
With the Smith interference microscope, the specimen must
be smaller than the separation of the two waves at the object
plane. On the image plane, the region where the astigmatic
image forms must be clear of primary images of other specimens. The size limits vary with the objective-condenser pairs:
With the 10X objective-condenser pair, the beams are separated by 330 μm; with the 40 objective-condenser pair, the
beams are separated by 160 μm; and with the 100 objectivecondenser pair, the beams are separated by 27 μm.
For specimens that are too large for the lateral shearing method described earlier, the interference microscope
comes with another set of condenser-objective pairs known
as the double focus system. Unlike the condenser-objective
pairs that permit shearing interference microscopy, where
the reference wave and the specimen wave are laterally
displaced, in the double focus system, the reference wave
164
is axially displaced so that the microscope forms an out-offocus image underneath the real image. This microscope is
easy to set up, good for qualitative microscopy as a method
to generate contrast, but cannot be used for quantitative
interference microscopy.
In interference microscopes that use birefringent beam
splitters, the numerical aperture of the condenser and the
objective should not be too high; otherwise the optical path
difference of the light that strikes the specimen from different angles will be too different and the optical path difference that is calculated will differ from the actual optical
path difference introduced by the specimen. This is known
as the obliquity error and it is approximately 0.06 percent
for a lens with a NA of 0.10 and about 10 percent for a lens
with a NA of 0.70 (Ingelstam, 1957; Richards, 1966).
THE USE OF TRANSMISSION
INTERFERENCE MICROSCOPY
IN BIOLOGY
Interference microscopy has been used to study pollen
development and mitosis in Tradescantia stamen hairs
(Davies et al., 1954), muscle contraction (Huxley and
Niedergerke, 1954, 1958; Huxley and Hanson, 1957;
Huxley, 1974), mitosis in endosperm cells (Richards and
Bajer, 1961), sea urchin egg development (Mitchison and
Swann, 1953), the growth of yeast cells (Mitchison, 1957),
osmotic behavior and density of chick fibroblasts (Barer
and Dick, 1957), spore development in fungi (Barer et al.,
1953), the mass of red blood cells (Barer, 1952a,b), the
mass of fibroblast nuclei (Hale, 1960) and sperm nuclei
(Mellors and Hlinka, 1955) as well as the biochemical
composition (Davies et al., 1954), the refractive index of
the Nebenkern of sperm (Ross, 1954), the mass of an onion
nucleolus (Svensson, 1957), chick nucleolus (Merrium and
Koch, 1960), and myoblast nucleolus (Ross, 1964), the
thickness of the wall of Nitella (Green, 1958, 1960), the
thickness of a bacterium (Ross and Galavazi, 1964), the mass
of cartilage (Goldstein, 1964; Galjaard and Szirmai, 1964),
the mass of the mitotic apparatus before and after isolation
(Forer and Goldman, 1972), the density of the endoplasm
of Nitellopsis and Chara (Wayne and Staves, 1991), and
auxin-regulated wall deposition and degradation (Baskin
et al., 1987; Bret-Harte et al., 1991).
One interesting experiment using interference microscopy was done by Hugh Huxley and Jean Hanson (1957)
using a Cooke-Dyson interference microscope. In developing the sliding-filament theory of muscle contraction,
they wanted to know where myosin was localized in the
sarcomere. Was it in the anisotropic (A) band or in the
isotropic (I) band? They used the interference microscope
to measure the optical path differences introduced by the
dry matter in the A band and I band of a sarcomere. Then
they treated the muscle with 0.6 M KCl, which selectively
Light and Video Microscopy
I
A
I
After 0.6 M KCL
Myosin
Structure
Densitometer trace
FIGURE 8-20 Diagrams and densitometer tracings of a sarcomere
before and after myosin extraction from Huxley and Hanson (1957).
dissolves and removes the myosin. Then they measured the
optical path differences again. They found that treating the
sarcomere with 0.6 M KCl selectively decreased the optical
path difference of the A band without affecting the I band.
This demonstrated that myosin is localized in the A band
and not in the I band of sarcomeres (Figure 8-20).
Following is a diagram of Andrew Fielding Huxley’s
(1952, 1954) interference microscope based on Smith’s
design using Wollaston prisms in the interferometer to split
and combine the waves. In his low-power microscope, the
Wollaston prisms were placed at the front focal plane of
the sub-stage condenser and at the back focal plane of the
objective. However, the Wollaston prisms cannot get close
enough to the back focal plane of the water-immersion
objective (NA 0.9) he needed to localize myosin. Therefore
Huxley (1954) built a “corrector,” which is placed above
the second Wollaston prism. It is made out of four pieces
of calcite placed such a distance and oriented in such a way
as to recombine the two rays that emerge from the second
prism (Figure 8-21).
REFLECTION-INTERFERENCE
MICROSCOPY
The principles used for transmitted-light interference
microscopy can also be used for reflected-light interference microscopy, or incident-light interference microscopy
as it is often called. A number of microscopes including
the Sangnac’s interference microscope, Linnik’s interference microscope, and the Zeiss (Raentsch) interference
microscope are based on the principle of a Michelson interferometer, where the incident wave is split into two orthogonal waves by a wave splitter. One wave, which is reflected
by the wave splitter, is incident on the specimen; the other
wave, which is transmitted by the wave splitter, strikes a
mirror. The specimen and reference waves are reflected
by the specimen and mirror, respectively, and then pass
165
Chapter | 8 Interference Microscopy
(a)
(b)
FIGURE 8-21 Diagrams of the optical arrangements designed by Andrew Fielding Huxley using various prisms made from quartz and calcite to
observe interference images of muscle (Huxley, 1952, 1954).
FIGURE 8-22 Diagram of two
possible arrangements used in
reflection-interference microscopes.
Eye
Beam
splitter
and
recombiner
M
Eye
Objective 2
M
Beam
splitter
and
recombiner
Tilting plates
Objective
Objective 1
M
through the wave recombiner where the specimen wave is
recombined with the reference wave and interfere in the
image plane (Figure 8-22). Other reflection interference
microscopes are based upon polarized light and use a single birefringent prism to split and recombine the specimen
and reference waves to make an interference image.
USES OF REFLECTION-INTERFERENCE
MICROSCOPY IN BIOLOGY
Reflection-interference microscopy can be used to measure
small distances, and has been used in biology to determine
the distance between a cell and its substrate (Curtis, 1964;
M
Opas, 1978). Knowledge of the distance helps to characterize the attractive forces between the cell and the substrate.
Izzard and Lochner (1976) studied the movement of fibroblasts on glass with reflection-interference microscopy.
The image obtained in a reflection-interference microscope
results from three reflections that interfere to make the
image: A reflection from the cover glass-medium interface,
one from the top of the cell-medium interface, and a third
from the bottom of the cell-medium interface (Figure 8-23).
Izzard and Lochner found that by using the widest possible numerical aperture, which gives the smallest depthof-field, they could focus on the top of the cell and capture
the reflections only from the glass-medium interface and
the medium-top of the cell interface. In this way, the
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Light and Video Microscopy
Eye
Glass
n1 1.515
Medium
n2 1.336
r12
r23
r34
Cytoplasm n3 1.356
Medium
n4 1.336
FIGURE 8-23 A ray diagram of the reflections that occur when looking at cell attachments with a reflection-interference microscope.
medium between the cell and the glass acts as a thin film
with a refractive index smaller than the refractive index of
the material above or below the medium.
There is a λ/2 phase change in the light reflected at the
medium-cell interface (r23) since the cell has a higher refractive index than the medium. On the other hand, there is no
phase change at the glass-medium interface (r12) since the
glass has a higher refractive index than the medium. If the
cell attached directly to the glass, the thickness of the medium
would be zero and the reflected white light would destructively interfere, giving a black image on a bright background.
As the distance between the cell and the glass increases, the
thickness of the medium increases, and the color of the cell
changes in the same order as Newton’s colors.
In this way, Izzard and Lochner (1976) were able to
measure the thickness of the thin film and showed that
cells attach to the substrate at focal contacts (0.25–0.5 μm
wide 2–10 μm long), which are separated from the
glass surface by 10 to 15 nm. The focal contacts are
not located at the edge, but near the edge of the advancing lamellapodia, which are separated from the glass by
100 nm or more.
Chapter 9
Differential Interference Contrast
(DIC) Microscopy
In Chapter 8, I discussed image-duplication interference
microscopy, in which the image results from the interference between a wave that propagates through a point in the
specimen and a reference wave that is laterally displaced
from that point in the specimen. In this chapter, I will discuss differential interference contrast microscopy (DIC).
Color plates 14 through 18 provide examples of images
obtained using differential interference microscopy.
In a differential interference contrast microscope, the
two waves are laterally displaced a distance that is smaller
than the resolving power of the objective lens. By producing two laterally displaced coherent waves, a differential interference contrast microscope is able to convert a
gradient in the optical path length into variations in light
intensity. Steep gradients in optical path length appear
either bright or dark, depending on the sign of the gradient, whereas areas that have a uniform optical path length
appear gray. A differential interference contrast microscope
can also be used to change gradients in optical path lengths
in transparent objects into spectacular differences in color.
If the two laterally separated images produced by a differential interference microscope were brought together in
perfect alignment, the introduced contrast would disappear
and the image of a transparent object would be invisible.
Gradients in optical path length are mathematically
equivalent to the first derivative of the optical path length
(Figure 9-1). Consequently, a differential interference
contrast microscope can be considered to be an analog
computer that gives the first derivative of the optical path
length of a specimen. By contrast, an image duplication
interference microscope can be considered to be an analog
computer that gives the integral of the optical path length.
DESIGN OF A TRANSMITTED LIGHT
DIFFERENTIAL INTERFERENCE
CONTRAST MICROSCOPE
Differential interference contrast microscopes were
designed and developed throughout the 1950s and beyond
by F. Smith, M. Francon, G. Nomarski, and H. Beyer (Pluta,
1989). The Zeiss Jena interference microscope uses a
Mach-Zehnder type interferometer to separate and combine
the specimen wave and the reference wave (Figure 9-2). The
lateral separation of the specimen and reference waves can
be controlled so that the same microscope can function as
an image duplication interference microscope, or as a differential interference microscope with minimal adjustment.
Most differential interference contrast microscopes, however, utilize birefringent prisms to split and recombine the
specimen and reference waves.
In the Zeiss Jena interference microscope, the specimen
is illuminated by a slit placed in the front focal plane of the
substage condenser. The image of the specimen appears in a
field plane just in front of the interferometer, and an image
of the slit is coaligned with another slit placed in an aperture plane in one arm of the Mach-Zehnder interferometer.
The light passing through this arm functions as the reference
wave. The light passing through the other arm functions
as the specimen wave. There is a tilting plate in the reference arm that is used to laterally separate the reference wave
from the specimen wave at the image plane, and a rotating
plate that is able to add additional optical path length into
the reference arm, which results in a colored image.
The differential interference microscope based on
polarized light has a certain similarity with the polarizing
dOPL
0
dX
OPL
X
Vesicle
Bright
Distance
Gray
Distance
Dark
FIGURE 9-1 A diagram of a vesicle, a graph of the optical path length across a vesicle, and a graph of the first spatial derivative of the optical path
length. In a differential interference microscope, the first spatial derivative of the optical path length gives rise to shades of gray or colors that represent
the first spatial derivative.
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
167
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Light and Video Microscopy
microscope and the image duplication interference microscope based on polarized light (Lang, 1968; Allen et al.,
1969; Figure 9-3). In a polarizing microscope, a single
beam of linearly polarized light that is produced by a polarizer passes through a birefringent specimen that is oriented
so that its slow axis is at a 45-degree angle relative to
the azimuth of maximal transmission of the polarizer. The
specimen splits a linearly polarized wave into orthogonal
linearly polarized waves. The phase difference between the
two waves is a function of the retardation introduced by the
specimen. The two out-of phase orthogonal linearly polarized waves can be considered as a single elliptically polarized wave. The component of the elliptically polarized
wave parallel to the azimuth of maximal transmission of
the analyzer passes through the analyzer. The brightness of
Camera
Interferometer
Eye
Specimen
FIGURE 9-2
Diagram of the Zeiss Jena interference microscope.
an image point depends on the degree of anisotropy in the
bonds that make up the conjugate point in the specimen.
In an image duplication interference microscope based
on polarized light, the linearly polarized light from the
polarizer is split into an ordinary wave and an extraordinary
wave that are laterally separated from each other by 10
to 500 μm. One wave passes through the specimen while
the other passes through the surround. The two waves are
recombined in the wave combiner and are turned into elliptically polarized light. The component of the elliptically
polarized wave parallel to the azimuth of maximal transmission of the analyzer passes through the analyzer. The
brightness of the image point depends on the phase difference between the wave that goes through the conjugate
point in the specimen and the reference wave.
In a differential interference contrast microscope, the
linearly polarized light from the polarizer is acted upon by
a prism that laterally separates the ordinary wave and the
extraordinary wave by only 0.2 μm to about 1.3 μm. The
two orthogonal waves that propagate through two nearby
points in the specimen are recombined in the wave recombiner and are turned into elliptically polarized light. The
component of the elliptically polarized wave parallel to the
azimuth of maximal transmission of the analyzer passes
through the analyzer. The brightness of the image point
depends on the phase difference between the waves that
propagate through the two nearby points in a specimen.
In differential interference microscopes based on
polarized light, the linearly polarized light from the polarizer is split into two orthogonal laterally displaced waves
and recombined into an elliptically polarized wave by
Wollaston prisms or modified Wollaston prisms, known as
Nomarski prisms (Figure 9-4).
Wollaston prisms are constructed from two wedges
of either calcite or quartz, which are cemented together
so that the optic axes of the two birefringent crystals that
make up a prism are perpendicular to each other. Wollaston
prisms are often too thick to be placed in front of the substage condenser lens or behind the objective lens so that
Analyzer
Compensator
+
Wollaston prism
Objective
Calcite prism
λ/2 plate
Calcite prism
Sub-stage
condenser
Polarizer
+
Wollaston prism
Polarizing
Image duplication
Differential interference contrast
FIGURE 9-3 A comparison of a polarizing microscope, an image-duplication interference microscope, and a differential interference contrast microscope.
169
Chapter | 9 Differential Interference Contrast (DIC) Microscopy
the center of the prism interface is located at the front focal
plane of the substage condenser lens and the back focal
plane of the objective lens, respectively. This problem can
be overcome by using Nomarski prisms, in which the optic
axis in the first crystal in a prism is oblique relative to the
second. Because of this arrangement, the waves are split
and recombined outside the prism. The Nomarski prisms
are placed in the microscope such that the plane outside the
prism, where the waves are split, is placed at the front focal
plane of the substage condenser and the plane, in which the
waves are recombined outside the second prism, is placed
at the back focal plane of the objective.
INTERPRETATION OF A TRANSMITTED
LIGHT DIFFERENTIAL INTERFERENCE
CONTRAST IMAGE
In order to understand how contrast is produced with a
differential interference contrast microscope based on
polarized light; consider four pairs of waves produced by
the lower Wollaston or Nomarski prism (Figure 9-5). The
interface of the prism is placed at the front focal plane of
the substage condenser so that the ordinary wave and the
extraordinary wave appear to diverge from the front focal
plane of the condenser and exit the substage condenser
as a parallel beam of in-phase, orthogonal ordinary and
extraordinary waves. Imagine that one pair of waves passes
through the surround (A), one pair of waves passes along
an edge of an object (B), one pair of waves passes through
the center of the object (C), and the last pair of waves
passes along the other edge of the object (D). The first and
third pairs of waves (A and C) experience no optical path
differences, whereas one of the waves of a pair in the second and fourth pair of waves (B and D) will experience an
optical path difference relative to the other wave of the pair.
Suppose that the object, like most biological objects,
introduces a λ/4 phase retardation between the ordinary and
extraordinary waves of a pair. Also suppose that the second
prism is set so as to introduce another λ/4 phase change
between the members of a pair and so that the ordinary ray
is retarded relative to the extraordinary ray (Figure 9-6).
Pairs where both the ordinary and extraordinary waves
go through the surround, or pairs where both the ordinary
and extraordinary waves pass through regions where there
are no differences in the optical path length will be λ/4 out
Eye
Analyzer
Eye
Wollaston
prism
(calcite)
Interference
fringes
Analyzer
Nomarski prism
Objective
Sub-stage
condenser
Wollaston
prism
(calcite)
Specimen
Interference
fringes
Interference
fringes
Objective (Ob)
Specimen
Polarizer
Sub-stage
condenser
Interference fringes
Nomarski prism
Polarizer
FIGURE 9-4 Differential interference microscopes comprised of negatively birefringent calcite Wollaston prisms (left) or positively birefringent
quartz Nomarski prisms (right).
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Light and Video Microscopy
A
B
C
D
0λ
λ/4
0λ
λ/4
Sub-stage
condenser
Wollaston
prism
oe
o e o e
o e
All waves
are in phase
FIGURE 9-5 Formation of a differential interference contrast image. The two members of each pair of waves have been laterally separated but not
axially separated.
Analyzer
A
λ/4
B
0λ
C
λ/4
D
λ/2
Beam
recombiner
Specimen
o e o e
o e
o e
FIGURE 9-6 Formation of a differential interference contrast image.
The two members of each pair of waves have been laterally separated and
axially separated.
of phase after they are recombined by the second prism
(e.g., A and C). The resultant wave will be circularly polarized and these regions will appear gray in the image. On
the other hand, pairs of waves whose ordinary wave experiences a phase shift as it passes through a specimen will
be λ/2 out-of-phase after being recombined by the second
prism (D). The resultant wave will be linearly polarized parallel to the azimuth of maximal transmission of the analyzer
and this point in the image will be bright. A pair of waves
whose extraordinary wave experiences a phase shift as it
passes through the specimen will be 0 λ out-of-phase after
being recombined by the second prism B. The resultant
wave will be linearly polarized parallel to the azimuth of
maximal transmission of the polarizer and this image point
will be dark. The contrasts would be white-black reversed if
the specimen were phase-advancing relative to the medium
instead of phase-retarding. As a result of the conversion of
gradients of optical path into intensity differences, the image
appears as if the specimen were a three-dimensional object
illuminated from the side. However, the three-dimensional
appearance of the image, like the appearance of a specimen
that is obliquely-illuminated (see Chapter 6), is only an illusion (Rittenhouse, 1786; Hindle and Hindle, 1959).
Only gradients in optical path length that are approximately the same size as the distance that the two waves
are laterally separated show up in relief. The microscopic
objects that have characteristic lengths approximating the
distance laterally separating the two waves include membranes, organelles, chromosomes, and vesicles in the cell.
To get an optimum image, the specimen should be rotated
so that the azimuth of separation between the two waves,
known as the azimuth of shear, maximally enhances the
particular structure we want to observe. The azimuth of
shear is the azimuth that contains both the E-ray, which is
perpendicular to the extraordinary wave front, and the Oray, which is perpendicular to the ordinary wave front, as
they emerge from the first Wollaston or Nomarski prism.
A single image obtained with a differential interference
microscope will not represent all asymmetrical specimens.
On the other hand, differential interference microscopy,
like oblique illumination, makes it easy to discover and
visualize asymmetries that may have gone undetected with
bright-field illumination. In order to distinguish between
asymmetries and symmetries in the specimen when using
differential interference microscopy, it is important to
rotate the specimen. The specimen can be rotated easily if
the microscope is equipped with a rotating stage.
Imagine that a specimen in a differential interference
contrast microscope based on polarized light is illuminated
with white light. There will be an infinite number of wave
pairs that pass through each point of the specimen, each pair
representing a different wavelength. Each wavelength will
experience the same retardation as the other wavelengths
going through a given point, but since the wavelengths differ, the phase angle introduced for each wavelength will
differ. Consequently, each wavelength will become elliptically polarized to a different extent and each wavelength
will pass through the analyzer to a degree dependent upon
its ellipticity.
The phase angles introduced by typical biological specimens are usually not large enough to produce interference
171
Chapter | 9 Differential Interference Contrast (DIC) Microscopy
Wave front emanating from specimen
λ/2
λ/4
0λ
Specimen
Incident wave front
FIGURE 9-7 Wave fronts approaching and leaving a transparent
specimen.
FIGURE 9-9 Axially separate the pair of laterally separated waves that
propagate through the specimen.
0λ λ /4 0λ λ /4 0λ
FIGURE 9-8 Allow a laterally separated pair of waves to propagate
through specimen.
colors. A first-order wave plate is either included with the
wave-combining prism or added as an accessory so that
the small retardations introduced by the specimen can be
added or subtracted from the 530 nm retardation introduced
by the fist-order wave plate. All microscope manufacturers provide a different wave splitting prism for each objective lens. The correct prism is inserted into the light path
by turning a turret on the sub-stage condenser to the position where the prism matches the objective. Some microscope manufacturers provide a single wave recombiner that
work for all objectives. In this case the wave recombiner
is inserted just under the analyzer. Other manufacturers
provide a different wave recombiner for each objective. In
this case the wave recombiners are inserted in the objective
mounts.
Earlier, I described image formation in terms of four
point pairs along the azimuth of shear. Now I would like to
use the concept of wave fronts to give an alternative description of how contrast is generated with a differential interference microscope. Although this treatment also applies
to waves split by a birefringent prism, I will specifically
describe waves that are produced by a Mach-Zehnder interferometer in the Zeiss Jena differential interference contrast
microscope as an example because this microscope can easily be adjusted for use as a bright-field microscope; an image
duplication interference microscope, in which two widely
separated wave fronts emanate from the specimen; and a
differential interference contrast microscope, in which two
minutely separated wave fronts emanate from the specimen.
Consider a spherical object that introduces a λ/4
increase in phase relative to the background in a brightfield microscope. Imagine that the object retards a plane
wave that is moving in an upward direction (Figure 9-7).
Now consider what happens when the wave coming
from the real image produced by the objective is split into
two coherent laterally displaced plane waves. This is what
happens in an image duplication interference microscope
FIGURE 9-10 Without axial separation of the two waves, the contrast
in the image of a vesicle will be symmetrical.
(Figure 9-8). Now consider what happens when these two
coherent waves are recombined to produce an interference
image and the reference wave is axially displaced until it
is in phase with the specimen wave coming from a given
position in the specimen (Figure 9-9). The specimen will
be bright in regions where there are no phase differences
between the two waves and dark in regions where the
phase change is λ/2. Regions that are λ/4 out of phase will
appear gray. Two images of the specimen with opposite
contrast are formed—one where the phase difference is 0λ
and one where the phase difference is λ/2.
Now consider what happens when the wave coming
from the real image produced by the objective is split into
two coherent plane waves that are minutely separated laterally, as occurs in a differential interference contrast microscope (Figure 9-10). Without any axial separation between
the two waves, a vesicle will appear like a doughnut with a
gray ring around a bright center. Now consider when one of
the laterally displaced waves is axially retarded relative to
the other. In the regions where the two waves are displaced
by 0 wavelengths, the image will be bright. In the regions
where the two waves are displaced by λ/2, the image will
be dark. Regions that are λ/4 out of phase will appear gray
(Figure 9-11). Consequently, the vesicle will appear in
pseudo-relief as if it were illuminated from the side.
When the specimen is illuminated with white light,
there are an infinite number of wave pairs, each with the
same optical path difference, but the phase angle for each
wavelength will be different. Thus when one wavelength
constructively interferes and produces a given color on
one side of an object, the other side will appear as the
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Light and Video Microscopy
complementary color. Additional color can be added in the
Zeiss Jena differential interference microscope by introducing an additional phase to the reference wave by inserting a glass wedge into the reference wave path.
In an image duplication interference microscope based
on polarized light, the amount of light transmitted through
the analyzer also depends on the phase of the two wave
fronts. In the description of a differential interference contrast microscope based on polarized light given earlier,
I described image formation in terms of four point pairs
along the azimuth of shear. To use the concept of wave
fronts to give an alternative description of how contrast is
generated, imagine that all the extraordinary rays of a given
wavelength are connected together in a group to form a
wave front and all the ordinary rays of that wavelength are
connected together in another group to form another wave
front. The first group would represent the extraordinary
wave front and the second group would represent the ordinary wave front that leaves the specimen. In regions where
the phase change between the extraordinary wave front
Gray
Bright gray
Black
λ /4
and the ordinary wave front is zero, the resultant is linearly
polarized in the azimuth of maximal transmission of the
polarizer and thus no light is transmitted by the analyzer
and the image in this region will be black. In regions where
the phase change between the extraordinary wave front and
the ordinary wave front is λ/2, the resultant is linearly polarized in the azimuth of maximal transmission of the analyzer
and the most light will be transmitted by the analyzer and
the image in this region will be bright. In regions where the
phase change is λ/4, the resultant will be circularly polarized and an intermediate amount of light will pass through
the analyzer and the image in this region will be gray.
In a differential interference microscope based on
polarized light, the amount of lateral separation is determined by the wave splitting prism and the axial separation
is set by the adjustable wave recombining prism. The wave
recombiner is adjusted until the two laterally displaced
waves are in-phase on one side of the object of interest and
λ/2 out-of-phase on the other side of the object of interest.
The differential contrast will be expressed only along the
azimuth of shear.
A differential interference contrast microscope introduces contrast into transparent objects and produces a
pseudo-relief image. The pseudo-relief image does not
relate to the topography itself but to the first derivative
of the optical path length of the specimen. Since details
in a real specimen introduce a variety of different phase
changes, the wave recombiner can be adjusted to give the
maximal contrast for a given specimen detail.
Consider what an image of a plant cell would look like
if we have gradients in the optical path length that are opposite in sign (Figure 9-12). For example, consider a cell with a
Gray
λ /4
λ /2
0λ
λ /4
FIGURE 9-11 With axial separation of the two laterally displaced
waves, the image of the specimen will be asymmetrical and appear to
have relief.
Plant
cell
1.4
Vacuole
1.33
Mitochondrion
1.5
1.4
Cytosol
1.4
Wave fronts
or
How we perceive the images
Light
Light
Light
Light
FIGURE 9-12 Representation of waves going through a plant cell containing organelles with high refractive index (e.g., mitochondria) and organelles with low refractive index (e.g., vacuole). Whether the organelles appear as hills or valleys depends on the direction from which we imagine the
organelles are illuminated. Since they are illuminated from the bottom, the image is only a pseudo-relief image, not based on topography, but on the first
spatial derivative of the optical path length.
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Chapter | 9 Differential Interference Contrast (DIC) Microscopy
vacuole (n 1.33) and a mitochondrion (n 1.5) in a cytoplasm with a refractive index of n 1.4. We can advance or
retard one of the waves relative to the other so that in one
case the illumination appears to be coming from the top right
and in the other case the illumination appears to be coming
from the top left. In one case, the vacuole appears as a hill
and the mitochondrion as a valley and in the other case, the
vacuole appears as a valley and the mitochondrion as a hill.
The apparent relief of the image depends on where we imagine the light to be coming from (Rittenhouse, 1786). In reality, it is being transmitted from the bottom.
The image seen in a differential interference contrast
microscope can be described by the following rules (Allen
et al., 1969).
1. The optical property of a microscopic object that
generates differential interference contrast is the gradient of optical path length across the object in the direction
of shear.
2. Contrast varies proportionally with the cosine of the
angle made by the azimuth of the object with the direction
of shear.
3. The pseudo-relief effect is emphasized when one
slope of the image in the direction of shear is brought to
extinction by varying the wave recombiner. This setting
also yields the highest possible contrast and the most faithful geometric image of the object.
4. Gradients of optical path length of opposite sign
produce shadows in opposite directions.
5. In a differential interference microscope, the contrast is generated independently of the aperture diaphragm.
Consequently, we can keep the aperture diaphragm maximally opened to get maximal resolution and a very shallow
depth of field that allows us to optically section.
light differential interference microscopy is based on the
same principles as transmitted light differential interference microscopy (Figure 9-13). In reflected light differential interference contrast microscopes based on polarized
light, linearly polarized light is generated by an epi-illuminator, which is then directed to a half-silvered mirror and
reflected through a Wollaston or Nomarski prism (where
the beam is split), then through an objective lens and onto
the specimen. The light is then reflected back through the
objective lens and Wollaston or Nomarski prism (where
the beams are recombined), through the half-silvered
8
7
1 2 (3)
4
1. Rotating polarizer
2. λ/4-plate
3. Additional λ-plate
4. Wollaston prism
5
5. Objective
6. Specimen
7. Half-silvered mirror
8. Analyzer
6
FIGURE 9-13 Diagram of a reflected light differential interference
microscope.
Reflected light differential interference contrast microscopy
reveals surface contours by changing differences in height
into variations in amplitude or color. It is used in biology,
medicine, microelectronics, and other disciplines. Reflected
Gray
Dark
Gray
Bright
Gray
Dark
Bright
Dark
Bright
DESIGN OF A REFLECTED LIGHT
DIFFERENTIAL INTERFERENCE
CONTRAST MICROSCOPE
Dark
Differential interference contrast microscopes are better than phase-contrast microscopes when viewing objects
whose optical path differences are greater than the depth
of field of a given objective lens. Differential interference
contrast microscopes that are based on polarized light are
not good for studying tissue cultured cells that grow on
birefringent plastic culture plates. In this case, we may
choose to view the specimens with a differential interference contrast microscope based on a Mach-Zehnder interferometer, oblique illumination, or Hoffman Modulation
Contrast microscopy (HMC; see Chapter 10).
FIGURE 9-14 Contrast is generated in a reflected light interference
contrast microscope as a result of differences in microtopography.
174
mirror and through the analyzer placed in the crossed position.
A full wave or a λ/4 plate can be inserted after the polarizer
in order to vary the retardation between the ordinary ray and
the extraordinary ray and thus vary the color of the image.
The Zeiss Jena interference microscope can also be
used for reflected light differential interference microscopy
by changing from the transmitted light illuminator to the
epi-illuminator and by changing the objectives from those
designed for use with transmitted light to those designed
for use with reflected light.
INTERPRETATION OF A REFLECTED LIGHT
DIFFERENTIAL INTERFERENCE CONTRAST
IMAGE
The illuminating linearly polarized light that passes through
the Wollaston or Nomarski prism is split into two laterally
separated orthogonal linearly polarized waves. Both waves
Light and Video Microscopy
then are reflected from the surface of the object and recombined in the original prism. When a pair of waves strikes
a horizontal surface, there is no phase change introduced
between the two, and the surface appears black.
However, when two waves of a pair strike an inclined
surface, a phase change will be introduced and, as a result,
the image will appear bright. The magnitude of the phase
change introduced by the incline depends on the slope of
the surface. The brightest spots in the image will appear
where the height difference between the two waves of a
pair equal λ/2 (Figure 9-14).
A λ/4 plate can be introduced after the polarizer so that
the horizontal areas are gray, and the gradients in topology
along the plane of shear appear white or black, depending
on the direction of the slope. If we introduce a first-order
wave plate after the polarizer, the horizontal areas will
appear lavender and the slopes along the plane of shear
will show additive (bluish) or subtractive (yellow-orangish)
colors, depending on the slope.
Chapter 10
Amplitude Modulation Contrast
Microscopy
According to Ernst Abbe, image formation by microscopes
can be understood in terms of diffraction (see Chapter 3;
Abbe, 18761878, 1889; Wright, 1907; von Rohr, 1936).
His thinking went like this: A microscopic specimen diffracts the illuminating light. The diffracted light captured by
the lens forms a diffraction pattern in the back focal plane
of the lens. This diffraction pattern is an imperfect representation of the actual diffraction pattern produced by the
specimen because the lens cannot capture the highest orders
of diffraction. The spots of the diffraction pattern in the
back focal plane of the objective act as sources of spherical
waves that interfere in the image plane to form the image.
Consequently, the image is related directly to the diffraction
pattern and indirectly only to the specimen itself.
Abbe’s theory is to date the most complete and useful
theory of microscopical vision and, along with G. Johnstone
Stoney’s (1896) application of Fourier’s Theorem to image
formation, provides a strong mathematical basis for using
digital image processors to determine the real structure of
a specimen from knowledge of the optical properties of the
microscope that convolve the image by introducing artifacts
like low pass filtering. However, Abbe’s diffraction theory
was developed from the study of high-contrast amplitude
objects and not transparent phase objects, and consequently,
it does not take into consideration differences in the refractive indices of the points in a specimen that cause lenslike refractions. Such considerations, although complex,
would yield a more complete theory of microscopic vision
(Nelson, 1891).
The word diffraction is derived from the Latin words dis
and frangere, which mean “apart” and “to break,” respectively. Diffracted light, according to G. Johnstone Stoney
(1896), is “light which advances in other directions than those
prescribed by geometrical optics.” Although diffraction
theory is ultimately more complete than geometric optical
theory, geometrical optics can be considered to be a reasonably approximate theory of image formation in the microscope when the ratio of object length to wave length is large.
Under this condition, the majority of the diffracted light is
almost indistinguishable from the nondiffracted light.
It is likely that few of us, if any, have the ability or the
computational power to apply diffraction theory in a rigorous enough way to perform a complete characterization
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
of a complex biological specimen (Meyer, 1949); consequently, many simplifying assumptions about the specimen
must be introduced. It is possible, however, that in making
the simplifying assumptions, elements that may be necessary to relate points in the image to points in the specimen
become unintentionally discounted or obscured.
The simultaneous or occasional application of geometric optical theory to image formation may provide us with
a certain degree of insight that may help in the construction
of a complete and universal theory of image formation.
For this reason, I present a few simple examples that will
remind us of the importance of refraction in image formation. After that, I will use refraction theory to describe how
images are formed in an amplitude modulation contrast
microscope (Hoffman and Gross, 1975a, 1975b; Hoffman,
1977). Gordon Ellis (1978) has used diffraction theory to
describe image formation in his version of an amplitude
modulation contrast microscope, which he calls a “singlesideband edge enhancement” or SSEE microscope. Color
plate 19 provides an example of an image obtained with a
Hoffman modulation contrast microscope.
The importance of refraction in understanding the
images of complex biological specimens formed by a
microscope can be seen by doing the following experiment.
Mix together water, oil, and air and place the mixture on
a microscope slide (Figure 10-1). The air bubbles, which
have a refractive index less than that of water, will act as
diverging lenses, and each air bubble will produce a virtual
image of the illuminating light beneath the bubble. That is,
f
Air
H2O
Oil
f
FIGURE 10-1 In a mixture of air, water, and oil, the oil drops act as
converging lenses and air bubbles act as diverging lenses. They project
a bright image of the aperture diaphragm above and below the lens-like
object, respectively.
175
176
Light and Video Microscopy
we will see a bright spot, which is the image of the aperture diaphragm, when we move the stage up. On the other
hand, the oil droplets, which have a refractive index greater
than that of water, will act as converging lenses, and each oil
droplet will produce a real image of the illuminating light
above the bubble. That is, we will see a bright spot, which
is the image of the aperture diaphragm, when we move the
stage down.
When this same experiment is done with a compound
microscope using oblique illumination, the air bubble,
which acts as a diverging lens, appears with the bright side
on the opposite side as the illuminating light beneath the
condenser. The oil droplet, which acts as a converging lens,
appears with the bright side on the same side as the illuminating light beneath the condenser (Figure 10-2).
This little demonstration should always be kept in mind
when interpreting the structure of biological specimens
since the cytoplasm can be considered to be a sample that
contains many spherical vesicles with refractive indices
greater than and less than the refractive index of the cytoplasm (Naegeli and Schwendender, 1892; Wright, 1907;
Gage, 1917). Thus each vesicle and organelle may act as a
converging or diverging lens.
HOFFMAN MODULATION CONTRAST
MICROSCOPY
The Hoffman modulation contrast microscope makes transparent specimens visible by converting gradients in optical path length into differences in intensity. According to
Hoffman, the direct light is responsible for image formation
and contains information about the specimen. Specifically,
it contains information about the gradients in optical path
length that exist in the specimen. The modulation contrast
microscope, like a differential interference contrast microscope, and a microscope that uses oblique illumination,
produces pseudo-relief images. The images of transparent
specimens produced by a modulation contrast microscope
are high in contrast and resolution. Differential interference
microscopes based on polarized light cannot be used for
birefringent objects or specimens growing in culture dishes
made of birefringent plastic, whereas modulation contrast
microscopy is not limited to isotropic specimens.
The Hoffman modulation contrast attachments are
made by Modulation Optics, Inc. to fit any bright-field
microscope. The system includes a set of objective lenses
that have been modified by adding a modulator to the
back focal plane, a turret condenser that has a rotating slit
whose size is specific for each objective lens, and a polarizer (Figure 10-3). Olympus markets this technique under
the name of “relief contrast” and Zeiss markets a similar
system under the name of “variable relief contrast” (Varel).
The Hoffman modulation contrast modulator is placed
asymmetrically in the back focal plane of the objective. It
has three regions that differ in their transmittance. The region
at one edge has a transmission of less than 1 percent, the next
region has a transmission of 15 percent, and the other side
has a transmission of 100 percent. The modulator introduces
only changes in amplitude without any change in phase.
The slit is placed in the front focal plane of the sub-stage
condenser and is off-center so it will produce oblique
Sub-stage
condenser
Sub-stage
condenser
s
f
f
f
f
f
f
f
f
s
s
Air bubble
as a diverging lens
Oil droplet
as a converging lens
s
FIGURE 10-2 With oblique illumination, the air bubble, which acts as a diverging lens, appears with the bright side on the opposite side as the illuminating light after passing through the objective, and the oil droplet, which acts as a converging lens, appears with the bright side on the same side as the
illuminating light after passing through the objective.
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Chapter | 10 Amplitude Modulation Contrast Microscopy
illumination. An image of the slit is produced by the substage condenser-objective pair, on the modulator in the back
focal plane of the objective. Part of the slit is covered with a
polarizer. When the polarizer that is placed above the field
diaphragm is crossed relative to the polarizer in the slit, the
slit effectively is reduced to one-half its maximal width.
When setting up a Hoffman modulation contrast microscope, the slit, which is placed in the front focal plane of
the condenser, is imaged on top of and aligned with the
15 percent transmittance portion of the modulator in the back
focal plane of the objective. Therefore, in the absence of
a specimen, the image plane will be filled with light that
is about 15 percent of the intensity of the light that passes
through the slit. Consequently, the background in the
image plane will appear gray (Figure 10-4).
Eye
Modulator
Objective
Modulator showing the
alignment of the slit
Specimen
Sub-stage
condenser
Open slit
Slit
P2
Polarizer
FIGURE 10-3
Slit covered
with polarizer
Diagram of a Hoffman modulation contrast microscope.
Objective
Sub-stage
condenser
In order to understand how an image is formed in a
Hoffman modulation contrast microscope, consider a gradient in optical path length to be equivalent to a prism
made from isotropic material. When the prism is placed in
the light path, in the position where the specimen would
be, the incident light will be refracted by the prism and the
image of the slit will be displaced laterally. That is, the slit
will be imaged on top of either the 100 percent (Figure 10-5)
or the 1 percent (Figure 10-6) transmittance portion of
the modulator, depending on the orientation of the prism.
If the refractive index of the prism is less than the refractive index of the surround, then the incident light will be
refracted to the opposite side of the modulator (Figure 10-7).
Figure 10-8 shows how a cell or a vesicle within the
cell can be modeled as a series of prisms with different
orientations.
Thus the intensity of a given point in a Hoffman modulation contrast image is determined by the gradient in optical path lengths in the object. Contrast is generated only by
gradients in the optical path lengths that are parallel to the
short axis of the slit. Consequently, the orientation of the
specimen determines how the pseudo-relief image appears
and a single image will not represent all asymmetrical
specimens. Like oblique illumination and differential interference contrast microscopy, Hoffman modulation contrast
microscopy makes it easy to discover and visualize asymmetries that may have gone undetected with bright-field
illumination. In order to distinguish between asymmetries
and symmetries in the specimen when using Hoffman
modulation microscopy, it is important to rotate the specimen using a rotating stage.
All the nonrefracted light goes through the 15 percent
transmission portion of the modulator when the azimuth of
maximal transmission of the polarizer that covers part of
the slit is perpendicular to the azimuth of maximal transmission of the first polarizer. This gives maximal contrast,
but a grainy image. Some of the incident light also goes
Modulator
1%
15%
100%
fc
fc
fob
fob
Slit
FIGURE 10-4 Ray diagram of a
Hoffman modulation contrast microscope in the absence of a specimen.
178
Light and Video Microscopy
Sub-style
condenser
Objective
Modulator
1%
15 %
fc
100 %
Image will
be bright
Slit
FIGURE 10-5
Ray diagram of a Hoffman modulation contrast microscope in the presence of a prism-like specimen of a given orientation.
Sub-stage
condenser
Objective
Modulator
1%
15 %
fc
100 %
Image will
be dark
Slit
FIGURE 10-6 Ray diagram of a Hoffman modulation contrast microscope in the presence of a prism-like specimen with the opposite orientation as
that in Figure 10-5.
np ⬎ ns
FIGURE 10-7
np ⬍ ns
Ray diagrams of prism-like specimens with a refractive index greater than or less than the surround.
nt ni
nt
nt ni
θt
Vesicle
ni
FIGURE 10-8
Model of a vesicle as a series of prisms.
ni
θi
θt
nt
ni
θi
nt
179
Chapter | 10 Amplitude Modulation Contrast Microscopy
through the 100 percent transmission portion of the modulator when the azimuth of maximal transmission of the
polarizer covering part of the slit is parallel to the azimuth
of maximal transmission of the first polarizer. This reduces
the contrast, but gives a smooth metallic-like image.
Thus the contrast of the image can be adjusted by rotating the first polarizer. The percent contrast of the image is
described by the following formula:
percent contrast (I b I i )/I b 100%
where Ii is the intensity of the image and Ib is the intensity
of the background.
Hoffman modulation contrast microscopy lets us obtain
good resolution without sacrificing the resolving power of
the objective lens. Since the full aperture of the objective
lens is used for Hoffman modulation contrast microscopy,
not only is the full resolving power of the microscope utilized, but the depth of field is minimized. Thus Hoffman
modulation contrast optics, like differential interference
contrast optics, lets us optically section the specimen.
Hoffman modulation contrast microscopy offers several
advantages:
● Good contrast is obtained at high resolution since
the illumination is oblique and the full numerical of the
sub-stage condenser and objective is utilized.
● Since the numerical aperture is high, the depth of
field is small and we can optically section.
●
Since the image is in black and white, we can use
relatively inexpensive achromats or plan achromats with a
monochromatic green filter.
● Birefringent specimens do not degrade the image
as they do in differential interference contrast microscopy, and in Hoffman modulation contrast microscopy,
the specimens can be observed in birefringent plastic Petri
plates, making the observation of transparent culture cells
possible. This is possible because in Hoffman modulation
contrast microscopy, the two polarizers are beneath the
specimen.
● We can do epifluorescence microscopy and modulation
contrast microscopy sequentially without having to remove a
Wollaston or Nomarski prism as we would have to do when
using differential interference contrast optics.
● Hoffman modulation contrast optics is relatively
inexpensive compared to differential interference contrast
optics since we do not have to buy the relatively expensive
Wollaston or Nomarski prisms.
● A type of dark-field microscopy can be done by
aligning the slit with the 1 percent transmission region of
the modulator.
The disadvantages of Hoffman modulation contrast microscopy are:
● We must be careful in interpreting an image of a vesicle as a hill or as a valley. The pseudo-relief image does
not necessarily represent actual three-dimensional objects,
but only gradients in optical path lengths.
● In interpreting the image, we must remember that
maximal image contrast arises from objects oriented perpendicular to the length of the slit.
● Images are not rendered in color, although optical
staining can be achieved in a homemade system by replacing the 1, 15, and 100 percent regions of the modulator with
colored filters. For example, if the 1 percent area were blue,
the 15 percent area gray, and the 100 percent area magenta,
then gradients of optical path length in one direction will
appear blue, gradients in the other direction will appear
magenta, and areas without gradients will appear gray.
REFLECTED LIGHT HOFFMAN
MODULATION CONTRAST MICROSCOPY
Hoffman modulation contrast optics can be used with
reflected light to convert variations in surface contours into
variations in image brightness (Hoffman and Gross, 1970).
In reflected light Hoffman modulation contrast microscopy, just like reflected light differential interference contrast microscopy, the three-dimensional image is a true
representation of the surface contour of the specimen.
The reflected light Hoffman modulation contrast microscope is set up in an optically similar way as the transmitted light version except that in the reflected light version,
an epi-illuminator and half-silvered mirror are added
(Figure 10-9).
In interpreting an image generated by reflected light
Hoffman modulation contrast microscopy, the specimen is
considered to be composed of reflecting surfaces, and the
direction of the reflected ray is described strictly by the
law of reflection given by geometric optical theory (see
Chapter 2). The reflected rays pass through the brighter or
darker region of the modulator, depending on the slope of
the surface of the specimen (Figure 10-10).
THE SINGLE-SIDEBAND EDGE
ENHANCEMENT MICROSCOPE
A single-sideband edge enhancement (SSEE) microscope
is a transmitted light microscope that is able to change
a gradient in optical path length into variations in intensity
(Ellis, 1978). It is a special case of oblique illumination. It
is not commercially available, but it can be built very easily (Figure 10-11).
The incident light in a single-sideband edge enhancement microscope passes through a collector lens and a field
diaphragm and is focused onto an aperture diaphragm
equipped with an adjustable semicircular half stop that is
placed at the front focal plane of the sub-stage condenser.
The adjustable half-stop is set to occlude one-half of the
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Light and Video Microscopy
Collector
lens
Half-silvered
mirror
1%
Slit
100%
15%
Modulator
Objective
Specimen
FIGURE 10-9
Diagram of the illuminating rays in a reflected light Hoffman modulation contrast microscope.
Image
1. First draw dashed lines to find image point
2. Then draw solid lines to show reflected light
1%
15%
100%
Modulator
Objective
Specimen
FIGURE 10-10 Ray diagram showing that contrast in a Hoffman modulation contrast microscope represents microtopography.
aperture diaphragm. The oblique light passes from the
sub-stage condenser to the specimen. The light then passes
into an ordinary objective. A relay lens then is used to project the back focal plane of the objective lens onto a carrier
attenuation filter. The relay lens also moves the image of the
specimen up the optical tube. There are two crossed polars,
one above and one below the carrier attenuation filter.
The carrier attenuation filter is in a conjugate plane
with the aperture diaphragm and the back focal plane of
the objective. It is aligned so that the nondiffracted wave,
which Ellis calls the carrier wave, passes through one half,
and the positive or negative orders of diffracted waves,
which Ellis calls the single sideband, passes through the
other half. Ellis (1978) has made a variety of carrier attenuation filters that are used to enhance contrast. One filter,
which is placed between parallel polars, is made up of two
Polaroids oriented perpendicular to each other. The filter
can be rotated so as to differentially absorb either the carrier or the single-sideband light, thereby enhancing or
reducing the contrast of various gradients in optical path
length in the specimen.
The intensities of the image points formed by differential interference contrast and modulation contrast microscopes reflect the first derivative of the optical path lengths
along a given azimuth. Computers excel in performing
mathematical operations like taking derivatives, integrals, and Fourier transforms rapidly and inexpensively. In
Chapter 14, I will discuss microscopes that include a video
or digital camera so that an electrical or numerical signal
that represents intensities and colors in the image can be
passed into a computer. The computer can then perform
a number of image processing functions, including taking
the first derivative of the brightness in order to produce
a pseudo-relief image.
Chapter | 10 Amplitude Modulation Contrast Microscopy
Eye
Projection lens
Analyzer
Retardation plate
Carrier attenuation filter
Polarizer
Relay lens
λ/2 plate
Objective
Specimen
Sub-stage condenser
Adjustable half-stop/aperture
diaphragm
Field diaphragm
Light source
FIGURE 10-11 A diagram of a single-sideband edge enhancement
microscope.
181
I have shown you that the various properties of light
(amplitude, phase, polarization, and wavelength) can be
used effectively by a variety of microscopes to produce
high contrast images of transparent biological specimens
with great resolving power. The correct interpretation of
these images provides us with quantitative information
about the structure and physical properties of the specimen
(e.g., mass, birefringence, entropy and enthalpy, thickness,
absorption spectrum, density). This ends our ability to use
geometric and physical optics to discuss image formation.
In Chapter 11, in which I will discuss fluorescence microscopy, we will have to introduce the quantum theory of radiation (Einstein, 1905a, 1909, 1917; Dirac, 1927; Heitler,
1944; Finkelstein, 2003; Loudon, 2003; Zajonc, 2003).
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Chapter 11
Fluorescence Microscopy
The popular revival of light microscopy was due, in part, to
the development of reflection fluorescence microscopy with
its ability to localize enzymes, substrates, and genes, and its
ability to characterize physicochemical properties of the
cell, including membrane potentials, viscosity, pH, Ca2,
Mg2, Na, and Cl with high resolution and contrast.
While classical optics have been very useful in understanding the formation and interpretation of microscopic images
formed by bright-field, dark-field, phase-contrast, polarization, interference, differential interference, and modulation
contrast microscopes, it will fail us in understanding the
formation of images in a fluorescence microscope. In order
to understand image formation is fluorescence microscopes,
we will have to explore the quantum nature of light. Color
plates 20 and 21 provide examples of specimens observed
with fluorescence microscopy.
DISCOVERY OF FLUORESCENCE
Perhaps fluorescence was first noticed by Nicolo
Monardes, the physician from Seville who had published
a book on the newly discovered medicinal plants from
America (Boyle, 1664; Priestley, 1772; Harvey, 1957). In
1575, Monardes noticed that the wood of Lignum nephriticum (Eysenhardtia polystachya), when hollowed out into
cups and filled with water, appeared to emit a bluish light.
An extract of the wood, which was used to treat kidney diseases, also emitted the light. This was so spectacular that
these cups were given to the royalty and visiting dignitaries for the next 100 years.
A century later, Robert Boyle (1664) noted that adding
vinegar (or other acids) to the extract decreased the amount
of fluorescence, whereas adding basic solutions (oil of tartar, solution of alum, spirit of hartshorn, or urine) restored
the fluorescence. Boyle concluded that the color of the
solution of Lignum nephriticum can be used to discern the
acidity or alkalinity of a substance. This set the scene for
using fluorescent compounds for measuring physiological
properties of the living cell (e.g., pH).
Throughout history, philosophers have thought about
how the color of a body is related to its fundamental
composition or structure. While experimenting with a
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prism and illuminating objects with monochromatic light,
Newton (1730) showed that the color of an object was not
an absolute property of the object itself, but depended on
the color of the illuminating light. He noticed that if an
object looked red when illuminated with white light, it
looked black when illuminated with anything but red light,
indicating that the color of these objects was due to the
color of light that was reflected from the object. Newton
thought about this relationship and proposed that, “The
bigness of the component parts of natural Bodies may
be conjectured from their Colours.” Sir David Brewster
(1833a) continued to study the cause of natural colors and
extracted chlorophyll from the Laurel (Prunus Lauro-cerasus)
and 19 other plants with alcohol. He wrote:
In making a strong beam of the sun’s light pass through the green
fluid, I was surprised to observe that its colour was a brilliant
red, complementary to the green…. I have observed the same
phenomenon in various other fluids of different colours, that it
occurs almost always in vegetable solutions…. One of the finest
examples of it which I have met with may be seen by transmitting a strong pencil of solar light through certain cubes of bluish
fluor-spar. The brilliant blue colour of the intromitted pencil is
singularly beautiful.
Brewster concluded that the absorption of rays by the
atoms of a substance must play some role in the change in
color. He wrote:
The true cause of the colours of natural bodies may be thus
stated: When light enters any body, and it is either reflected or
transmitted to the eye, a certain portion of it, of various refrangibilities, is lost within the body; and the colour of the body,
which evidently arises from the loss of part of the intromitted
light, is that which is composed of all the rays which are not
lost; or, what is the same thing, the colour of the body is that
which, when combined with that of all the rays which are lost,
compose the light. Whether the lost rays are reflected or detained
by a specific affinity for the material atoms of the body, has not
been rigorously demonstrated. In some cases of opalescence,
they are either wholely or partly reflected; but it seems almost
certain, that in all transparent bodies, and in that great variety of
substances in which no reflected tints can be seen, the rays are
detained by absorption.
Perhaps even more amazing than a green solution giving off red light, was to find a colorless solution that gave
off blue light when irradiated with invisible ultraviolet
183
184
light. John Herschel (1845a,b) observed a solution of quinine sulphate and found:
Though perfectly transparent and colourless when held between
the eye and the light, or a white object, it yet exhibits in certain
aspects, and under certain incidences of the light, an extremely
vivid and beautiful celestial blue colour, which from the circumstances of its occurrence, would see to originate in those strata
which the light first penetrates in entering the liquid….
George Gabriel Stokes (1852, 1854) repeated Herschel’s
observation with sulphate of quinine. Stokes wrote, “It was
certainly a curious sight to see the tube instantaneously
lighted up when plunged into the invisible rays: it was literally darkness visible. Altogether the phenomenon had
something of an unearthly appearance.” Stokes irradiated
the solution with variously colored light obtained by passing
sunlight through a prism. He noticed that the emitted light
always had a longer wavelength than the incident light. He
wrote (1885):
Perhaps the most striking feature in this phenomenon is the
change in refrangibility of light which takes place in it, as a result
of which visible light can be got out of invisible light, if such an
expression may be allowed: that is, out of radiations which are of
the same physical nature as light, but are of higher refrangibility
than those that affect the eye; and in the same way light of one
kind can be got out of light of another, as in the case for instance
of an alcoholic solution of the green colouring matter of leaves,
which emits a blood red light under the influence of the indigo
and other rays. Observation shows that this change is always in
the direction of a lowering.
Stokes called this phenomenon, where specimens absorb
light of one wavelength and reemit it at a longer wavelength,
fluorescence, after the mineral fluor-spar, which shows the
same phenomenon. The phenomenon that the light emitted
by fluorescent objects always has a longer wavelength than
the light absorbed is now known as Stokes’ Law. Frances
Lloyd (1924) described the working situation where Stokes
came up with the great law that bears his name:
To grasp clearly the nature of fluorescence was the work of Sir
George Stokes, who, my friend and colleague Professor A. S. Eve,
tells me, was given to working in the ‘back scullery and a small
one at that’, using the leaves of laurel and other plants which grew
in his garden; and thus was led to the establishment ‘of a great
principle with accommodation and apparatus which would fill the
modern scientific man with dismay’.
Stokes also postulated that fluorescence was related to
phosphorescence. The only difference is that light given
off by specimens that showed fluorescence stopped immediately after the incident light was shut off, whereas phosphorescent specimens continued to glow for relatively long
periods of time after the incident light was removed. Indeed,
with fluorescence, light emission stops almost immediately
(within 108 s) after the cessation of the activating (or actinic)
radiation, whereas with phosphorescence the emitted light
persists for seconds, minutes, hours, days, or even months,
depending on the material, after the cessation of the actinic
radiation (Dake and De Ment, 1941).
Light and Video Microscopy
Stokes (1852) tried to come up with a physical mechanism to describe how short wavelength light could turn into
long wavelength light after it interacted with the fluorescent molecules. He weakly proposed that the incident light
sent the atoms in a fluorescent molecule into a vibration
and the light emitted from this vibration was of a longer
wavelength. He did not like this conclusion, and believed
that his explanation made no physical sense since it was
physically impossible, according to classical wave theory,
to get a short wavelength wave to give rise to a long wavelength wave. A better explanation had to await the development of quantum theory.
PHYSICS OF FLUORESCENCE
In Chapters 2 and 3, I discussed how Huygens (1690) and
Newton (1730) realized that the various phenomena of
light required taking into consideration that light and the
ether through which it traveled, had the complementary
properties of particles and waves. The distinction between
Huygens’ and Newton’s ideas is that Huygens believed that
light was a wave that traveled through a particulate ether,
while Newton believed that light consisted of particles that
traveled through a vibrating ether.
Up until the mid-nineteenth century, prominent scientists supported Newton’s conception that light was particulate, and forgot about his need to include the wave nature of
the ether for a full description of light (Anonymous, 1803,
1804; Young, 1804b). However, after Foucault’s (1850)
demonstration that the speed of light was faster in air than
it was in water, Maxwell’s (1865) miraculous equations that
unified electricity and magnetism, and Heinrich Hertz’s
(1893) demonstration that electromagnetic waves can be
transmitted, received, reflected, refracted, focused, polarized, and interfere with each other, the electromagnetic
wave theory of light became the widely accepted theory of
light. The need to incorporate Huygens’ particulate nature
of the ether, in general, was neglected and forgotten.
As Maxwell’s equations were enjoying success in
describing optical phenomena, the laws of thermodynamics
were being applied to the study of radiation from hot bodies or incandescence. Initially, incandescent bodies served
as model systems to understand solar radiation (Herschel,
1800a, 1800b; Leslie, 1804; Carson, 2004). However,
Kirchhoff realized that there must be a universal function,
dependent only on wavelength and temperature, and independent of the material in which an incandescent body is
made, which describes the radiation (Kirchhoff, 1860,
1861; Draper, 1878; Houstoun, 1930). Black body radiators
are black because they absorb all wavelengths of radiation,
and when a black body radiator is heated to incandescence,
it emits all wavelengths of radiation in a temperaturedependent manner (Figure 11-1).
Wilhelm Wien (1893, 1896, 1911; Drude, 1939) was
interested in finding the universal function that described
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Chapter | 11 Fluorescence Microscopy
black body radiation and turned to Maxwell’s (1897)
kinetic theory of gases, which described the effect of temperature on the mean velocity and the distribution of velocities of molecules in a gas to use as an analogy to describe
the effect of temperature on black body radiation (Figure
11-2). Wien made the following assumptions:
Energy density
1. Maxwell’s kinetic theory of gases, which describes
the influence of temperature on the mean velocity and
Visible
Using these assumptions, Wien came up with an equation, which related the energy density (eλ in Jm3) of any
given wavelength in a black body cavity to the temperature
of the black body and Wien’s equation was similar in form
to Maxwell’s velocity distribution equation. The formula,
known as Wien’s radiation law, required two constants to be
dimensionally correct.
6,000 K
5,000 K
4,000 K
100
500
3,000 K
1000
1500
2000
Wavelength (nm)
e (c1 /5 )(exp(c 2 / T))
(c1 /5 )(1/exp(c 2 / T))
2500
FIGURE 11-1 The emission spectrum of a black body radiator.
0°C
Number of molecules
distribution of velocities of gas molecules, should apply
to the mean velocity and distribution of velocities of the
atoms that make up the solid wall of a black body radiator.
2. The wavelength of light emitted by an atom depends
only on the velocity of vibration of the atom. The wavelength is inversely proportional to the velocity and therefore
the higher the velocity, the shorter the wavelength emitted.
3. The intensity of the light emitted at a given wavelength is proportional to the number of atoms vibrating at
the velocity necessary to emit light at that wavelength.
1000°C
2000°C
Speed of molecules
FIGURE 11-2 The Maxwell distribution of molecular velocities as a
function of temperature.
where c1 (in J m) and c2 (in mK) were constants that could
be determined empirically. Lummer and Pringsheim
(1899a, 1899b, 1900) built a black body radiator that was
optimal enough to test Wien’s radiation law and found
that it described the energy density of short wavelengths,
but was inadequate to describe the energy density of long
wavelengths (Figure 11-3; Kangro, 1976; Kuhn, 1978).
Other aspects of Maxwell’s thermodynamics were used
to find a theoretical foundation to the black body radiation
curve. Lord Rayleigh (1900, 1905a, 1905b, 1905c), helped
by Sir James Jeans (1905a, 1905b, 1905c, 1924) applied the
principle of equipartition, which states that each particle in
a group of identical particles collides with each other elastically, and as a consequence has a nearly identical energy.
According to the wave theory of light, the energy of a wave
10,000K
Planck’s law
Energy density
Wien’s law
9,000 K
8,000 K
7,000 K
6,000 K
100
200
300
400
500
600
700
800
900
Wavelength (nm)
FIGURE 11-3 Wien’s law describes the distribution of short wavelengths radiated from a black body but deviates from the experimental results at
long wavelengths.
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Light and Video Microscopy
Number of half
wavelengths
1
Rayleigh-Jeans Law
2
4
Energy density
3
5
Observed
spectrum
6
0
FIGURE 11-4 How waves of different lengths can be packed into a
space. According to the wave theory of light, the energy contributed to
the black body radiation by each wavelength is a function of the number
of half-wavelengths in the space. The number of modes equals the number of half-wavelengths minus one.
is proportional to the square of the amplitude. Following
the principle of equipartition, Rayleigh assumed that the
amplitude of waves of all wavelengths in the cavity would
be the same. However, waves with shorter wavelengths
would have more regions of maximal amplitude that fit in a
given volume than waves with longer wavelengths. Usually,
regions of zero amplitude within the cavity, called modes,
are counted instead of regions with maximal amplitude. The
number of modes equals the number of regions of maximal
amplitude minus one (Figure 11-4). According to the boundary conditions of electromagnetic theory, standing electrical
waves must have zero amplitude at the edge of the cavity.
Thus if one half-wave with a wavelength equal to twice the
length of the cavity would fit, two half-waves with a wavelength half as long would fit and three half-waves with a
wavelength one-third as long would fit in the cavity. This
trend goes on such that an infinite number of waves with an
infinitely short wavelength would fit in the cavity.
Using the principle of equipartition of energy, Rayleigh
and Jeans came up with an equation that related the
energy density (eλ in J/m3 per given wavelength) to the
temperature:
e (8π/ 4 )kT
where k is Boltzmann’s constant (1.38 1023 JK), kT
describes the energy in the cavity at a given temperature
T (in Kelvin), and (8πλ4) describes the number of modes
for a given wavelength. The Rayleigh-Jeans equation was
able to explain the distribution of long wavelengths, but
400
500
600
700
Wavelength (nm)
800
FIGURE 11-5 The “Ultraviolet catastrophe” that was predicted by the
classical electromagnetic wave theory of light.
failed in predicting the distribution of short wavelengths
in that it predicted that a black body should give off an
infinite amount of short wavelength light (Figure 11-5).
Lord Kelvin (1904) described the inability of classical
theory to describe black body radiation as one of the two
“Nineteenth Century Clouds over the Dynamical Theory of
Heat and Light,” and in 1911, with 2020 hindsight, Paul
Ehrenfest gave the moniker, the “ultraviolet catastrophe”
to the poor prediction.
In 1899, Max Planck saw that there was an element of
truth in Wien’s radiation law for short wavelengths and an
element of truth in the Rayleigh-Jeans law for long wavelengths, but neither of them alone was capable of giving a
theoretical foundation for understanding black body radiation or predicting what the spectrum would be at a given
temperature. Planck (1949a, 1949b) reluctantly but courageously questioned the statistical assumptions upon which
both laws were based. What if, he thought, all wavelengths
do not share the thermal energy of the cavity equally and
that shorter wavelengths are underrepresented? And what
if the atoms in the wall did not give off radiation continuously, but in discreet packets he called quanta?
According to Planck’s new hypothesis, black body
radiation would be governed by two effects, one that
was described by Wien’s radiation law and one that was
described by the Rayleigh-Jeans radiation law. First, since
a greater number of short wavelength light can fit in a
given volume compared with long wavelength light, there
will be a tendency to fill the cavity with shorter wavelength
light than longer wavelength light. Second, Planck postulated that the probability of the atoms in the walls radiating
187
Chapter | 11 Fluorescence Microscopy
1/exp[x] used by Maxwell and Wien. Planck visualized the
oscillating atoms in the wall of the cavity as having discrete energy levels. That is, as the oscillating atom went
from an excited state to a ground state, it lost energy in
steps of one quantum, and at the same time, emitted the
quantum of energy into one quantum of radiation. In order
to achieve the curve generated by black body radiation,
Planck assumed that the energy (E, in J) in one quantum of
radiation was related to the frequency (ν) and wavelength
(λ) of the radiated light by the following formula:
Energy density
Thermal source at 2.728 K
COBE measurements
E hν hc/ 0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Wavelength (cm)
FIGURE 11-6 The black body distribution of the cosmic microwave
background radiation. Note the identity of the experimental ( ) and theoretical (
) results.
Metallic
electron
emitter
Light
Collector
e (8π/ 4 )(hc/)[1/(exp(hc/( kT)) 1)]
(8πhc/5 )[1/(exp(hc/ ( kT)) 1)]
e
A
Ammeter
Voltmeter
V
Power supply
FIGURE 11-7
tric effect.
where h is known as Planck’s constant (6.626 1034 J s)
and c is the speed of light (2.99792458 108 m/s). Planck’s
assumption contrasts with the assumption of the wave theory of light where the energy is independent of the wavelength and proportional to the square of the amplitude.
Planck created an equation that related the energy density of a given wavelength to the temperature of the black
body radiator. That equation, as follows, exactly fit the
experimental data at the time and also fits the observational
data currently being obtained for the cosmic microwave
background radiation, which is a remnant of the incandescence of the universe that occurred shortly after the big
bang (Figure 11-6). Planck’s radiation law is:
Diagram of the apparatus used to measure the photoelec-
shorter wavelength light was less than the probability of
radiating longer wavelength light. Planck proposed that an
increase in the temperature increased the probability that
short wavelength light would be radiated.
In order for the probability of radiation to be wavelength-dependent, Planck had to unwillingly assume that
the energy did not flow continuously but was emitted in
discrete quantities. This required using sums rather than
integrals to account for all the wavelengths of the spectrum
and gave a solution in the form of 1(exp[x]-1) instead of
Notice that this equation is similar to Wein’s except that
[1(exp(hcλkT) 1)] replaces [1exp(c2λT)] and Wein’s
constants are replaced with the fundamental constants, h, c,
and k. Wein’s c1 became 8πhc and Wein’s c2 became hc/k.
Planck’s radiation law, which accounts for the whole black
body spectrum, reduces to the Rayleigh-Jean radiation law
for long wavelengths, and to Wien’s radiation law for short
wavelengths (Richtmyer, 1928; Richtmyer and Kennard,
1942, 1947; Richtmyer et al., 1955, 1969; Ter Haar, 1967).
The energy density can be converted into intensity in
J m2 s1 by multiplying the energy density by c/4.
Planck solved the problem of black body radiation by
introducing quantization and assuming that the emitted
energy was inversely proportional to wavelength. This really
interested Albert Einstein since it implied that light itself
was both particulate and wave-like. Einstein (1905a) proposed that not only is light emitted in quanta but also it is
absorbed in quanta and travels in quanta that have energies
equal to hc/ λ. Einstein (1905a) asserted that this dual nature
of light, which really goes back to Newton and Huygens,
would be useful in understanding fluorescence. He also
showed that the relationship between energy and wavelength was useful in understanding the photoelectric effect,
which recently had been discovered by Heinrich Hertz and
elucidated by Philipp Lenard in 1902 (Figure 11-7).
The photoelectric effect is the phenomenon where light
causes the release of electrons from the surface of metals.
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Light and Video Microscopy
Although the classical theory predicted that the kinetic
energy (½ mv2) of the released electrons should be proportional to the square of the amplitude of the incident light,
Lenard found that the kinetic energy of electrons did not
depend on the intensity (amplitude squared) of the incident light, but depended on its wavelength (Figure 11-8).
Moreover, there was a threshold wavelength above which
electrons were not ejected. At the threshold wavelength,
electrons were ejected but virtually without any kinetic
energy. As the light intensity increased more electrons
were released but they had virtually no kinetic energy.
The kinetic energy could be increased only by decreasing
the wavelength of the light. As long as the wavelength was
below the threshold, there was an immediate release of photoelectrons no matter how low the intensity of the light was
(Serway et al., 2005).
If the wavelength of the incident light is short enough,
the quantum of light has enough energy to overcome the
electromagnetic binding forces that keep the electron in the
metal. This amount of energy is known as the work function (w, in J) of the metal. If the wavelength is too long, the
quantum does not have enough energy to overcome the work
function. So no matter how many quanta arrive at the metal
at one time, no electrons will be ejected unless the wavelength is short enough. Einstein suggested the following formula to explain the relationship between the kinetic energy
(KE, in J) of the photoelectron and the wavelength of light:
KE ½ mv2 hc/ w
Lenard measured the kinetic energy of the electron by
making the electrical potential (V, in volts) of the collector plate more and more negative until the photoelectrons
from the metallic emitter no long had enough energy to
overcome the potential energy barrier created by the electric field. The kinetic energy was obtained by equating
KE to eV, where e is the elementary charge of an electron (1.6 1019 C). Robert Millikan (1917, 1924, 1935;
Kargon, 1982) used this relationship to determine the value
of Planck’s constant.
Einstein (1917) stressed that particles of light have
momentum equal to h/λ, and soon afterward, Arthur
Compton (1929a, 1929b) observed that the wavelength of
light scattered from electrons increased in a manner we
would predict if light were composed of particles with
energy (E ω hν) and momentum (p k hλ). The
change of the wavelength upon scattering is known as the
Compton Effect. Compton’s experiment provided what was
considered experimental proof for the existence of the particulate nature of light. Quanta are now known as photons,
a name proposed by Gilbert Lewis. Interesting enough,
Lewis (1926a, 1926b) gave the name photon to something
that was not quite light itself. Lewis (1926b) took “the liberty of proposing for this hypothetical new atom, which
is not light but plays an essential part in every process of
radiation, the name photon.” Could he actually have given
that name to the light-ether relation? Eventually, the ether
could no longer be reconciled with the theory of special relativity and a photon came to be synonymous with
a mathematical point of light. Lorentz (1924) argued that
the photon had lost its spatial extension that gave light its
wave-like properties.
Louis de Broglie (1922, 1924) and S. N. Bose (1924)
independently realized that there was a logical inconsistency in the derivation of Planck’s radiation law in that
assumptions based on classical wave hypotheses, such
as the number of degrees of freedom of the ether, were
required to obtain the temperature-independent prefactor in
Planck’s quantum radiation law. De Broglie and Bose then
worked out a strictly quantum derivation by characterizing
the momentum of photons using a six-dimensional phase
space. They assumed that the total number of cells in the
phase space was equal to the number of possible ways of
placing a quantum of light in the phase volume and then
multiplied the answer by two since there were two azimuths
of polarization. By doing so they obtained the prefactor of
Planck’s radiation law. The prefactor can also be derived in
the following reasonable, although nontraditional way.
A photon is moving through a vacuum at velocity c, has
an equivalent mass (m) equal to hcλ, which is obtained by
equating the photon’s relativistic mass-energy to its light
energy (mc2 hcλ). Once the photon’s equivalent mass is
established, it is possible to combine classical and quantum theory to extend the mechanical idea of a photon and
determine its radius (r) from its angular momentum (L).
According to quantum mechanics, the angular momentum of all photons is (h2π) and according to classical
physics, the angular momentum is equal to mvr, where m
is the mass of a particle, v is its angular velocity, and r is its
radius. Since v ωr, then mωr2. Substituting 2π(cλ)
for m, we get r 1k, since k ωc 2πλ. That means
that the radius of a photon is equal to the inverse of its
angular wave number or its wavelength divided by 2π.
As mentioned in Chapters 3 and 8, the phenomena of
diffraction and interference suggest that light has a wave
width as well as a wavelength. Given the radius of the
photon given earlier, the cross-section of a photon would
be π(λ2π)2. If the photon oscillated longitudinally with
a length between 0 and λ (see Appendix II), the average
length of a photon would be λ2, and the average volume
(Vλ) of a photon with wavelength λ would be:
V π( 2π)2 2 3 /8π
The reciprocal volume of a photon would be:
1/V 8π3
The energy density of a photon with an energy of hc/λ
would be 8πhc/λ4 and the energy density per given wavelength would be 8πhcλ5. According to this calculation, for
189
V 6.22 105 m/s
700 nm
V 2.96 105 m/s
550 nm
e
400 nm
e
v 0 m/s
Metal
FIGURE 11-8 In the photoelectric effect, the kinetic energy of the emitted electron is a function of the frequency of the incident light.
a given energy in a black body cavity, the prefactor represents how many photons of a given wavelength can fit into
the volume of the cavity. The greater the temperature in the
cavity, the greater the number of photons that are created,
the smaller the volume of those photons, and the greater
the energy density. Assuming that the radiant energy density per unit wavelength distributed within a black body
cavity is quantized into photons with a real volume, and
assuming the probability of producing those photons is
[1(exp(hcλkT) 1)], the energy density per unit wavelength of the cavity would be:
e (8πhc/ 5 )[1/(exp(hc/ kT) 1)]
which is the Planck radiation law.
In the early years of the quantum theory, many physicists
proposed models of the structure and properties of the photon, yet the photon still remains an enigma (Lamb, 1995),
being considered alternately as a mathematical point and an
infinite plane wave. Some models propose that the photon is
not an elementary particle, but a compound structure composed of two complementary elementary particles (Bragg,
1907a, 1907b, 1907c, 1911; Bragg and Madsen, 1908; de
Broglie, 1924, 1932a, 1932b, 1932c, 1933, 1934a, 1934b,
1934c, 1946; Jordan, 1928, 1935, 1936a, 1936b, 1936c;
Jordan and de L. Kronig, 1936; de Broglie and Winter, 1934;
Born and Nagendra Nath, 1936a, 1936b; Nagendra Nath,
1936; de L. Kronig, 1935a, 1935b, 1935c; Dvoeglazov, 1999;
Valamov, 2002; Appendix II). Currently, the most complete
description of the interaction with light and matter is given
by the theory of quantum electrodynamics (Feynman, 1988).
When the light emitted by an excited atom is passed
through a prism or a diffraction grating, the light is split
into a series of discrete bands known as a line spectrum
(Figure 11-8; Nernst, 1923; Sommerfeld, 1923; Pauling and
Goudsmit, 1930; Herzberg, 1944; Hund, 1974; Bohm,1979).
In 1885 Balmer came up with a formula that fit the observed
wavelengths of light emitted from hydrogen (656.210,
486.074, 434.01, and 410.12 nm). His formula, in modern
notation, is:
1/ R[1/n f 2 1/n i 2 ]
where ni stands for an integer that represents the initial position, nf stands for an integer that represents the final position,
Absorption
Fluorescence
Intensity of absorption or fluorescence
Chapter | 11 Fluorescence Microscopy
Absorption
Fluorescence
Wavelength
FIGURE 11-9 Energy diagram of a fluorescent molecule. The absorption and fluorescent emission spectrum of the molecule are shown on the
right.
and R is the Rydberg constant (1.0973732 107 m1). By
applying Planck’s quantization ideas to the quantization of
angular momentum of electrons in orbitals, Einstein’s concept of the photoelectric effect, in which the energy of a photon is related to the binding energy of an electron, and select
principles of classical mechanics, Niels Bohr (1913) derived
Balmer’s formula, replacing the empirical Rydberg constant
with fundamental constants:
1/ (m e e 4 )/(8εο 2 h3 c) [1/n f 2 1/n i 2 ]
where e is the elementary charge (1.6 1019 C), me is the
mass of an electron (9.1 1031 kg), o is the electrical
permittivity of a vacuum (8.85 1012 F/m), h is Planck’s
constant, and c is the speed of light (3 108 m/s).
Atomic absorption results in the transfer of an electron from a low energy ground state (ni) to a higher energy
excited state (nf ni) in a process that takes about one
period of light vibration (1015 s). The negative value of
1/λ indicates that energy is added to the atom in the form of
a photon. Emission occurs when an electron falls from the
excited state (ni) to the ground state (nf ni). The absorption spectrum and the emission spectrum of a gaseous
atom are identical. The wavelength of emitted light gives
a signature of the energy differences between electrons in
the ground and excited states (Figure 11-9).
hc/[E m E ground ]
The emitted wavelength depends on the energy difference
between the excited state and the ground state according to
the following formula:
E excited E ground kc ω hν hc/ When gaseous atoms are combined together into gaseous
molecules, the electrons are shared between nuclei of different atoms and form molecular orbitals. The nuclei that
share an electron can vibrate and rotate relative to each
other. Consequently, complex molecules have many vibrational and rotational states and form band spectra instead
of line spectra. Gaseous atoms give relatively clean spectra
190
that correspond to transitions in the ultraviolet and visible
region, and gaseous molecules give relatively clean band
spectra that correspond to transitions that correspond to
ultraviolet, visible, and infrared wavelengths. The spectra
of liquids or solids, on the other hand, become broadened
because a range of transition energies result from the interactions between molecules. The various lines and bands
become overlapping and the spectrum appears as a continuous spectrum. In solids, the spectrum appears as a continuous band as described by Planck’s radiation law.
A flexible molecule has many vibrational states and
rotational states (Figure 11-9). Consequently, the excited
state of a flexible molecule can dissipate energy in a variety of ways, which takes 1015 to 109 s. Initially, the
electronic energy can be conserved within the molecule,
in a process known as internal conversion or radiationless
transfer, where the electronic energy is converted to kinetic
energy, which accompanies the vibrational and rotational
movement of the molecule. Eventually, the kinetic energy
is completely lost to the surround through collisions or as
thermal energy with wavelengths of 2.5 – 100 106 m
for each vibrational transition and wavelengths of
50 350 106 m for each rotational transition.
Once an electron reaches the lowest vibrational or rotational level of the excited state, it can return to the ground
state only by emitting a photon in a process known as fluorescence, which takes about 108 s. Because some of the
original radiant energy is converted to kinetic energy, the
wavelength of the emitted photon is greater than the wavelength of the absorbed photon. This is the reason behind
Stokes’ Law and the basis for fluorescence microscopy.
The ratio between the number of photons absorbed
and the number of photons emitted by fluorescence is called
the fluorescence quantum yield (QFL). The fluorescence
quantum yield ranges between 0 and 1, and depends on the
chemical nature of the fluorescing molecule, fluorophore
or fluorochrome, the excitation wavelength, and other factors, including pH, temperature, hydrophobicity, and viscosity. The greater the fluorescence quantum yield, the
better the dye is for fluorescence microscopy.
The fluorescence quantum yield can be decreased by
quenching or photobleaching. Quenching is the decrease
in fluorescence as a result of the transfer of energy from
the excited state to the ground state through a radiationless pathway between molecules. This occurs when the
excitation and emission peaks overlap, and the fluorescent
light given off by one molecule is reabsorbed by another.
Bleaching results from the destruction of the molecule
directly by light or though the light-induced production of
free radicals. Bleaching can be minimized by adding antifade agents like propylgallate, (0.05%) phenylenediamine,
or (0.05%) other antioxidants, including ascorbic acid to
the preparation.
Understanding the physics of fluorescence helps in the
design of fluorescent dyes that are both selective and bright
Light and Video Microscopy
as well as high resolution fluorescence microscopes that
introduce enough contrast to allow the detection of a single
fluorescing molecule.
DESIGN OF A FLUORESCENCE
MICROSCOPE
In 1903, Siedentopf and Zsigmondy (1903) developed
the ultraviolet microscope in order to “beat” the limit of
resolution set by visible light and visualize colloidal particles (Siedentopf, 1903; Cahan, 1996). In 1911, Heinrich
Lehmann and Stanislaus von Prowazek used this as the
basis for the first fluorescence microscope (Rost, 1995).
The first obstacle to overcome in developing a fluorescence microscope was to find a light source that was intense
enough in the ultraviolet range. Initially carbon arcs were
used, but they were replaced with mercury vapor lamps,
xenon lamps, and lasers. In a fluorescence microscope, the
excitation light is passed through an excitation filter that
should match the excitation spectrum of the fluorochrome.
The excitation filter can be a colored absorption filter,
which passes the light that is not absorbed by the dyes in
the filter or an interference filter, which passes the wavelengths that constructively interfere and reflect the ones
that destructively interfere.
There are three methods of illuminating the specimen
found in fluorescence microscopes (Figure 11-10): (1) the
bright-field method, which was originally made by Zeiss in
1911; (2) the dark-field method, which was originally made
by Reichert in 1911; and (3) the reflected light method,
which was first made commercially by Zeiss around 1930.
The bright-field fluorescence microscope does not block
enough of the excitation light, so the image contrast is
low. The contrast can be increased by using a dark-field
type of sub-stage condenser, but the numerical aperture of
the objective must be reduced, thus limiting resolution. The
reflected light or epi-illumination fluorescence microscope
permits high contrast and high resolution without compromise (Ploem and Tanke, 1987; Oldfield, 1994).
Since fluorescent light is often extremely weak compared to the excitation light, a good fluorescence microscope must filter out the excitation light completely in
order to distinguish the fluorescent light. This is relatively
easy since the wavelengths of fluorescent light are typically
longer than the excitation wavelengths, as described earlier.
In epi-fluorescence microscopes, the light filtering is done
by a chromatic (or dichromatic) beam splitter and a barrier
filter. The chromatic beam splitter works on the principle
of constructive and destructive interference. The chromatic
beam splitter is a typical interference filter tipped at a
45-degree angle. At this angle, 90 percent of the light with
wavelengths shorter than a certain value is reflected and
10 percent is transmitted. Similarly, 90 percent of the fluorescent light, which is longer than the cut off is transmitted
191
Chapter | 11 Fluorescence Microscopy
A
B
Eye
Eye
Emission light
Emission light
Barrier filter
Barrier filter
Objective
Objective
Mixture of excitation
and emission light
Specimen
Specimen
Sub-stage
dark-field
condenser
Sub-stage
condenser
Excitation light
Excitation filter
Excitation light
Excitation filter
Darkfield type
Brightfield type
C
Eye
Emission light
Barrier filter
Excitation
Blue light
Light
Red
Excitation
filter
Blue
Blue
Red
Chromatic beam
splitter
Objective
Reflected-light type
FIGURE 11-10
Specimen
Diagrams of bright-field (A), dark-field (B), and reflected light (C) fluorescence microscopes.
through toward the ocular, and 10 percent is reflected back
to the light source. Because of this property, a chromatic
beam splitter is more efficient than a standard half-silvered
mirror (Mellors and Silver, 1951; Ploem, 1967). Figure
11-11 is a ray diagram that shows the aperture and field
planes in an epi-fluorescence microscope.
The fluorescent light that passes through the chromatic
beam splitter is then filtered again by a barrier filter that
further removes the excitation light. This filter can be a
long pass filter, a wide bandpass, or a narrow bandpass
interference filter. The more selective the filter, the dimmer the image will be. Consequently, we must select filters
with bandwidths based on the tradeoff between brightness
and selectivity.
The original fluorescence microscopes used ultraviolet
light for excitation and these microscopes required fluorite
objectives. However, ultraviolet photons are energetic and
are often deadly to cells. Consequently, dyes, whose excitation spectrum falls in the visible range, have been developed,
making high numerical aperture apochromatic objective
lenses more desirable. Moreover, the numerical aperture
of the objective lens is especially important in the epiillumination mode, since the objective lens is used both as
the condenser and the objective, and the brightness of the
image depends on the fourth power of the numerical aperture divided by the square of the magnification.
Mary Osborn and Klaus Weber (1982) have developed a
unique technique to make stereo pairs of immunofluorescence
192
Light and Video Microscopy
Intermediate
image plane
Aperture
diaphragm
Tube lens
Field
diaphragm
Barrier filter
Chromatic
beam
splitter
Condenser
Excitation
filter
Objective
Specimen
FIGURE 11-11 Ray diagram of a reflected light fluorescence microscope showing the conjugate aperture and field planes.
micrographs that combines oblique illumination with epifluorescence. It requires a commercially available Zeiss
intermediate ring that is used to increase the tube length
for a given objective. It is inserted between the objective
and the nosepiece. It also requires a stereo insert, which
can be constructed by you by welding a half moon diaphragm into a Zeiss differential interference contrast slider.
Put the slider into the intermediate ring so it covers half
the field in the rear of the objective at a time. In this way
the specimen is illuminated with oblique illumination and
only half the diffraction orders are collected to make the
image. After photographing the specimen with the moon
in one position, the half moon is put in the opposite position and the specimen is photographed again. Rotate the
two micrographs by 90 degrees and then mount them side
by side. When viewed with a 2x stereo viewer, they give a
three-dimensional image.
FLUORESCENCE PROBES
Many cells have native molecules that are fluorescent. For
example, chlorophyll fluorescence can be used to study
the development of fern spores (Scheuerlein et al., 1988)
and lignin fluorescence can be used to study the formation of secondary walls. However, the real effectiveness of
the fluorescence microscope in understanding the dynamics of cell structure and function is due in large part to the
development of sensitive and selective artificial dyes, in
the form of free molecules or a quantum dots (Taylor et al.,
1992; Tsien et al., 2006).
With bio-organic chemists developing dyes with engineered properties that relate to fluorescence and binding,
the sky is almost the limit in finding a dye that will perform a desired function. Fluorescent dyes that accumulate
only in living cells have been developed as a quick way of
determining cell viability. Other fluorescent dyes are able
to selectively stain certain cell organelles and cytoplasmic fibers (Haigler et al., 1980; Morikawa and Yanagida,
1981; Wick et al., 1981; Wolniak et al., 1981; Wang et al.,
1982; Terasaki et al., 1984, 1986; Pagano and Sleight, 1985;
Parthasarathy, 1985; Parthasarathy et al., 1985; Upsky and
Pagano, 1985; Matzke and Matzke, 1986; Lloyd, 1987; Wu,
1987; Pagano, 1988, 1989; Chen, 1989; Mitchison, 1989;
Pringle et al., 1989; Quader et al., 1989; Terasaki, 1989;
Wang, 1989; McCauley and Hepler, 1990; Zhang et al.,
1990). Dyes, whose fluorescent excitation spectra, emission spectra, and/or quantum yield depend on their local
environment, have also been developed to measure viscosity, hydrophobicity, membrane potentials, pH, Ca2, Cl,
Na, K, or Mg2, and such (Saunders and Hepler, 1981;
Grotha, 1983; Liu et al., 1987). High molecular mass fluorescent probes can be used to measure permeability (LubyPhelps et al., 1986, 1988; Luby-Phelps, 1989; Hiramoto and
Kaneda, 1988). Even higher molecular mass dyes that are
unable to permeate the plasma membrane have been used as
an assay for endocytosis (Ginzburg et al., 1999). Enzymatic
substrates that are conjugated to dyes that become fluorescent only after an enzyme acts on the substrate can be used
to visualize enzymatic reactions in the cell.
Many marine organisms, including the jellyfish
(Aquorea victoria), the anemone (Discosoma striata), and
the anthrozoans (Entacmaea quadricolor and Anemonia
majano) are luminescent, in part because they contain proteins that fluoresce (Harvey, 1920, 1940; Barenboim et al.,
1969; Morise et al., 1974; Prendergast and Mann, 1978;
Zimmer, 2005; Pieribone and Gruber, 2006). The gene
sequences that code the fluorescent proteins have been
cloned (Prasher et al., 1992). The DNA sequence for the
fluorescent protein can be inserted into a gene of interest
so that the engineered gene produces a fluorescent chimerical protein. In this way the dynamics of the chimerical protein, which hopefully represents the dynamics of the native
protein, can be visualized in a fluorescence microscope
(Chalfie et al., 1994). Originally only green fluorescent
protein from the jellyfish was used, but now many colored
proteins having emission spectra that span the visible spectrum have been isolated and varied by mutagenesis (Shaner
et al., 2005). This makes it possible for cells to express
many fluorescent proteins at a time. Genetically targetable
fluorescent proteins can be used to measure intracellular
calcium (Palmer and Tsien, 2006). Again, the sky is the
limit (Tsien, 2003, 2005; Giepmans et al., 2006)!
Quantum dots are semiconductors made out of siliconor carbon-based crystals that are 2 to 10 nm in diameter
and are composed of 100 to 100,000 atoms. Quantum dots
are almost like artificial “designer” atoms with electrons
confined to specific orbitals whose sizes depend on the
size of the quantum dots (Reed, 1993). The more an electron is confined in a space like an atom or a quantum dot,
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Chapter | 11 Fluorescence Microscopy
the higher its energy is. When an excited confined electron
returns to the ground state, it gives off light whose color
and energy are determined by the size of the quantum dot.
Quantum dots can be targeted to specific protein in the cell
to localize those proteins (Howarth et al., 2005).
PITFALLS AND CURES IN FLUORESCENCE
MICROSCOPY
When doing fluorescence microscopy, it is important
always to test for autofluorescence under the same conditions you use to observe an introduced fluorochrome. This
control lets you make the claim that the observed fluorescence is due to the added fluorochrome. Moreover, since
fluorescence microscopy often requires an intense light
source, molecules in the cell can be altered, and this may
alter the autofluorescence in a time-dependent manner.
We can minimize autofluorescence problems by using
more selective excitation and/or barrier filters or by using
a dye that fluoresces in a different region of the spectrum
than the autofluorescent molecules. Autofluorescence is
not always a problem. van Spronsen et al. (1989) used the
autofluorescence of chlorophyll to image the structure of
the grana in living chloroplasts.
Richard Williamson (1991) pointed out a very interesting and important point when it comes to resolution in the
fluorescence microscope. We can localize proteins that are
smaller than the limit of resolution, but resolving where
they are and how they are arranged is still limited by diffraction. For example, using antibodies or green fluorescent
protein, we can fluorescently stain microtubules that are
normally 24 nm in diameter. The image is inflated through
diffraction to the limit of resolution of the lens, which is
about 200 nm.That is, if two microtubules in reality are
about 100 nm apart (4 diameters), they will appear as one
microtubule. Therefore, unconnected microtubules may
appear as branched microtubules, or overlapping microtubules may appear as one very long one. So fluorescence
allows the detection but not resolution of 24 nm microtubules. We need an electron microscope to resolve them.
The image in a fluorescence microscope is often dim.
This can be rectified by using a brighter lens with a higher
numerical aperture and/or a lower magnification. It may be
rectified by using a fluorite lens, if we are using ultraviolet
excitation. The dimness problem can also be rectified by
using lasers in a confocal microscope (see Chapter 12) and/or
a more sensitive digital imaging system (see Chapter 13).
If photographic images are underexposed, set the exposure
meter in the camera to the setting that is appropriate to photograph scattered bright objects in a dark field (see Chapter 5).
Quenching of the dye can be remedied by decreasing
the dye concentration, and bleaching of the dye can be
minimized by using antifade agents.
If there is too much background light, reduce the dye
concentration or focus the excitation light for critical illumination by focusing the arc at the level of the specimen. If traditional methods fail, use confocal microscopy (see Chapter 12)
and/or digital image processing (see Chapter 14).
WEB RESOURCES
Fluorescent Microscopy
Molecular Expressions web site: http://micro.magnet.fsu.edu/primer/
techniques/fluorescence/fluorhome.html
Nikon Microscopy U: http://www.microscopyu.com/articles/fluorescence/
fluorescenceintro.html
Olympus Microscopy Resource Center: http://www.olympusmicro.com/
primer/techniques/fluorescence/fluorhome.html
Leica Microsystems: http://www.fluorescence-microscopy.com
Fluorescent Dyes
Tsien Laboratory: http://www.tsienlab.ucsd.edu/Default.html
Invitrogen: http://www.probes.comwww.probes.com
Fluorophores.org: http://www.fluorophores.org
Green Fluorescent Protein Applications Page: http://www.yale.edu/
rosenbaum/gfp_gateway.html
Fluorescence Microscopy and Fluorophores: http://www.micro-scope.de/
fluoro.html
Interference Filters
Semrock: http://www.semrock.com/Catalog/BrightlineCatalog.html
Omega Optical: http://www.omegafilters.com
Chroma: http://www.chroma.com
Zeiss: http://www.micro-shop.zeiss.com/us/us_en/spektral.php?cp_sid&fdb
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Chapter 12
Various Types of Microscopes
and Accessories
Microscopes have allowed us to peer into the world of
small things and also have allowed us to see the microscopic building blocks of the macroscopic world. In this
chapter, I describe how optical microscopes can be combined with lasers and centrifuges to study better the microscopic nature of the world. I will describe how other
electromagnetic waves from X-rays through radio waves
can be used to probe the structure of biological specimens.
I will also describe how the Fresnel diffraction pattern, as
opposed to the Fraunhöfer diffraction pattern, can be captured to form a high resolution image that beats Abbe’s diffraction limit. I will also describe how longitudinal sound
waves can be used in an acoustic microscope to image the
viscoelastic properties of biological specimens. I will close
by describing microscope accessories that help us study
the microscopic world. The descriptions of these techniques are cursory, by necessity because my experience is
limited. Even though this chapter borders on the limits of
my knowledge, I present this information to my students to
give them an idea of the unlimited potential of microscopy
in forming a variety of images, each of which captures a
different aspect of the reality of the specimen.
CONFOCAL MICROSCOPES
The first confocal microscope was invented and built by
Marvin Minsky (1988) in 1955. Minsky was interested in
taking a “top-down” approach to understand the brain, but
when he looked at the whole brain, he saw nothing:
And here was a critical obstacle: the tissue of the central nervous system is solidly packed with interwoven parts of cells.
Consequently, if you succeed in staining all of them, you simply can’t see anything. This is not merely a problem of opacity
because, if you put enough light in, some will come out. The
serious problem is scattering. Unless you can confine each view
to a thin enough plane, nothing comes out but a meaningless
blur. Too little signal compared to the noise: the problem kept
frustrating me.
Minsky had a chance to overcome this problem as a Junior
Fellow at Harvard:
This freedom was just what I needed then because I was making
a change in course. With the instruments of the time so weak,
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
there seemed little chance to understand brains, at least at the
microscopic level. So, during those years I began to imagine
another approach…. In the course of time, that new top down
approach did indeed become productive; it soon assumed the fanciful name, Artificial Intelligence…. Artificial Intelligence could
be tackled straight away—but my ideas about doing this were
not yet quite mature enough. So (it seems to me in retrospect)
while those ideas were incubating I had to keep my hands busy
and solving that problem of scattered light became my conscious
obsession. Edward Purcell … obtained for me a workroom in
the Lyman laboratory of Physics…. (That room had once been
Theodore Lyman’s office. Under an old sheet of shelf paper
I found a bit of diffraction grating that had likely been ruled, I was
awed to think, by the master spectroscopist himself.) One day it
occurred to me that the way to avoid all that scattered light was
to never allow any unnecessary light to enter in the first place. An
ideal microscope would examine each point of the specimen and
measure the amount of light scattered or absorbed by that point.
But if we try to make many such measurements at the same time
then every focal image point will be clouded by aberrant rays of
scattered light deflected [by] points of the specimen that are not
the point you’re looking at. Most of those extra rays would be
gone if we could illuminate only one specimen point at a time.
There is no way to eliminate every possible such ray, because of
multiple scattering, but it is easy to remove all rays not initially
aimed at the focal point; just use a second microscope … to
image a pinhole aperture on a single point of the specimen. This
reduces the amount of light in the specimen by orders of magnitude without reducing the focal brightness at all. Still, some
of the initially focused light will be scattered by out-of-focus
specimen points onto other points in the image plane. But we can
reject those rays, as well, by placing a second pinhole aperture
in the image plane that lies beyond the exit side of the objective lens. We end up with an elegant, symmetrical geometry: a
pinhole and an objective lens on each side of the specimen. (We
could also employ a reflected light scheme by placing a single
lens and pinhole on only one side of the specimen-and using a
half-silvered mirror to separate the entering and exiting rays.)
In the 30 years in which confocal microscopes have
been produced commercially, microscopists all over the
world have continued blazing the trail initiated by Minsky
by using their knowledge of the physical nature of light to
increase the resolving power and application of the confocal microscope (Shack et al., 1979; Hall et al., 1991; Denk
et al., 1990; Pawley, 1990; Wilson, 1990; Hell et al., 1994).
The ability to illuminate a single point on the specimen
with sufficient intensity was facilitated by the introduction
of lasers as illuminating sources for microscopes. Lasers
provide high intensity, coherent, monochromatic light. The
195
196
laser light in a confocal microscope, in contrast to a widefield microscope set up with Köhler illumination, is focused
on the specimen or field plane as opposed to the aperture or
Fourier plane. In this way, the illumination used in confocal
microscopes is similar to critical illumination (see Chapter 4).
However, in confocal microscopes, only a tiny region of the
specimen, close to the limit of resolution, is illuminated at
a given time. In a wide-field microscope with either Köhler
or critical illumination, all points in all the parts and levels
of a specimen are simultaneously illuminated so that each
point gives off light that obscures the neighboring details,
but in confocal microscopes, the obscuring light is rejected
in the formation of each image point. This characteristic of
confocal microscopes is particularly important when viewing thick specimens. Images taken with a confocal microscope seem to be perfectly thin optical sections (Jovin and
Arndt-Jovin, 1989). A series of images taken at different
axial levels can be combined by a digital image processor
to reconstruct a true three-dimensional image.
The term confocal relates to the fact the plane containing the illumination pinhole, the plane containing the specimen, and the plane containing the detector pinhole are all
conjugate planes (Figure 12-1). Consequently, the image
of the illumination pinhole is in focus at the specimen
plane and at the detector plane. Although confocal microscopes can be used in the transmission mode, usually they
are used in the reflected light mode. Moreover, any kind
of microscopy can be done with a confocal microscope,
but in practice, confocal microscopes typically are used for
fluorescence microscopy. Using a confocal microscope to
do fluorescence microscopy is so widely used because the
pinhole eliminates much of the out-of-focus fluorescence
that reduces the contrast in the image (Figure 12-2).
In a confocal scanning fluorescence microscope, light
from a laser passes through a pinhole, which is at the front
focal plane of a converging lens. Axial light emerges from
the lens and is reflected by a chromatic beam splitter
through the objective lens to irradiate a point in the specimen, which is placed at the focus of the objective lens. The
fluorescent light that is emitted from that point passes back
through the objective lens as parallel light. It then passes
straight through the chromatic beam splitter and through a
barrier filter. After leaving the barrier filter, the light passes
through a projection lens where it is focused on a pinhole
adjacent to the light sensitive region of a photomultiplier
tube. The output voltage of the photomultiplier tube then is
digitized and stored in a computer memory along with the
x,y,z coordinates of the specimen point.
The image is created point by point from the scanned
object, and the scan can be accomplished in two general
ways. Either the specimen can be moved through the
beam, as was done in Minsky’s original confocal microscope, or the beam can be moved over the specimen. Either
way, the x,y,z coordinates of the specimen point have to be
stored along with the intensity information. The specimen
Light and Video Microscopy
Object stage
Mechanical scan control
Objective
lens
Illumination
pinhole
Chromatic
beam splitter
Laser
Projection
lens
Computer
Detector
pinhole
Monochromator
Photomultiplier
detector
Computer
display
FIGURE 12-1 Diagram of a confocal microscope showing the conjugate field planes.
Detector
Detector
pinhole
Projection
lens
Laser
Chromatic
beam splitter
Illumination
pinhole
Scanning unit
Objective
In focus
Out-of-focus
Object
FIGURE 12-2 In a confocal microscope, the out-of-focus fluorescence
is blocked by the pinhole.
is moved through the beam by stepper motors connected
to the stage with a reliability of 10 to 20 nm, about onetenth of the expected optical resolution. The advantage of
moving the specimen is that the excitation and fluorescent
light is propagated on-axis through the objective lens and
light going to and coming from each point in the specimen
experiences the same optical conditions (Brakenhoff et al.,
1989). Moreover, the field of view in an on-axis confocal
microscope is limited only by the mechanical scanning
197
Chapter | 12 Various Types of Microscopes and Accessories
hv
hv
hv
Fluorescence
S
S*
two-photon
absorption
hv
Thermal
decay
Fluorescence
one-photon
absorption
S*
hv
S
FIGURE 12-3 Energy diagram illustrating one- and two-photon
absorption.
distance of the stage. The disadvantage of a moving stage
is that the stage must be moved relatively slowly in order
not to deform the specimen. The slow movement limits the
ability of a moving stage confocal microscope to follow
rapid cellular processes at high resolution.
It has proved difficult to keep the specimen stationary
and move the optical system so that rapid on-axis imaging can be accomplished without deforming the specimen.
Consequently, most manufacturers build confocal microscopes that scan the specimen by moving the light spot
using a series of moving mirrors, or slits in a rotating disk.
This is known as off-axis imaging. In off-axis imaging, the
incident and fluorescent light going to and coming from
each point in the specimen experiences a different optical path. Moreover, the size of the field is limited by the
objective lens. The advantages of off-axis imaging are that
it allows fast acquisition times and does not deform the
specimen.
Denk et al. (1990) developed a two-photon confocal
laser scanning fluorescence microscope that uses a colliding-pulse, mode-locked dye laser that produces a stream of
pulses that have a duration of 100 fs and a repetition rate
of 80 MHz. With this laser, it is possible to pump photons
into a molecule so quickly that a molecule will absorb two
long wavelength photons nearly simultaneously, thus providing an electron with the equivalent energy of a single
short wavelength photon (Figure 12-3). The idea for the
two-photon confocal microscope came from knowledge
of studies on two-photon absorption in photosynthesis
(Shreve et al., 1990).
The two photon excitation technique has many advantages. The first is that the ability to optically section is
improved because two photons must be captured nearly
simultaneously in order to excite the fluorochrome. This
means that the probability of fluorescence emission is
proportional to the square of the excitation light intensity
instead of the intensity itself. In general, the probability of
emission is given by the following equation:
probability of emission ΦF1 (excitation intensity)n
where ΦFl is the fluorescent quantum yield, and n is the
number of photons needed to excite the molecule. The
intensity of the laser is set so that the only plane where
the intensity is great enough to excite the fluorochrome is
at the very focus of the laser beam, thus minimizing any
One-photon confocal microscope
Two-photon confocal microscope
FIGURE 12-4 Diagrams illustrating the depths to which a one- and
two-photon confocal microscope excites a specimen. In the two-photon
microscope there are only enough photons to excite the fluorochrome
at the x.
out-of-focus images that would lower the contrast and
obscure the image (Figure 12-4). The tight focusing of the
excitation light can be seen in experiments set up to bleach
dyes. The area bleached by a typical one-photon confocal
microscope is enormous compared to the area bleached by
a two-photon confocal microscope. Another advantage of
the two- or multiphoton excitation process is that the multiphoton excitation spectra of dyes are wider than they are
for dyes excited by single photons (Xu and Webb, 1996).
This makes it possible to excite a number of fluorochromes
at the same time with the same infrared laser.
Interestingly, in a multiphoton confocal microscope, the
light used to excite the fluorochromes has a longer wavelength than the emission light, and consequently, a chromatic beam splitter that reflects long wavelength light and
transmits short wavelength light must be used.
The resolving power of the confocal microscope is
being improved by a technique known as stimulated emission depletion microscopy (STED). Stimulated emission
depletion microscopy reduces the size of the excited region
by following the excitation pulse with a ring-shaped depletion pulse, which surrounds the excitation pulse and is
tuned to the emission wavelength of the dye. The depletion pulse causes most of the electrons except those in the
very center of the excitation pulse to fall from the excited
state to the ground state, giving off fluorescent light by
stimulated emission. Whereas the fluorescence from the
excitation pulse enters the aperture, the stimulated emission is focused as a ring around the aperture, and does not
contribute to the image. In this way, the size of the imaged
spot is decreased and the resolving power of the confocal
microscope is increased (Hell and Wichmann, 1994; Klar
et al., 2000, 2001).
A confocal microscope can be used to image single
molecules interacting with a surface using a technique
known as total internal reflectance fluorescence microscopy (TIRF; Figure 12-5). As a consequence of binding
kinetics, the presence of many molecules is required for
a single molecule to bind to a receptor surface. If the molecules are fluorescent, the fluorescence of the bound molecule
will be overwhelmed by the fluorescence of the free molecules. In order to increase the contrast of bound fluorescent
198
Light and Video Microscopy
Evanescent
wave
θc
Aqueous
medium
S*
S*
Donor
energy
transfer
Glass
microscope
slide
(n 1.518)
hv
hv
Critical
angle
FIGURE 12-5 Diagram of the illumination of a specimen in a total
internal reflection fluorescence microscope.
molecules, the surface of the specimen is placed about
100 nm from the surface of the microscope slide. The
excitation light hits the surface of the slide at the critical
angle so that the light is reflected away from the specimen
by total internal reflection (see Chapter 2). However, if
the fluorescent molecules are close enough to the surface,
the evanescent wave will excite them and they will fluoresce while the free fluorochromes, which are too far from
the surface for the evanescent wave to excite, will remain
in the ground state (Axelrod et al., 1982; Axelrod, 1984,
1990; Tokunaga and Yanagida, 1997). With the contrast
generated, one can visualize proteins translating across a
strand of DNA (Gorman et al., 2007). In order to determine
the axial location of a single molecule, a second reflecting
surface can be introduced so that interference microscopy
can be done with the fluorescent light that comes from a
single molecule. This technique is known as spectral selfinterference fluorescence microscopy (SSFM; Moiseev
et al., 2006).
A confocal microscope can be used to determine the
distance between two interacting molecules by making use
of the fluorescence (or Förster) resonance energy transfer
(FRET) technique (Figure 12-6). With this technique, one
molecule is labeled with a donor fluorochrome and the other
is labeled with an acceptor fluorochrome, and then the sample is irradiated with the excitation wavelength of the donor
fluorochrome and observed at the emission wavelength of
the acceptor fluorochrome. The two fluorochromes, which
are typically color variants of green fluorescent protein, are
inserted into proteins of interest using genetic engineering
techniques. When the two molecules are within 1 to 10 nm
of each other, energy can be transferred between the donor
fluorochrome and the acceptor fluorochrome and subsequently, the acceptor fluorochrome gives off the excitation
energy absorbed by the donor fluorochrome as fluorescence.
The efficiency of resonance energy transfer is due to a
dipole-dipole interaction that is inversely proportional to the
sixth power of the distance. Consequently, if the two target
molecules are not in close proximity, the excitation energy
is given off as fluorescence from the donor fluorochrome.
Protein conformational changes can also be monitored by
putting the donor and acceptor fluorochromes on the same
protein (Periasamy and Day, 2005).
S
S
Donor
Acceptor
FIGURE 12-6 Energy diagram for fluorescence resonance energy transfer between two fluorochromes.
A confocal microscope can also be used to localize specific genes in chromosomes or chromatin using a technique
known as fluorescent in-situ hybridization (FISH). With
this technique, the gene of interest is stained with a fluorescent probe made from fluorescent nucleotides arranged
in an order that is complementary to the order of nucleosides in the gene of interest (Zhong et al., 1996, 1998;
Jackson et al., 1998). Fluorescent in-situ hybridization can
also be done with a wide-field fluorescence microscope
and often is used in in vitro fertilization clinics for determining which alleles exist in an embryo.
A confocal microscope can be used to measure the
rate of movement of molecules tagged with fluorescent
probes using a technique known as fluorescence recovery
or redistribution after photobleaching (FRAP). With this
technique, the fluorescence in a given area is measured
and then the fluorescent molecules are bleached with an
intense light source so that the fluorescence disappears.
The intense beam is shut off and as fluorescent molecules
from other regions diffuse into the bleached area, the fluorescence recovers. The diffusion coefficient of the moving
molecules can be determined from the rate in which the
fluorescence recovers (Axelrod et al., 1976; Edidin et al.,
1976; Wang, 1985; Baron-Epel et al., 1988; Gorbsky et al.,
1988; Luby-Phelps et al., 1986).
For further information and practical guidance on how
to use a confocal microscope, consult Fundamentals of
Light Microscopy and Electronic Imaging, by Douglas
B. Murphy (2001).
LASER MICROBEAM MICROSCOPE
Lasers also are used in wide-field microscopes to perform
laser microsurgery (Figure 12-7; Aist and Berns, 1981;
Berns et al., 1981, 1991; Koonce et al., 1984; Aist et al.,
1991; Bayles et al., 1993), the principles of which are the
199
Chapter | 12 Various Types of Microscopes and Accessories
Light
Monitor
Light
Light
Light
Image
Processor
n1
TV
-c
am
er
a
n2
Laser 2
Laser 1
FIGURE 12-7 Diagram of a microscope with a laser microbeam and a
laser optical trap.
same as those used in laser surgery of humans (Berns,
1991). In a microscope, the laser light is routed though the
epi-fluorescence port. The laser does selective damage to a
subcellular component in one of three ways:
●
The damage may be due to classical absorption of the
intense, coherent, monochromatic light by natural or added
chromophores with the subsequent generation of heat.
●
The damage may be due to the light stimulated
addition of a chemical, for example, the light stimulated
binding of psoralen to nucleic acids.
●
When the photon density is high enough, heat can
be generated by multiphoton absorption.
A clever and frugal person can do microsurgery using
the ultraviolet light source on an epi-fluorescence microscope (Forer, 1965, 1991; Leslie and Pickett-Heaps, 1983;
Wayne et al., 1990; Forer et al., 1997).
OPTICAL TWEEZERS
Photons have both linear momentum (k h/ λ) and
angular momentum (); (Nichols and Hull, 1903a, 1903b;
Poynting, 1904, 1910; Einstein, 1917; Schrödinger, 1922;
Dirac, 1924; Beth, 1936; Friedberg, 1994; Kleppner, 2004)
and can be used to move or rotate macroscopic objects
(Lebedew, 1901; Nichols and Hull, 1903a, 1903b; Gerlach
and Golsen, 1923), cells, organelles, and proteins (Ashkin
and Dziedzic, 1987, 1989; Ashkin et al., 1987, 1990; Block
et al., 1990; Svoboda and Block, 1994; Neuman and Block,
2004) and even stop atoms (Frisch, 1933; Ashkin, 1970a,
1970b, 1978; Bjorkholm et al., 1975; Chu, 1997; Cohen,
1997; Phillips, 1997; Johnson et al., 2007). By routing the
light from an infrared laser through the epi-fluorescence,
we can add “optical tweezers” to a microscope (Greulich,
1992; Ashkin and Dziedzic, 1987, 1989; Ashkin et al.,
n1
Cell n2
moves
n1
Cell
moves
n2
Cell stays stationary (if intensity is high enough).
FIGURE 12-8 Ray diagrams of light passing through a specimen. The
specimen (n2) recoils as the light passes out of it and into the medium
(n1 where n2 n1).
1987, 1990; Block et al., 1990; La Porta and Wang, 2004;
Moffitt et al., 2006).
The optical tweezers can be used to measure force or
resistance by determining the light intensity (in J m2 s1)
necessary to move a stationary object or to hold a moving
object stationary. The force (in N) exerted on an object can
be determined with the following equation:
F η(light intensity)(area of object)/c
where η is a dimensionless number between 1 for totally
absorbing objects and 2 for totally reflecting objects and c
is the speed of light. Optical tweezers can hold a moving
cell still because the photons that leave the object cause the
object to rebound in the opposite direction consistent with
Newton’s Third Law that states that for every action there
is an equal and opposite reaction (Figure 12-8).
LASER CAPTURE MICRODISSECTION
Laser capture microdissection is a method that allows us
to isolate and capture pure cells and their contents, particularly RNA, from heterogeneous tissue slices under
the microscope (Emmert-Buck et al., 1996; Bonner et al.,
1997; Nakazono et al., 2003; Woll et al., 2005; Cai and
Lashbrook, 2006; Nelson et al., 2006; Spencer et al., 2007;
Zhang et al., 2007). With this technique, a transparent
transfer film is applied to the surface of the tissue section
while the other side is bonded to a cap. The transparent
transfer film is then irradiated with a pulsed infrared laser
beam that is focused through the objective onto the target
cells in the tissue. The special transfer film then melts and
bonds to the targeted cells and consequently, the target cells
and their contents become attached to the cap. The DNA,
RNA, or proteins in the target cells can then be analyzed.
The PALM MicroLaser Systems manufactured by Zeiss
combines laser microbeam microdissection (LMM) and
laser pressure catapulting (LPC) techniques. In this system,
a pulsed ultraviolet laser is focused through an objective to a
beam spot size of less than 1 micrometer in diameter that is
used for cutting the targeted cells out of the tissue. After the
cells are cut out, the targeted cells within the confines of the
cut are ejected out of the object plane and catapulted directly
200
into the cap of a microfuge tube using a single defocused
laser pulse.
Light and Video Microscopy
PMT
Microscope
LASER DOPPLER MICROSCOPE
The laser Doppler microscope is based upon the Doppler
Effect. The Doppler Effect was first noticed by Johann
Christian Doppler (1842) when he posited that the color of
binary stars may be caused by their movement toward or
away from an observer. Following the introduction of the
newly-invented, rapidly-moving steam locomotive, Buijs
Ballot (1845) tested Doppler’s theory by placing musicians
on a railroad train that traveled 40 mph past musically
trained observers. The stationary observers found that notes
were perceived to be a half-note sharper when the train
approached and a half-note flatter when the train receded.
Three years later, Russell (1848) noticed that when he was
on a train moving at 50 to 60 mph, the pitch of the whistle of a stationary train was higher when the train moved
toward it and lower when the train moved away. Think of
a police car with its siren going. As it approaches you, the
sound waves move closer together and thus the frequency
(or pitch) gets higher and higher. As the police car moves
away from you the sound waves move farther and farther
apart, thus the frequency drops and the sound has a lower
and lower pitch.
Doppler realized that if light were a wave it should also
show a shift in the frequency and wavelength. Consequently,
when a light emitting source approaches an observer, the waves,
measured at an instant in time, appear to be closer together
and thus blue-shifted to the observer. By contrast, when the
light emitting source moves away from the viewer, the waves,
measured at an instant of time, appear farther apart and thus
red-shifted. When the waves are measured over time at a single point in space by the observer, the frequency of the waves
appear to increase or decrease, depending on whether the
source is approaching or receding from the observer, respectively. The temporally and spatially varying amplitude (Ψ(x,t))
of a wave perceived by an observer moving with a velocity (v)
relative to the source is given by the following equation:
Ψ (x,t) Ψo cos(k observer x ωsource [ √ (c v)/√ (c v)]t)
where kobserver angular wave number measured from the
observer’s frame of reference and ωsource is the angular frequency measured from the source’s frame of reference. The
angular wave numbers measured from the source’s frame
of reference and the observer’s frame of reference are equal
when v 0 and the source and observer are at rest relative
to each other. The above equation, which includes the relativistic Doppler Effect, implies that the speed of light (c)
as measured by the properties of the propagation medium
(i.e. the electric permittivity and the magnetic permeability) is not equal to the speed of light measured as the ratio
of the angular frequency of the source to the angular wave
r
Lase
Chamber
with
cell
FIGURE 12-9
Diagram of a laser Doppler microscope.
number measured by the observer moving relative to the
source.
The laser Doppler microscope can be used to measure
the speed of moving particles within a cell or the speed
of moving cells by determining how much the wavelength
(or frequency) of the incident light is shifted by the moving
particle. Laser Doppler velocimetry has been used to study
cytoplasmic streaming (Mustacich and Ware, 1974, 1976,
1977; Langley et al., 1976; Sattelle and Buchan, 1976;
Earnshaw and Steer, 1979), phloem transport in plant cells,
motility of sperm (Dubois et al., 1974) and algae (Druez
et al., 1989), as well as chemotaxis in bacteria (Nossal and
Chen, 1973). Similar techniques are used to measure the
velocity of blood flow (Stern, 1975; Tanaka et al., 1974).
In a laser Doppler microscope, light from a laser passes
through a neutral density filter and strikes the cell. The
light that is scattered at a given angle passes through an
aperture (0.8 mm) and a half-silvered mirror and is focused
on a pinhole (2 mm) that is placed immediately in front of
a photomultiplier tube. The light that is reflected by the
half-silvered mirror passes up through a microscope. The
electrical signal from the photomultiplier tube then passes
through an amplifier and a spectrum analyzer where it is
added to a reference signal of 2 to 200 Hz.The two signals
interfere to produce “beats.” In this way the frequency of
the incoming light can be determined. Figure 12-9 shows a
setup for a laser Doppler microscope.
In systems like cytoplasmic streaming, where the velocity of streaming decreases with distance from the location
of the motive force, an objective lens will give an average velocity over the distance equal to the depth of field.
A high numerical aperture lens will let one sample the velocity in an optical section, whereas a low numerical aperture
lens will give an average velocity (Staves et al., 1995).
CENTRIFUGE MICROSCOPE
The centrifuge microscope can be used to measure force
and resistance (Hayashi, 1957; Hiramoto, 1967; Kaneda
201
Chapter | 12 Various Types of Microscopes and Accessories
Image
processor
Video camera
Timing
sensor
Rotor
Video
tape
recorder
FIGURE 12-10 Diagram of a
centrifuge microscope.
Video
monitor
Objective
Xe tube
Pulse generator
tachometer
Stroboscope
controller
et al., 1987, 1990; Kamitsubo et al., 1989, 1988; Kuroda
and Kamiya, 1989; Oiwa et al., 1990; Wayne et al., 1990;
Takagi et al., 1991, 1992). There are simple types of centrifuge microscopes that one can build with surplus materials.
These include the Harvey (1938) type and the Brown (1940)
type centrifuge microscopes that use either electrical motors
or air-driven motors and low magnification objectives. I
will describe the centrifuge microscope of the stroboscopic
type. The centrifuge microscope of the stroboscopic type
is composed of a video-enhanced contrast microscope that
uses bright-field optics combined with an analog image
processor that creates a pseudo-relief image of the cell in
real time (Kamitsubo et al., 1989). The objective lenses are
long working distance objectives (Nikon 20x/0.40, 40x/0.55
LWD, Plan 60x/0.7 Ph3DL LWD CF), and the sub-stage
condenser is a long working distance sub-stage condenser
(NA 0.65). The optical system is completely isolated from
the rotor. The rotor replaces the stage.
The rotor is 16 cm in diameter and the radius for centrifugation is adjustable in the range of 4.5 to 7.0 cm. The
rotor can be rotated at 250 to 5000 rpm (4 – 1900 xg) while
examining the specimen with a 60x objective lens. The rate
of rotation can be varied by changing the voltage supply.
The rate of rotation (in rpm) is recorded on the videotape
and is played on the monitor.
The illumination source is a xenon bulb that flashes
for 180 ns per pulse. The rate of the pulse is controlled by
a trigger pulse generator. The bulb is capable of flashing at
rates up to 100 Hz (6000 times per minute). The position
of the specimen is detected by a photocoupler that consists
of a light-emitting photodiode, a phototransistor, and an
amplifier. A piece of metal attached to the rotor edge opposite the position of the specimen interrupts the light beam
emitted by the photodiode once per rotation. The change in
the light intensity is detected by the phototransistor and is
converted into an electrical pulse, which triggers the strobe
light to flash. Since the strobe flashes only when the cell is
under the objective and afterwards the cell is dark, the stationary parts of the cell seem to stand still (Figure 12-10).
Centrifuge microscopes can also be used to study the effect
of centrifugal fields on birefringent and fluorescent specimens (Inoué et al., (2001a, 2001b).
X-RAY MICROSCOPE
X-ray microscopes, which work with electromagnetic
waves with wavelengths of about 1 to 10 nm, have the
potential of producing images with high spatial resolution,
although currently the resolution is about 30 nm (Schmahl
and Rudolph, 1984; Howells et al., 1991; Michette et al.,
1992). X-rays provide image contrast by interacting with
the electrons that make up the inner shells of light atoms.
This provides good contrast between carbon-containing
organic matter and water. Rosengren (1959) developed a
method to measure the mass of small cells using an X-ray
microscope. The X-rays he used had wavelengths between
0.6 and 1.2 nm because it was found that almost all biological molecules have similar absorption coefficients for
wavelengths in this range and thus absorption is proportional to the concentration of matter. The x-ray microscope
is similar in accuracy to an interference microscope and
has a sensitivity of 1.3 10–16 kg.
Some X-ray microscopes use Fresnel zone plates to
focus the X-rays. A zone plate consists of a silicon nitride
membrane that supports thin concentric gold rings. The
202
X-rays that pass through the zone plate are diffracted
again and brought to a focus—just as a regular glass lens
diffracts again the light rays that come from an object
and brings them to a focus. Some X-ray microscopes do
not use lenses but record the far-field or Fraunhöfer diffraction pattern (Maio et al., 1999; Shapiro et al., 2005;
Hornberger et al., 2007). The resolution attainable with
lens-less microscopes is not limited by the resolution of
the lens. Lens-less microscopes are also free from spherical aberration. Veit Elser (2003) has written the algorithm
that converts the diffraction pattern that is produced by the
object into an image to and interestingly enough, the same
algorithm can be used to make and solve Sodoku puzzles
(Thibault et al., 2006).
Construction of microscopes that use π-mesons for the
illuminating rays is under way (Breedlove and Trammell,
1970). Perhaps there will be “antimatter microscopes”
that bombard specimens with positrons and generate large
numbers of gamma rays in regions of high electron density
when the positrons combine with electrons. This is how
positron emission tomography (PET), which is currently
used in many hospitals, works.
INFRARED MICROSCOPE
Fourier transform infrared (FTIR) microscopes have been
developed to determine the absorption characteristics in the
infrared region of various molecules in the cell. The only
unusual aspect of this microscope is that all the lenses are
made of mirrors that have no chromatic aberration, so visible light can be used to focus the object while an infrared
spectrum is obtained (Schiering et al., 1990).
NUCLEAR MAGNETIC RESONANCE
IMAGING MICROSCOPE
I have been discussing microscopes that utilize electromagnetic waves from various regions of the spectrum,
including X-rays, ultraviolet light, visible light, and infrared light, to interact with electrons in a specimen in order
to derive information about the electronic properties of
that specimen. Radio waves can also be used to image a
specimen; however, radio waves interact with the nuclei of
atoms instead of the electrons. Radio waves are utilized by
nuclear magnetic resonance (NMR) imaging microscopes
(Goodman et al., 1992, 1992; Callaghan 1991, 1992;
Bowtell et al., 1990; Woods et al., 1989; Jelinski et al.,
1989) in the same way they are used in magnetic resonance
imaging (MRI). The distribution of 1H, 13C, 19F, 23Na, 31P,
or any nucleus that has an odd number of nucleons and
thus a net magnetic spin can be determined with magnetic
resonance imaging.
Basic NMR works by aligning the magnetic moment (M)
of a nucleus in a magnetic field (B), then giving the
Light and Video Microscopy
(a) Magnetization
M0
B
M
Static
magnetic field
Sample
M created
(b) Excitation
M
RF
pulse
M
RF
transmitter
M rotated 90
(c) Relaxation
RF
signal
V
RF
receiver
t
Signal from
sample
FIGURE 12-11 Illustration of how the nuclear spins respond to a radiofrequency pulse using magnetic resonance imaging.
specimen a radio frequency pulse oriented 90 degrees relative to the magnetic field vector. Then the radio frequency
pulse is absorbed, and the magnetic moment reorients
along the direction of the pulse. The nucleus emits the
radio frequency radiation and the magnetic moment slowly
returns to the direction it was facing before the pulse,
which is the lowest energy state in the magnetic field. The
emitted energy identifies the atom and/or the environment
surrounding the atom. This energy usually is given in frequency terms or relative terms called chemical shift. The
frequency, pulse width, and pulse pattern of the radio frequency radiation is chosen to selectively excite the atom
of interest (e.g., 1H, 3C, 31P). The frequency of the energy
emitted depends on which element is in the magnetic field
(Figure 12-11).
The magnetic fields that orient the nuclei of specific
atoms move across the specimen in the x, y, and z directions. The intensity of the emitted signal at each x,y,z coordinate is reconstructed in a point-by-point manner to form
an image. Nuclear magnetic resonance microscopes, which
have a spatial resolution of 105 m, have been used to map
the distribution of water in large single cells (Xenopus
eggs; Aguayo et al.., 1986), as well as in whole plants and
animals (Jenner et al., 1988; Goodman et al., 1992).
STEREO MICROSCOPES
Stereo microscopes, also known as dissecting microscopes,
produce three-dimensional upright images enlarged up to
about 600x with large and flat fields, a tremendous depth
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Chapter | 12 Various Types of Microscopes and Accessories
of field, and long working distances. Stereo microscopes
fall into two categories: those designed according to the
Greenough design principle and those designed according to the telescope principle. The Greenough design utilizes two identical, nearly side-by-side objectives. The
two objectives project two separate images to two oculars.
Most stereo microscopes are made according to the telescope design. These microscopes consist of two partial
microscopes, which share one large objective.
Stereo microscopes now offer highly corrected, apochromatic, distortion-free, flat field optics equipped with
zoom lenses. They are available with transmitted and/or
reflected light bright-field optics as well as with darkfield, epi-fluorescence and polarizing optics. They come
equipped with a variety of stages including rotating and
glide stages. They have iris diaphragms to control the depth
of field, and ports to mount video and/or digital cameras.
Many fiber optic illumination sources are available for stereo microscopes that give dramatic lighting effects.
The zero perspective imaging microscope uses a 35 mm
camera with a macro lens to obtain a three-dimensional
image with maximal depth of field using the full resolving power of the lens (Peres and Meitchik, 1988). In this
microscope, a thin sheet of light whose plane is perpendicular to the optical axis illuminates a section of the object.
The line must be thinner than the depth of field of the
objective lens. The camera then focuses at this depth. This
specimen is then driven up or down by a motor while
the camera shutter remains open. In this way every plane
in the vertical axis is perfectly in focus in the image.
SCANNING PROBE MICROSCOPES
Scanning probe microscopes include the near-field scanning optical microscope, the scanning tunneling microscope, and the atomic force microscope.
Synge (1928, 1932) proposed that Abbe’s limit of resolution, which is based on the formation of a Fraunhöfer or
far-field diffraction pattern could be overcome by capturing the Fresnel or near-field diffraction pattern. Near-field
scanning optical microscopy (NSOM) produces an image
by capturing the Fresnel diffraction pattern. The near-field
scanning optical microscope can be used in the transmission, reflection, or fluorescence mode. In the reflection
or fluorescence mode, the specimen is illuminated by
light that passes through a subwavelength aperture at the
end of an optical fiber probe, and the same optical fiber
probe collects the reflected light (Pohl et al., 1984; Lewis
et al., 1984; Liberman et al., 1990; Betzig et al., 1991;
Wiesendanger, 1998; Courjon, 2003). A feedback mechanism maintains a constant distance of a few nanometers
between the specimen and the probe (Figure 12-12). The
feedback voltage at each point is used to create a pointby-point image that is a function of the microtopography
A feedback system
that controls the
probe's vertical position
Coarse
positioning
system
A probe tip
Specimen
A scanner
to move the sample
under the probe or the
probe over the sample
Computer
and monitor
FIGURE 12-12
Diagram of a scanning probe microscope.
of the specimen. The maximum depth-of field of the nearfield optical scanning microscope is about 300 nm, the
minimum is 0.65 nm (Revel, 1993; Querra, 1990).
Many varieties of scanning probe microscopes have
been and are being developed to probe matter at atomic
dimensions (Kalinin and Gruverman, 2007; Morita, 2007).
The scanning tunneling microscope (STM) differs from the
near-field scanning optical microscope in that the probe
acts as a conductor of electrons to or from the surface
through a distance small enough (0.2 nm) to allow quantum mechanical tunneling, which is analogous to an evanescent wave, when an electrical potential is applied across
the gap between the specimen and the probe. The amount
of current depends on the distance between the specimen
and the probe. The computer then reconstructs an image,
point by point, from the position of the probe and the magnitude of current that flows through the probe at each point.
The 1986 Nobel Prize in Physics went to Gerd Binnig and
Heinrich Rohrer at the IBM Zurich Research Laboratory
for developing the scanning tunneling microscope (Binnig
et al., 1982; Amato, 1997).
Image contrast is obtained in a scanning tunneling
microscope because the probe produces pressure-induced
elastic deformations of the electronic orbitals, which
result in molecular orbitals close to the Fermi energy
and therefore, enhanced tunneling (McCormick and
McCormick, 1990). Although the scanning tunneling
microscope usually is used in materials science (Hawley
et al., 1991), it has also been used to image cell membranes
and macromolecules (Cricenti et al., 1989; Ruppersberg
et al., 1989; Welland et al., 1989; Edstrom et al., 1990;
Yang et al., 1990; Clemmer and Beebe, 1991).
204
Light and Video Microscopy
Aqueous
chamber
Object attached
to mylar film
Piezoelectric
film transducer
Piezoelectric
film transducer
Electromagnetic
Output signal
Electromagnetic
Input signal
Sapphire output crystal
Sapphire input crystal
Mylar film to
support object
FIGURE 12-13
Diagram of an acoustic microscope.
The atomic force microscope measures one of a number
of interaction forces between the tip of the probe and surface
of interest (Marti and Amrein, 1993; Morris et al., 1999).
The choice of probe determines the interaction force that is
measured. When the probe has a tip with a small diamond,
a carbon nanotube, a silicon chip, or silicon nitride chip, the
atomic force microscope measures the electrostatic forces
between the tip of the probe and the surface of the specimen.
When the probe has a tip whose resistance changes with
temperature, the atomic force microscope measures the thermal conductivity of the surface. When the probe has a tip
that is susceptible to magnetic fields, then the atomic force
microscope measures magnetic forces. When the probe is
dragged across the surface of the specimen, then the atomic
force microscope can measure frictional forces.
In the atomic force microscope, the various probes
are mounted on a cantilever so that the sharp point faces
the sample and it rides directly on the sample. A laser is
focused on the mirrored back surface of the cantilever and
the position of the reflected beam is monitored with a photocell. The specimen can be scanned across the probe with
a lateral resolution of a few nanometers. A computer generates a three-dimensional image by reconstructing, point
by point, the position of the probe tip in three dimensions
(Robinson et al., 1991).
ACOUSTIC MICROSCOPE
Up until now I have been talking about imaging specimens
with transverse electromagnetic waves from the X-ray region
of the spectrum though the radio wave region of the spectrum. Specimens can also be imaged with longitudinal sound
waves that have approximately the same wavelength as light
waves. Sound travels through a specimen with a velocity
that depends on the mechanical (viscoelastic) properties
of the specimen. For example, sound travels at a velocity of
1531 m/s in water at room temperature and at a velocity of
about 300 m/s in air (Airy, 1871; Rayleigh, 1894). In general,
the speed of sound is equal to the square root of the ratio of
an elastic property of the medium to an inertial property of
the medium. The best indicator of the elastic property is the
bulk modulus (in N/m2) and the best indicator of the inertial
property is the density (in kg/m3). In general, the more rigid
the material is, the faster sound moves through it.
The wavelength of sound can be found from the dispersion relation that relates the wavelength (λ), frequency (ν),
and speed (c) of a wave.
λ c/v
The wavelength of a 1000 MHz sound wave traveling
through water is (1531m/s) (1000 106 s1)1 1.5 10–6 m,
which is close to the wavelength of visible light. Using the
Rayleigh criterion, and assuming the numerical aperture of
a lens in a acoustic microscope is 1.4, the limit of resolution
for a 1000 MHz sound wave would be 0.61 (1.5 106 m)/
NA 0.65 10–6 m; similar to the limit of resolution of a
light microscope (Lemmons and Quate, 1974, 1975).
Creating images using the interaction of light with matter
reveals information about the electrical properties of the specimen. By contrast, the interaction of sound with matter reveals
information about the elastic and inertial properties of matter
known as the viscoelastic properties. The viscoelastic properties of the specimen can alter both the phase and the amplitude of the sound waves traveling through the specimen. The
amplitudes of the sound waves are differentially damped when
they travel through media with different viscoelastic properties (density, viscosity, elasticity). For example, the greater
the viscosity, the greater the absorption. There are amplitude contrast acoustic microscopes as well as phase-contrast,
dark-field, and differential interference contrast acoustic
microscopes (Wickramasinghe, 1989).
205
Chapter | 12 Various Types of Microscopes and Accessories
In an acoustic microscope, electrical energy is transformed into acoustic energy by a piezoelectric film at the
surface of a sapphire crystal (Figure 12-13). The acoustic
wave then propagates as a plane wave through the sapphire
crystal. The other side of the sapphire crystal meets a water
cell. The acoustic wave hits the sapphire-water interface and
perceives it as a converging lens since the acoustical refractive index of water is greater than the acoustical refractive
index of sapphire. As a result, the spherical sound waves are
focused to a point. This makes up the acoustic transmitter
that transmits sound waves with a wavelength of 106 m.
The sound waves then pass through the specimen, which is
attached to a Mylar film, and at the focus of the transmitter.
The specimen is also at the focus of the receiver. The
receiver in the acoustic microscope is constructed exactly the
same way as the transmitter. The sound waves pass through
the specimen and through the water to the sapphire-water
interface as spherical waves. The spherical sound wave
experiences a converging lens that turns them into a plane
wave. The plane wave then strikes a second piezoelectric
film that transforms the sound waves into electrical waves.
The limit of resolution is set by the wavelength of the
acoustic signal. Therefore, increasing the frequency of the
sound increases the resolving power of the acoustic microscope. Unfortunately the attenuation of sound is proportional
to the frequency, and this property sets a limit on the focal
length of the lens. In an acoustic microscope, the specimen is
translated on a mechanical stage through the acoustic beam.
The acoustic microscope has been used to contrast
regions with differing viscoelastic properties in cells
(Johnston et al., 1979; Israel et al., 1980; Lüers et al., 1991;
Hildebrand et al., 1981; Bereiter-Hahn et al., 1995). An ultrasound imager is a macro version of an acoustic microscope.
HORIZONTAL AND TRAVELING
MICROSCOPES
Microscopes can be mounted horizontally so that the stage
is parallel to the vector of gravity. Although the stage is vertical, the optical system is horizontal, thus the name horizontal microscope. A horizontal microscope has been used
to measure gravity sensing in plant cells (Sack and Leopold,
1985; Sack et al., 1984, 1985; Wayne et al., 1990).
A traveling microscope is a microscope that does not
have a stage. It can be oriented in any direction. It is used
commonly with a low-power objective as a horizontal
microscope to observe an object mounted in some kind of
bulky apparatus. A traveling microscope has been used in
a turgor balance, an apparatus that measures noninvasively
the osmotic pressure of plant cells (Tazawa, 1957). A traveling microscope also has been used to measure the density of cell components (Kamiya and Kuroda, 1957) and
the tension at the surface of an endoplasmic drop (Kamiya
and Kuroda, 1958).
MICROSCOPES FOR CHILDREN
The microscope can help open up the world to children of all
ages. Microscopy Today publishes a Microscopy Bibliography
for Children (e.g., supplement Issue #00-10, December
2000). This bibliography includes books, CD-ROMS,
and videotapes on teaching microscopy, optics, the microscopic world, and specimen preparation for primary and
middle school children. In order to find age-appropriate
materials and learn how to buy children’s microscopes, visit
The Microscopy Society of America’s web site at http://
www.msa.microscopy.org/ProjectMicro/PMHomePage.
html; the Southwest Environmental Health Sciences Center
web site at http://swehsc.pharmacy.arizona.edu/exppath/
micro/edu/education.html; or the microscopy.info web site at
http://www.mwrn.com/microscopy/educational/books.aspx.
MICROSCOPE ACCESSORIES
Once you know how to use a microscope, it can offer
you unlimited opportunities to study cells at high magnification. Many accessories are made to assist you in your
goals.
There are specialized stages, including rotating stages
(Abramowitz, 1990), motorized stages, temperaturecontrolled stages (Hartshorne, 1975, 1976, 1981; Skirius,
1984; Moran and Moran, 1987; Wilson and McGee, 1988;
McCrone, 1991; Valaskoveic, 1991). If you need a stage
cold enough to photograph snowflakes, you can always
take your microscope outside (Nakaya, 1954; Bentley and
Humphreys, 1962; LaChapelle, 1969; see references in
Delly, 1998).
If you want to study dynamic processes in cells over
extended times you must construct or buy special culture
chambers that keep the temperature, pH, CO2, O2, osmolarity, nutrients, and growth factors constant (Smith, 1856;
Davidson, 1975; McKenna and Wang, 1989). These chambers must also be optically transparent so that the specimen
can be seen with optimal resolution and contrast. Do not
forget that you can make good chambers with cover slips
cut with a phonograph needle (glued with Elmer’s Bonding
Cement), parafilm, or VALOP (1 part vaseline, 1 part lanolin, 1 part paraffin oil).
A number of instruments, known as micromanipulators, are available that allow you to move, inject, or cut
microscopic objects under the microscope. Microcapillary
pipette pullers, bevellers, and microforges let you make
pipettes capable of injecting large substances and organelles into cells (McNeil, 1989), measuring the electrical
properties of cells and membranes, or measuring the forces
that drive motile processes in cells. The only things that
limit the design and applications of a microscope are the
laws of physics and your own imagination! Contribute
your imagination to discovering new laws of physics and
to microscopy!
206
WEB RESOURCES
Light and Video Microscopy
http://www.moleculardevices.com/pages/instruments/microgenomics.
html
Confocal Microscopy
Marvin Minsky’s Memoir on the Invention of the Confocal Microscope
and Homepage: http://web.media.mit.edu/~minsky/papers/Confocal
Memoir.html and http://web.media.mit.edu/~minsky/
Leica Microsystems: http://www.leica-microsystems.com/Confocal_Microscopes
Nikon Microscopy U: http://www.microscopyu.com/articles/confocal/
confocalintrobasics.html
Molecular Expressions: http://micro.magnet.fsu.edu/primer/techniques/
confocal/index.html
Zeiss: http://www.zeiss.com/4125681f004ca025/Contents-Frame/f544501
1b5a0a89f852571d200714c4d
Total Internal Reflections Fluorescence Microscopy: http://www.olympusmicro.com/primer/techniques/fluorescence/tirf/tirfhome.html
Fluorescence Resonance Energy Transfer (FRET): http://www.olympusfluoview.com/applications/fretintro.html
Optical Tweezers
Michelle Wang’s Web site: http://people.ccmr.cornell.edu/~mwang/
overview.html
Laser Capture Microdissection
http://dir.nichd.nih.gov/lcm/LCM_Website_Introduction.htm)
http://www.lasercapturemicrodissection.org/
http://www.palm-microlaser.com/dasat/index.php
X-Ray Microscopes
http://xray1.physics.sunysb.edu/research/links.php
Scanning Probe Microscopes
http://www.olympusmicro.com/primer/techniques/nearfield/nearfieldintro.
html
http://www.mobot.org/jwcross/spm/
http://nobelprize.org/nobel_prizes/physics/laureates/1986/index.html
Acoustic Microscopes
Sonoscan: http://www.sonoscan.com/
Sonix: http://www.sonix.com/learning/ultrasonics.php3
Accessories
World Precision Instruments: http://www.wpiinc.com/products/
Research Precision Instruments: http://www.rpico.com/company.html
Narishige: http://www.narishige.co.jp/main.htm
In vivo Scientific: http://www.invivoscientific.com/
Olympus Fluoview: http://www.olympusfluoview.com/resources/
specimenchambers.html
Chapter 13
Video and Digital Microscopy
There are many ways to accomplish the goal of creating a
high-resolution and high-contrast image. Once we understand
how light interacts with matter and how optical components
of a microscope transform the light emitted by a specimen
into a high contrast image, it becomes easy to understand, by
using analogous physical principles, how electronic devices
can be used in conjunction with a few optical components to
produce a high-contrast image. In order to take advantage of
electronics in image processing, we must convert the optical
signal into an electronic signal. This is the job of a video or
digital camera (Allen et al., 1981a, 1981b; Allen and Allen,
1983; Allen, 1985; Cristol, 1986; Inoué, 1986; Dodge et al.,
1988; Aikins et al., 1989; Spring and Lowy, 1989; Weiss
et al., 1989; Varley et al., 2007).
THE VALUE OF VIDEO AND DIGITAL
MICROSCOPY
Just as a diverging lens made of flint glass reverses the
chromatic aberration caused by a converging lens made of
crown glass, video and digital microscopy can be used to
reverse the aberrations introduced by the optical system.
Whereas, traditionally, the aberrations are corrected by
optical means, video and digital cameras allow the aberrations to be corrected by electronic means. In addition,
just as additions to the light microscope, including phasecontrast, differential interference contrast, and modulation
contrast optics can be used to surpass the limitations of the
bright-field microscope and produce images that are high in
both resolution and contrast, video and digital microscopies
can be used to overcome the same limitations.
Video and digital microscopies are also useful when
doing fluorescence microscopy. The light emission from a
specimen in a fluorescence microscope is relatively low and
consequently, when using film cameras, one must take long
exposures with high-speed film (ISO 800–1600) in order to
capture an image. However, image capture is fast and easy
when the image is captured with a video or digital camera since the light sensitivity of video and digital cameras
can be as high as ISO 1,000,000. Today, specimens that
emit only a few photons per point, be they distant galaxies
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
or fluorescent microscopic objects, can be imaged with a
photon-counting camera.
Video and digital microscopies are also useful for
polarization microscopy, where resolution often is sacrificed for maximal extinction because high numerical aperture objective lenses tend to depolarize the light that strikes
their surfaces. Video and digital microscopy combined
with background subtraction (see Chapter 14) can be used
to eliminate any background brightness without reducing
the light that arises from a birefringent object, thus achieving maximal resolution and contrast simultaneously.
Moreover, video and digital microscopies let us take
images of moving objects in rapid succession. Moving pictures began in 1872 when then California Governor Leland
Stanford hired Eadweard Muybridge to see if all four
hooves of a horse leave the ground when it gallops (Bova,
1988). Muybridge (1887, 1955) set up 12 cameras at a
racetrack and took 12 consecutive photos. All four hooves
do leave the ground when a horse gallops and Stanford
won a $25,000 bet. Today, digital cameras can take images
of moving bullets and biological objects as fast as 400,000
frames per second.
Video and digital cameras convert an optical signal into
an electric signal, thus making it possible to operate on the
image with inexpensive electronic means instead of expensive optical devices (de Weer and Salzber, 1986). The use
of video and digital cameras for image processing has not
even begun to see its full potential. Imagine putting an
imaging chip in the back focal plane of an objective lens,
or better yet in the aperture plane of an infinity corrected
microscope. The chip in the aperture plane would collect
the diffraction pattern of the specimen and convert the
light intensity at each point into an electrical signal. The
signal at each point could be digitized and sent to a computer where the information could be stored numerically.
If the specimen were illuminated sequentially with points
of light in the form of an annulus at the front focal plane of
the condenser, we could obtain many high-resolution diffraction patterns of the same specimen. Then the computer
could do an inverse Fourier transform on each diffraction
pattern, combine the inverse Fourier transforms, and construct an image of the specimen.
207
208
VIDEO AND DIGITAL CAMERAS: THE
OPTICAL TO ELECTRICAL SIGNAL
CONVERTERS
A video or digital camera provides the interface between
the optical system and the electronic system. The imaging
device converts the intensity of each designated area in the
optical image into an electrical signal. The video camera is
attached to a microscope using an optical coupler known as
a “c mount,” and digital cameras can be attached to microscopes, either by c mounts, or by a variety of optical couplers that have not yet been standardized. The formation of
an electrical signal depends on the interaction of a photon
with an electron. Since the interaction depends on the relationship between the work function of the photosensitive
surface and the energy of the photon, the response of electrical detectors is wavelength-dependent.
Semiconductors typically are used to convert light energy
into electrical energy (Pankove, 1971). Semiconductors traditionally are made of silicon atoms arranged in a crystal
lattice where each atom has tetrahedral bonding with four
of its nearest neighbors (Figure 13-1). Semiconductors are
called semiconductors because they are neither good conductors nor good insulators. In order for a material to conduct electricity, the valence electrons have to be freed from
the atomic orbitals, which make up the valence band, and
allowed to migrate freely through the material, in what
Covalent
bonds
Pentavalent
(5) atom
Excess
electron
Excess
hole
Silicon
atom
Trivalent
(3) atom
FIGURE 13-1 Diagram of a silicon wafer with excess electrons and
holes.
Conduction band
Electron energy
Imagine that we could program the computer to remove
the Fourier components that represent the diffracted light
from one side or the other of the diffraction plane before it
reconstructs an image. This would produce a pseudo-relief
image reminiscent of an image produced by oblique illumination. Imagine illuminating the object with oblique slit
illumination and then programming the computer to adjust
the numerical value of Fourier components, depending
on which point in the diffraction plane they represent. We
would obtain a modulation contrast image if we multiplied
the values of the Fourier components in the region conjugate with the slit by 0.15, and multiplied the values of the
Fourier components on one side of the conjugate region by
0.01, and multiplied the values of the Fourier components
on the other side by 1.
It is also possible to produce a differential interference
contrast image using analog electronics by converting the
light intensity of a line across the image plane into an electronic signal, then duplicate the signal, and then advance or
retard the duplicated signal with respect to the original signal (see Chapter 14). When the two signals are recombined,
a differential interference contrast image is obtained without the use of expensive interferometers. Use your imagination: I bet that you can think of many ways to use relatively
inexpensive and versatile computers and electronics to do
the job of more expensive specialized optical components.
Light and Video Microscopy
Forbidden
gap
A
Valence band
B
C
FIGURE 13-2 Energy diagram of a conductor (A), an insulator (B), and
a semiconductor (C).
is known as the conduction band. A good conductor has
a conduction band that is minimally separated from the
valence band, and it takes only 4 1021 J of energy to
boost the electrons across the band gap into the conduction band. This energy is readily provided by the thermal
energy available at room temperature (kT 1.38 1023
J/K 300 K 4 1021 J). By contrast, a good insulator has a large band gap between the valence band and the
conduction band, and it requires more than 10–18 J of energy
to move an electron across the band gap from the valence
band to the conduction band. An electron can be moved
from the valence band to the conduction band of an insulator using the electrical energy (eV) of an applied voltage
(1.6 10–19 C 10 V) 1.6 10–18 J). In a semiconductor, the gap between the valence band and the conduction
band is intermediate between a conductor and an insulator
and visible light (hc/λ 6.63 10–34 Js (2.99 108 m/s)/
(500 109 m) 4 1019 J) provides sufficient energy to
boost an electron from the valence band to the conduction
band (Figure 13-2).
209
Chapter | 13 Video and Digital Microscopy
p–type
n–type
p
n
p
n
Voltage
Voltage
(A)
(B)
Voltage
FIGURE 13-4 Diagram showing a p-n junction and the electrical potential across it when it is connected to a battery with a forward (A) or a
reverse (B) bias configuration p-n junction without bias (---); p-n junction
with bias (—).
Distance
FIGURE 13-3 Diagram of a p-n junction and the electrical potential
across it.
The conduction of electricity through a semiconductor
involves the movement of electrons through the conduction
band and the movement of holes through the valence band.
When an electron makes the transition from the valence
band to the conduction band and becomes a free electron,
it leaves behind a vacancy or hole in the valence band.
Another electron in the valence band can then occupy the
hole and consequently a new hole is created. When an
electric field is applied to a semiconductor, the holes move
to the negative pole of the battery and the electrons move
to the positive pole.
The conductivity of a semiconductor can be increased
by introducing impurities into the silicon, which is called
doping the silicon (Shockley, 1956). When pentavalent
atoms (e.g., arsenic, phosphorous, or antimony) are introduced into the tetravalent silicon, there will be one too
many electrons to satisfy the quadravalent bonding system
of the silicon. This extra electron can readily be removed
from the valence electrons to become a free electron. When
trivalent atoms (e.g., boron or gallium) are introduced as
an impurity, holes are created in the quadravalent bonding system of the silicon. The semiconductors that have a
surplus of negatively charged electrons are known as negativetype or n-type semiconductors, and the semiconductors
that have a surplus of positively charged holes are known
as positive-type or p-type semiconductors.
When a p-type semiconductor is brought in contact
with an n-type semiconductor, the excess electrons in the
n-type semiconductor diffuse to the p-type semiconductor
and at the same time, the excess holes in the p-type semiconductor diffuse to the n-type semiconductor (Figure
13-3). Consequently, near the junction, the n-type semiconductor becomes positively charged and is an anode and the
p-type semiconductor becomes negatively charged and is
a cathode. The electric field set up by diffusion mitigates
the concentration-dependent diffusion of electrons to the
p-type semiconductor and the concentration-dependent diffusion of holes to the n-type semiconductor and sets up an
equilibrium condition. The recombination of electrons and
holes right at the junction depletes the electrons from the
conduction band, thus forming a nonconducting layer or
a “depletion zone” at the junction. The depletion zone in
the p-n junction results in a reduction in conductivity compared to the conductivities of the p-type and n-type semiconductors individually.
The depletion zone at the p-n junction can be reduced
by connecting a battery in the forward-bias mode where the
positive pole of the battery is connected to the p-type semiconductor and the negative pole of the battery is connected to
the n-type semiconductor (Figure 13-4). In this arrangement,
the electrons in the n-type semiconductor are repelled by the
negative pole of the battery and move toward the junction
and the holes in the p-type semiconductor are repelled by the
positive pole of the battery and move toward the junction. At
the junction, the recombination of electrons with holes further depletes the conduction band of electrons. The greater
the forward-biased voltage, the smaller the depletion zone,
and the better the p-n junction acts as a conductor.
The depletion zone in the p-n junction can be widened when a battery is connected to the p-n junction in
the reverse-bias mode. In this arrangement, the positive
pole of the battery is connected to the n-type semiconductor and the negative pole of the battery is connected to the
p-type semiconductor. Consequently, the excess electrons in
the n-type semiconductor move to the positive pole of the
battery and holes in the p-type semiconductor move to the
negative pole of the battery, further increasing the width of
the depletion zone. The greater the reverse-bias voltage,
the wider the depletion zone, and the less conducting the
p-n junction becomes. The p-n junction functions as a diode
because it lets current flow across it only in the forwardbias mode and not in the reverse-bias mode. When light is
able to control the amount of current that flows through the
p-n junction in the reverse-bias mode, that diode is known
as a photodiode.
210
Light and Video Microscopy
When light strikes a photodiode, held at constant voltage in the reverse-bias mode, the light excites an electron
from the valence band to the conduction band, creating an
electron hole pair. The electron then flows in the conduction
band through the n-type semiconductor to the positive pole
of the battery and the hole flows through the p-type semiconductor to the negative pole of the battery. The greater the
light intensity, the greater the number of electron hole pairs
created and the greater is the photocurrent. In the reversebias mode, the current is linear with light intensity, but this
is not the case for the forward-bias mode.
As an aside, diodes, made out of aluminum gallium
arsenide, aluminum arsenide phosphide, aluminum gallium phosphide, and indium gallium nitride will emit red,
orange, green, and blue light, respectively, when a battery
is connected in the forward bias mode. In the forwardbias mode, electrons and holes flow into the junction and
recombine. Upon recombination, the electron falls from
the conducting band to the valence band, converting electrical energy into radiant energy. The semiconductors used
to create each color have different band gap energies. The
wavelength (λ) of the radiated light depends on the energy
of the band gap (Ebg) according to the following equation:
III) that has 21 million pixels packed into a 36 24 mm
array. The area taken up by each pixel, known as the
pixel pitch, is 6.4 μm. The arrays are made using CMOS
(complementary metal-oxide semiconductor) technology.
Other cameras, which are made for scientific imaging, give
21-megapixel resolution using a one-half inch, one-megapixel
chip with subpixel imaging. Subpixel imaging involves the
rapid shifting or wobbulation of the photodiode array within
the camera using a piezoelectric device. A composite image
is formed from the many images captured by a shifting
array. As long as the signal from the chip can be captured
quickly enough from each position, the movement of the
array within the camera increases the spatial resolution, just
as the movement of our eyes increases our visual acuity.
A charge-coupled device (CCD), which was invented
in 1969 by Willard Boyle and George E. Smith at Bell
Laboratories while trying to make a “picture phone,” is
similar to a photodiode array in that a CCD also converts
light intensities into electrical signals. In both cases, light
causes the formation of electron-hole pairs. However,
a CCD differs from a photodiode array in that each element in a photodiode array acts as a diode, whereas each
element in a CCD acts as a capacitor (Figure 13-6).
λ hc/E bg
where h is Planck’s constant and c is the speed of light. Light
emitting diodes (LED) and laser diodes are built on this
principle. Light emitting diodes can be combined in a twodimensional array to make high definition monitors. Some
of the light emitting diodes used in these monitors are being
made from semiconductors composed of organic polymers.
Millions of photodiodes can be combined into a twodimensional photodiode array (Figure 13-5). A photodiode
array captures images and converts them into electrical
signals. The current emerging from each photodiode in the
array is related to the light intensity that strikes that photodiode. Each photodiode acts as a picture element or pixel.
There should be a one-to-one correspondence between the
brightness of a point in the specimen and the current that
emerges from the photodiode in the corresponding pixel.
Currently, Cannon markets a digital camera (EOS 1Ds Mark
1, 27, 255, 12
ADC
Serial register
Imaging area
21 million pixels
One
picture
element
pixel
FIGURE 13-5 Millions of photodiodes in an array. Each photodiode
constitutes one pixel.
Incoming light
Electrical connection
Polysilicon
Gate
Silicon dioxide
e e
e
e
e
e
e
Silicon
Potential well
FIGURE 13-6
Diagram of a charge-coupled device (CCD).
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Chapter | 13 Video and Digital Microscopy
Currently, Hasselblad produces a CCD with 39 million
pixels in a 36 mm 44 mm chip. Each pixel has a pixel pitch
of about 6.8 μm. When light strikes a pixel in a CCD, it produces a free electron. An electrical potential is applied across
each pixel so that the electrons freed by the photons flow
from the silicon into a potential well where they are stored.
The charge created by the light is stored until the well is
discharged. When the well is discharged, the electrons flow
from the potential well through a buried channel to the output of the CCD. The information from each pixel in a CCD
chip must be transferred to a memory chip (Figure 13-7).
This happens in a full-frame CCD, when the shutter closes
and a sequence of voltage pulses cause the charge in each
pixel of a parallel array, which is also called the parallel shift
register, to be transferred one row at a time until it reaches
one edge of the chip known as the serial shift register. One
row of pixels at a time is transferred from the parallel register
to the serial shift register. The charge travels down the serial
shift register pixel by pixel, and then the charge of each pixel
is converted to a voltage by an amplifier. The shutter then
opens so that the next image can be acquired.
The full-frame transfer CCD is relatively slow, and
consequently reliable images can be obtained only for slow
or static processes. Some CCDs, with frame-transfer rates
of 4 to 5 frames/second, work well under low-light conditions. The charge stored in the wells of these cameras is
proportional to the product of the image intensity and the
integration time. The slow cameras are also extremely precise because they use high-resolution electronics that are
relatively slow; however, the precision electronics limit the
temporal resolution.
Typical CCD sensors produce 30 complete images per
second, which is what we perceive as real time. In order
to capture images in real time, an interline transfer CCD
can be used (Murphy, 2001). Interline transfer CCDs have
alternating columns of imaging pixels and light-insensitive
data-transfer columns. After image acquisition, the data
from each imaging column is transferred to the data-transfer
columns. In progressive scan cameras, the data-transfer
columns are read from the top of the chip to the bottom.
When each data-transfer column is read, the charges in each
data-transfer column are transferred to the serial shift register. The charge travels down the serial shift register pixelby-pixel, and then the charge of each pixel is converted to a
voltage. While the data are being transferred, a new image
is acquired by the pixels in the imaging columns. Image
acquisition and data-transfer take less than 1/30 s.
Under low light conditions, too few electrons are stored
in the CCD potential cells and the signal-to-noise ratio will
be too low. The signal-to-noise ratio can be increased at the
expense of spatial resolution by combining the electrons
in neighboring pixels. This process is known as binning
(Figure 13-8).
In a digital CCD camera, the voltage output from the
serial register is digitized. That is, the voltage is converted
into a series of integers that represent the spatial distribution of light intensities. These numbers then are transferred
to a computer for processing and display. The bit-depth
Voltage
Output node
Time
Serial register
0, 2, 4, 2, 0
Parallel register
ADC
FIGURE 13-7
Producing a voltage signal by reading out a charge-coupled device.
8 μm
4 μm
1 1 binning
12 μm
8 μm
4 μm
2 2 binning
12 μm
3 3 binning
FIGURE 13-8 If the light intensity is too low, the electrons from neighboring wells can be combined in a process called binning. Binning increases
the speed and decreases the spatial resolution of the imager in a way analogous to increasing the speed and decreasing the spatial resolution of film by
making larger grains.
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Light and Video Microscopy
Exposure
Charge transfer
and digitization
Transfer to
computer memory
Image display
Total time
Total system throughput FIGURE 13-9
# of pixels
total time
Diagram of the processes that contribute to the total system throughput.
of the imaging chip determines the number of distinct
shades of gray in which the intensity of each pixel can be
expressed. The bit-depth of an n-bit analog-to-digital converter (ADC) is equal to 2n. That is, an 8-bit, 10-bit, 12-bit,
16-bit, and 24-bit analog-to-digital converter produces 256,
1024, 4096, 65,536, and 16,777,216 shades of gray.
There are a number of ways to make a color CCD
camera. One way is to spin a red, green, blue filter wheel
over a single chip and capture three separate and sequential images that can be combined to give a full-colored
image. Another way is to use a beam splitter that splits the
incident light into three images that fall on three different
chips, each one covered by a red, green, or blue filter. In
a third method, each pixel is composed of three subpixels,
one that is covered by a red filter, one that is covered by
a green filter, and one that is covered by a blue filter. In
the latter case, the voltage output of each subpixel goes
through an 8-bit analog-to-digital converter to yield a
24-bit color-depth, giving 256 256 256 16,777,216
different colors. Twenty-four bit color images can be stored
as tagged image file format files (tiff).
The speed in which the signal is converted from the
start of the light exposure to the final image display is
known as the system throughput. The system throughput
depends on the number of pixels and the number of frames
per second. The system throughput is the number of pixels
on the chip divided by the amount of time needed to display the image. A system with a throughput rate of 65,000
pixels/second can display an image from a 1.6 megapixel
chip in about 25 seconds. One with 650,000 pixels/second
can display the same image in 2.5 seconds. To display this
image in real time (1/30 s) would require a throughput of
48 106 pixels per second (Figure 13-9).
Video cameras still prove to be the best option for capturing images for extended lengths of time. The imager in
a video camera is either a CCD chip, whose signal output
has not been digitized, or a vacuum tube. Vacuum tubes,
originally known as Crooke’s tubes or cathode ray tubes,
are the oldest form of technology used to convert light
intensities representing an image into electronic signals.
Photomultipliers are very sensitive light detectors made of
vacuum tubes. Photons cause the emission of electrons from
a photocathode placed in a vacuum tube. The photocathode
is coated with a material whose work function is low enough
to allow electrons to be released by photons in the ultraviolet and visible range. An applied voltage causes the electrons
Voltage
Time
0V
RL
A
D
D
D
D
D
D
hν
C
1 kV
FIGURE 13-10 Diagram of a photomultiplier tube. Anode (A), dynode
(D) and cathode (C).
to flow toward the anode, creating a current that is correlated
with the light intensity. The photocurrent is then amplified
by secondary emission by placing dynodes between the
cathode and the anode.
The dynodes have potentials intermediate between the
cathode and anode. When an electron is accelerated toward
the first dynode, it strikes it with enough kinetic energy
to release two or more secondary electrons from the dynode surface. These secondary electrons are attracted to the
next dynode surface and hit with enough kinetic energy to
release two or more electrons for each incoming electron.
This process continues until the original electron from the
photocathode causes the release of 106 electrons from the
final dynode. Thus the original signal is amplified approximately one-million times (Figure 13-10)!
Philo T. Farnsworth and Vladamir Zworykin, among others, converted the vacuum tube into a video imaging tube by
adding a light-sensitive layer (Farnsworth, 1989; Godfrey,
2001; Swartz, 2002). The light sensitive layer in video tubes
can be made from a variety of light sensitive materials,
213
Chapter | 13 Video and Digital Microscopy
Focusing
coil
Faceplate
Photoconductive
layer
Dielectric
layer
Electron path
Electrode
Cathode
(electron gun)
Deflecting
coils
FIGURE 13-11
Camera tube
Diagram of a typical video tube.
including CdSe (Chalnicon), CdZnTe (Newvicon), PbO
(Plumbicon), SeAsTe (Saticon), Si (Silicon or Ultricon), or
Sb2S3 (Vidicon or Sulfide Vidicon). The light-sensitive layer
is enclosed in a vacuum tube that is usually two-thirds to
1 inch in diameter and 4 to 7 inches long (Figure 13-11). The
light-sensitive layer is placed at the front end of the tube. The
light-sensitive layer is a sandwich that consists of a back-plate
electrode, the dielectric layer, and the photoconductive layer.
The electron gun (or cathode) produces electrons that
are accelerated toward the light-sensitive layer by placing
a positive voltage (10–100 V) between the cathode and the
back-plate electrode. The electrons are focused and guided
by focusing, alignment, horizontal-, and vertical-deflecting
coils. The electron beam forms a small focused spot on the
target. The small focused spot defines the size of the pixel
(Figure 13-12).
Farnsworth, who grew up on a farm, got the idea of
scanning the beam across the tube from his day-to-day
image of the back and forth motion used to plow a field.
In a video camera, the horizontal- and vertical-deflecting
coils sweep the beam across the target. As the beam sweeps
across the target, it charges the back surface of the photoconductive layer with electrons. In the dark, the photoconductive layer acts as an insulator so that the electric charge
remains on the back surface of the photoconductive layer.
However, when light strikes the photoconductive layer,
the resistance of the layer drops as electron-hole pairs are
created. The decrease in resistance is proportional to the
intensity of illumination.
Since the back-plate electrode is 10 to 100 V more positive than the cathode, the electrons begin to flow through
the photoconductive layer once light causes the resistance
to drop. The flow of current is then proportional to the
intensity of illumination. The amount of current that flows
in response to the incoming intensity of light is known
Target
Grid
Signal
current
i
Heated cathode
Electron
beam
R
Video signal
voltage
10100 V
Target voltage
supply
6.3 V
Heater
power
supply
FIGURE 13-12 Diagram of how a video tube creates the voltage signal
of each pixel.
as the responsivity of the tube. It is measured in μA/lm
per ft2 at 2854 K. The positive current flows from the positive terminal of the power supply (as defined by Benjamin
Franklin) through a resistor, through the back-plate electrode, the dielectric layer, the photoconductive layer, the
electron beam, the cathode, and then to the negative terminal of the power supply. Of course, the electrons actually move in the opposite direction. The current (I) flowing
through the resistor (R) gives rise to the output voltage (V)
according to Ohm’s Law (V I R).
The horizontal- and vertical-deflectors drive the raster. In
general (in the 525/60 NTSC scan mode), the raster lands
on a particular point on the target every 1/30 of a second.
Therefore the given point or pixel accumulates light for
1/30 of a second (33.3 ms) and thus acts as an integrator of light intensity information by storing electron-hole
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Light and Video Microscopy
pairs. The resistance decreases over this period, but current
is not allowed to flow until the electron beam completes the
circuit. When the electron beam lands on that pixel, current
flows and an output voltage is created for that pixel. As the
current flows, the electron beam simultaneously recharges
the pixel and the resistance becomes high again.
A video camera converts a two-dimensional optical
image into a sequence of electrical pulses (Figure 13-13).
The magnitude of the pulse represents the intensity of the
pixel and the temporal position of the pulse represents
the spatial position of the pixel in the image. The image
is scanned from left to right in a series of horizontal scan
lines that move from top to bottom. If the scan starts at A
it moves to A. Then it is made to fly back to the beginning
of the next scan line B. The fly back is much faster than the
image scan and the signal is blanked out during this period.
The blanking prevents the fly back trace from contributing
to the signal.
The image is scanned so that every other line of the
frame is converted into an electrical signal. Then the intervening horizontal lines are scanned and converted into an
electrical signal. The two scans are then interlaced. This
format is known as a 2:1 interlace. Thus two fields obtained
at 1/60 s give rise to one frame that is made in 1/30 s.
Spatial coordinates
A
B
B
C
C
D
D
N
N
Picture is brighter
Y
A
Electrical signal (volts)
X
a
a
b
b
c
c
d
d
n
n
Time
(b)
(a)
FIGURE 13-13 (a, b) Transformation of an optical image composed of
points with different intensities into an electrical signal, whose amplitude
at each point in time represents the intensity of a point in space.
Voltage
The information about the scan rate is carried in the
electrical signal that leaves the video camera. The horizontal (H) and vertical (V) sync pulses are inverted relative to the image signal so they can be distinguished from
the image signal when they are combined to form the composite video signal. The composite video signal is 1.0 V
peak to peak, where 0.286 V is used by the sync signal and
0.714 V is used by the image signal (Figure 13-14).
The number of horizontal scan lines in a video camera determines, in part, the vertical resolution of a camera
(Figure 13-15). A typical video camera has 525 horizontal
scan lines. This would be enough to distinguish 525 TV
lines, which is equivalent to 263 black lines on a target separated by 262 white lines. However, the vertical resolution
of video cameras in practice is not equal to the number of
horizontal scan lines but is related to the number of horizontal scan lines multiplied by a factor known as the Kell
factor, which is typically 0.7. Consequently, the vertical
resolution of a typical video camera is about 368 TV lines.
It is easy to see why the vertical resolution of tube
cameras is actually smaller than the number of scan lines.
A test object, composed of three alternating horizontal bars,
where each bar and each space between the bars is the
height of a scan line, will be resolved by a video camera
only if the bars and spaces coincide exactly with the scan
lines. But if the bars fall equally across two scan lines, the
three bars will be unresolved.
The 525 horizontal lines are scanned in 1/30 of a second, which means that 15,750 lines are scanned in one
second and it takes 63.5 μs to scan each line. To have a
horizontal resolution of 400 TV lines, which is approximately equivalent to the vertical resolution, the electronics
would have to scan each vertical TV line in about 160 ns.
By convention, a video camera can scan 15 TV lines accurately in 1/30 s, but the accuracy decreases as the lines get
closer and closer together, because the electronic circuits
in the camera are not fast enough to follow the rapid spatial changes in contrast. Consequently, while the voltage
output of a video camera imaging a test pattern composed
Picture signal
0
Time
H blank
H-Sync
pulse
Time
Sync pulses
FIGURE 13-14
Picture
black level
0
0.3
Time
0
Voltage
Signal (volts)
Composite video signal
0.7
H
Generation of a composite video signal.
63.5 μsec
215
Signal voltage
Chapter | 13 Video and Digital Microscopy
(a)
Vertical sweep
FIGURE 13-15 The vertical resolution is smaller than we would predict
from the number of scan lines because it depends how the image on the
imaging surface aligns with the scan lines.
Low (RC)
Rise time
(b)
90%
High (RC)
10%
Rise time
(c)
Voltage
Optimal
(RC)
A
Rise time
Time
Q
(d)
FIGURE 13-17 Increasing the resolution of the video camera by adjusting capacitors and resistors that influence the rise time. Square wave
of object (a), under-compensated (b), over-compensated (c), optimally
compensated (d).
P
Amplitude response P/Q (%)
FIGURE 13-16 Mask used to determine the resolution of an imagine
device (A), the ideal electrical response (Q), and the actual electrical
response (P).
of alternating black and white lines should be a square
wave, in reality, it is a saw-tooth wave (Figure 13-16). This
means that the contrast falls as the width of the black bar
decreases. The resolution of the camera can be increased
by adjusting the capacitance and resistance of the amplifier, which decreases the time constant of the circuit so
that the rapid changes in intensity can be followed more
faithfully (Figure 13-17). The downside to increasing the
resolving power of the amplifier is the addition of more
noise. The modulation contrast function (MTF) can be
used to quantify the resolving power of a video camera,
just as it was used to quantify the resolving power of film
(see Chapter 5).
The Modulation Transfer Function (MTF) is a measure
of how faithfully the image detail represents the object
detail (Young, 1989). Here, the modulation transfer function relates the actual peak-to-peak amplitude of the video
output for a target with any number of TV lines across the
imaging surface (P) to the peak-to-peak output for 15 TV
lines across the imaging surface (Q). Remember, the modulation transfer function is given by:
MTF (Hmax Hmin )/(H max min )
(Hmax Hmin )/(H max H min )
where H is the ideal amplitude of the output and H is the
actual amplitude of the output. The subscripts min and
max represent the minimum and maximum amplitudes,
respectively. This equation usually is multiplied by 100%
to give the amplitude response in percent. The resolution
of a video camera is often given as the amplitude response
(P/Q 100%) at 400 TV lines (Figure 13-18).
How good does the resolution of a video camera have
to be in order to utilize the full resolving power of the
microscope? Let us consider that we are using a 63x/1.4
NA objective lens and a 3.2x projection lens to view an
object with 546 nm green light. The limit of resolution will
be, according to the Rayleigh Criterion:
d im 1.22λ/(2NA) 1.22(0.546 μm)/((2)(1.4))
0.2379 μm
0.2379 μm 0.0002379 mm
4203 line pairs per mm 4203 l pm
8406 TV l ines/mm
As a result of the magnification produced by the objective lens (63x) and the projection lens (3.2x), the limit of
216
Light and Video Microscopy
Amplitude response (%)
100
A
50
B
D
C
0
0
100
200
300
400
500
600
700
TV line number
Resolution ABCD
FIGURE 13-18
of TV lines.
Graph depicting the amplitude response versus number
resolution at the image plane will be 8406/[(63)(3.2)] or
41.7 TV lines/mm. This is equivalent to 1059 TV lines in a
camera with a 1-inch imaging surface.
Typically, tube video cameras do not have the required
resolution. In order to fully utilize the resolving power of
the microscope, the magnification of the projection lens has
to be increased. We can also relate the pixel pitch of digital
camera to the number of TV lines. A solid state CCD or
CMOS imaging chip with a pixel pitch of 7 μm would be
able to resolve about 428 TV lines per mm. This is more
than sufficient resolving power to utilize the full diffractionlimited resolving power of the light microscope.
The limiting horizontal resolution of a video or digital camera depends on the light intensity. Normal cameras
may have better resolving power than low-light intensity
cameras at normal light intensities, but the low-light intensity cameras will have better resolving power than the normal camera at low-light intensities. This is because the
normal camera will not be able to produce any contrast if
the light intensity is too low to activate the imaging surface.
The signal output of a video camera depends on the
intensity of light at the faceplate of the camera. The slope
of this function, which relates the log of the signal output to
the log of the signal input, is called the gamma of the video
camera. The gamma is determined by the composition of
the light-sensitive material and varies from 0.4 to 1.0. Many
video cameras have a gamma of 0.4, which gives them a
greater flexibility to capture images throughout the whole
dynamic range of light intensities. Other video cameras
with a gamma of 1.0 are ideal for quantitative work.
The dynamic range expresses the range of intensities on
the faceplate to which the video camera responds meaningfully. Below the dynamic range, the signal is indistinguishable from the noise. Above the dynamic range, the camera
is saturated and an increase in light intensity does not give
rise to an increase in the signal output. The dynamic range
is expressed as the ratio of maximum and minimum useful intensities and is typically 70:1 to 100:1, although it
can be as high as 100,000:1 for a CCD used in astronomy.
The dynamic range curves are similar to characteristic
curves (H-D curves) for film (see Chapter 5). The dynamic
range of video camera can be varied with the gain control. The gain control may be manual or automatic. The
automatic gain control (AGC) keeps the brightness of the
image constant as the light intensity changes. Initially this
is very helpful for qualitative work, but the automatic gain
control must be shut off for quantitative work.
The imaging surfaces produce random signals at room
temperature, because the band gap energy is not that much
greater than the ambient thermal energy. A video camera
can be cooled with liquid nitrogen or by thermoelectric
Peltier coolers to reduce the thermal noise. This is particularly useful when doing low-light level microscopy.
Because of the finite nature of the band spectra of
semiconductors, a given imaging surface does not respond
equally to each and every wavelength. This must be considered when doing quantitative microscopy with more
than one color of light.
The consumer electronics market has driven the development of digital imaging devices for still and video cameras and has moderated the costs. Consequently, for most
applications, video and digital cameras marketed to the
home electronics consumer may not only be less expensive but actually may be superior to the cameras that are
developed for the scientific market, given that the cameras developed for the scientific market are often out of
date before they even reach the market. This is especially
true when considering cameras that will connect to rapidly
evolving computers running on rapidly evolving operating
systems. However, when the light microscopist is interested in specimens moving at high speeds or specimens
emitting low-intensity fluorescent light, he or she should
shop for a good scientific video or digital camera.
MONITORS: CONVERSION OF AN
ELECTRONIC SIGNAL INTO AN OPTICAL
SIGNAL
The image of the microscopic specimen taken by a video or
digital camera can be viewed on a monitor or on a hardcopy
printout. A monitor reverses the process that takes place in a
video or digital camera by converting an electric signal into
light (Figure 13-19). The vacuum tube-type video monitor
is essentially the reverse of the video tube camera and has
many of the same properties and features. A television can
be used as a video monitor, but the video signal will first be
converted into an RF signal. The RF signal has a lower bandwidth than the video signal and will thus limit the resolution.
The cathode ray tube type monitor contains a heated
cathode, which is located in the neck of the picture tube. The
heated cathode gives off a beam of electrons. The electron
beam is accelerated by a high voltage anode. The electron
beam is then focused on the phosphor screen, which is just
217
Chapter | 13 Video and Digital Microscopy
Phosphor
coating
Heated
cathode
Beam current
control grid
(a)
Faceplate
Apparent noise
Electron
beam
Deflection
region
(b)
Anode
R
FIGURE 13.19 A monitor converts an electrical signal into an optical
image.
under the faceplate of the picture tube. The accelerated electrons land on the phosphor screen and the screen gives off
light. The position of the electron beam is controlled by the
horizontal and vertical sync signals of the composite video
signal. The brightness of the phosphor varies with the accelerating voltage and the current of the beam. The magnitude
of the beam current is regulated by the amplitude of the
video signal part of the composite signal. The amplitude of
the video signal controls the beam current by controlling the
beam current control grid.
The brightness of the monitor is not linearly proportional to the signal input. The brightness (I) is related to
the signal (S) by the following formula:
I Sγ
where γ is the gamma of a monitor and is usually between
2.2 and 2.8. The gamma of the monitor compensates the
gamma of “television cameras,” whose gamma is typically
0.45 and provides a camera operator with a large dynamic
range. The nonlinear response of the monitor is good for a
qualitative image but not for quantification. The image can be
enhanced by using the brightness and contrast controls. These
controls help to realize the maximal resolving power of the
monitor (Figure 13-20). Cathode ray tube (CRT) technology
has been shrunk to the size of a pixel. Image-viewing panels
that are made from arrays of pixel-sized cathode ray tubes are
known as surface-conduction electron-emitter displays (SED).
The need for displays on home computers and high definition televisions has driven the development of new and
better display technologies. Now images can be viewed on
liquid crystal displays (LCD) and plasma display panels
(PDP). The pixels in an LCD are composed of liquid crystals sandwiched between parallel polars. The liquid crystal
is a birefringent polymer that can be oriented in an electric
field. In the absence of an electronic signal, the crystal is
oriented so that no light passes through the crossed polars
and the pixel is black. The greater the voltage, the brighter
(c)
FIGURE 13-20 The brightness (offset or black level) and contrast
(gain) controls on a monitor lets you process the image to get maximal
resolution. Original signal (a). Signal after increasing the contrast (b) and
decreasing the brightness (c).
the pixel is. A colored filter is placed after the second polar
to make a colored pixel. It takes one red, one blue, and one
green subpixel to make up a pixel.
The pixels in a plasma display panel are filled with
a nobel gas, like neon or xenon. In the absence of an electronic signal, the gas in un-ionized and no light is emitted
from the pixel and the pixel is dark. In the presence of an
electronic signal, the gas becomes ionized and the ions collide with a phosphor, which then emits light. The greater
the voltage, the more the gas is ionized and the more
bright the pixel is. A color pixel is generated by combining
a subpixel containing a red phosphor, a subpixel containing
a blue phosphor, and a subpixel containing a green phosphor.
A hard copy of the image can be made with the aid of
a digital printer. The resolution of the picture is determined
by the number of dots per mm (typically given in dots/inch
or dpi). Currently, the spatial resolution of a good ink jet
printer (e.g., Canon PIXMA Pro9000) is about 4800 2400
dpi, which is equivalent to 189 94 dots per mm. Each dot
is composed of a number of colors, so the resolution of the
printer has to be divided between the number of inkjets used
to make a single dot. In the 4800 2400 dpi printer described
earlier, a single dot is composed of eight colors. Thus, the
resolution is actually 24 12 dots per mm. This is equivalent
to 0.04 0.08 mm between dots, which is almost at the limit
of resolution of the human eye (0.07 mm between dots). The
color depth of the printer is 6,144 colors. The consumer digital photography market is driving printer development, and
the technology used in the printer as well as quality of the
paper and the permanency of the ink are improving.
STORAGE OF VIDEO AND DIGITAL IMAGES
Hours and hours of video images can be recorded by videocassette recorders (VCR) and stored on videotapes.
218
Light and Video Microscopy
Video
camera
Time-date
generator
E-to-E
For more widespread and in-depth coverage on video
and digital imaging, see Inoué (1986), Inoué and Spring
(1997), and Murphy (2001).
WEB RESOURCES
Monitor 1
HI-Z
Video and Digital Cameras
E-to-E
Microscope
Processor
75 Ω
Monitor 2
75 Ω
Recorder
E-to-E
75 Ω
FIGURE 13-21 Diagram for connecting video components together.
Digitized images can be stored conveniently on computer
hard drives, compact discs (CDs), digital video discs
(DVDs), or any mobile memory stick with sufficient storage capacity. The images can be stored as is with no loss
of resolution or with reduced resolution by compressing
the images to save memory space.
CONNECTING A VIDEO SYSTEM
Digital imaging devices are connected to a computer
through a FireWire or USB cable. Transferring analog
signals require a little more care, since the last cable that
passes a video signal must be set at a termination impedance of 75 Ω in order to maintain a 1.0 V peak-to-peak
voltage of the composite video signal (otherwise the highlights will be distorted and ghosts will occur). All other
connections must be set at high impedance or Hi-Z. Video
processors and videotape recorders are exceptions to this
rule since they generate new video signals (Figure 13-21).
Low Light Intensity Cameras: (http://www.rulli.lanl.gov/) and http://www.
dagemti.com/?pageproduct_detail&product_idVE-1000-SIT
High Speed Cameras: (http://www.delimaging.com/products/ultrahs.htm)
High Resolution Cameras: http://www.dpreview.com, http://www.hasselblad.com/products/h-system/h3d.aspx, and http://www.manufacturingtalk.com/news/kne/kne118.html
Review of Digital Cameras: http://www.imaging-resource.com/
DIGCAM01.HTM
Dage-MTI: http://www.dagemti.com/
Diagnostic Instruments: http://www.diaginc.com/cameras/
Fairchild Imaging: http://www.fairchildimaging.com/products/cameras/
scientific/index.htm
Hamamatsu Photonics: http://jp.hamamatsu.com/en/product_info/index.html
Lumenera: http://www.lumenera.com/scientific/index.php
Optronics: http://www.optronics.com/
Princeton Instruments: http://www.piacton.com/
Optical Couplers for Mounting Digital
Cameras on Microscopes
Edmund Optics: http://www.edmundoptics.com/onlinecatalog/Display
Product.cfm?productid241
The Microscope Depot: http://www.microscope-depot.com/digadapt.asp
Microscope Vision and Image Analysis: http://www.mvia.com/Coolpix/
clpxadpt.htm
Great Scopes: http://www.greatscopes.com/photo.htm
ScopeTronixs: http://www.scopetronics.com/mvp.htm
Printers
http://www.imaging-resource.com/PRINT.HTM
Chapter 14
Image Processing and Analysis
The seventeenth and eighteenth century microscopists
hand-drafted the images they saw under the microscope. The
images were subsequently engraved onto copper plates and
printed (Espinasse; 1956; Harwood, 1989; Bennett et al.,
2003; Cooper, 2003; Chapman, 2004; Jardine, 2005). The
nineteenth and twentieth century microscopists, including myself, used photography to document microscopic
observations and to enhance contrast. However, when taking photographic images, we had to process the film and
develop the prints before we could become aware of the
quality of the image and before we were able to share the
image. By the time we saw the first photograph, the specimen was most likely dead, or otherwise unavailable for
taking better pictures with optimal contrast and resolution.
Analog and digital processing allows instant feedback so
that we may optimize the contrast and resolution in real time.
In addition, measurements on the image that extract a tremendous amount of quantitative data, or image analysis, can
be done on digitized images with high temporal and spatial
resolution. Analog and digital image processing have been
very welcome additions for the light microscopist (Walter
and Berns, 1986; Bradbury, 1988, 1994; Moss, 1988).
ANALOG IMAGE PROCESSING
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
Video
camera
Raster scan
of image
Analog
signal
FIGURE 14-1 A video camera converts intensities into voltages.
Volts out
2.0
M 2.5
M 2.5
1.0
M1
0
M 0.5
M 0.5
0.5
M1
1.0
Outgoing signal
Time
Volts in
Incoming signal
Above the atomic level, nature is continuous and analog, and
unless we are working at the single photon limit, the intensities of light coming from the specimen are continuous and
analog. Analog video cameras are used for many applications that require low light or require capturing images in
rapid succession with high resolution. Even when we plan
to convert information from the microscope into a digital image, we must first make sure that the analog signal is
optimized to take full advantage of the dynamic range of the
analog to digital converter. In fact, the introduction of digital technology has created the need for more and more varied analog circuits (Zumbahlen, 2008). We must understand
how the components of those circuits can affect, both positively and negatively, the signal that is being processed.
An analog video camera transforms an optical signal into
an analog electrical signal, which temporarily stores information about the light intensities of the image projected on the
camera. Information of a two-dimensional image is stored
in the amplitude of the electrical signal and the positional
information is stored, along with the sync signals, in the
length of the electrical signal (Figure 14-1). Once the intensities of the image are encoded in an electrical signal, it is
possible to use all the technology available in electrical
amplifiers to enhance the image. Analog image enhancement lets us adjust the contrast in an image by manipulating
the gray levels of neighboring pixels. Contrast is defined as
the difference in brightness or color of two nearby pixels.
For simplicity, consider that the object is a stepped gray
wedge with equal contrast between each step. The video output signal that arises from this object can be amplified with
a linear amplifier so that the output signal is proportional
FIGURE 14-2
intensities.
Linear amplification of an electrical signal that represents
219
220
Light and Video Microscopy
to the input signal (Figure 14-2). When the amplifier has a
gain of 1.0, the contrast of the video image is the same as the
contrast of the optical image focused on the video camera.
When the gain is greater than one, the contrast of very small
details that lose contrast due to the process of video scanning
is increased. When the gain is less than one, the large details,
whose contrasts are not lost through the scanning process,
are made more visible. Thus, a linear amplifier can selectively enhance the contrast of small or large details in the
specimen. The following equation relates the output signal
(in volts) of a linear amplifier to the input signal (in volts):
Volts out
1.0
0.5
0
0
0.5
1.0
Volts in
Outgoing signal
Time
output signal m(input signal)
output signal (input signal)γ
We can decrease the brightness of the image by adding negative voltages to the video signal. In doing so,
we redefine the black level. Normally signal voltages of
0 volts produce a black image. After adding 0.5 volts
to the video signal, all input values less than 0.5 volts become
black. By changing the baseline, we can increase the contrast between two neighboring bright points.
output signal input signal b
where b is the offset voltage.
By varying the gain, the gamma, and the offset, we
can selectively increase the contrast of any given region of
interest in the image and the output signal will be related
to the input signal by the following equation:
output signal m(input signal)γ b
We can reverse the polarity of the video signal and cause
the bright regions to become dark and the dark regions to
become bright. The polarity control causes the input signal to
be multiplied by 1 and then 0.7 V is added to the product.
In this way, bright regions with an input signal of 0.7 volts
give an output signal of 0 volts, and dark regions with an
input voltage of 0 volts give an output signal of 0.7 volts. The
polarity control allows us to see different details in a manner
analogous to how a negative phase-contrast objective brings
out different details than a positive phase-contrast objective.
It is also possible to pass the signal through amplifiers
with more than one stage so that the contrast of any given
detail can be enhanced (Figure 14-4).
output signal m 2 [m1 (input signal)γ1 b1 ]γ 2 b 2
Incoming signal
where m is the gain of the linear amplifier.
A nonlinear amplifier can selectively enhance the
bright regions or the dark regions. The degree of nonlinearity of an amplifier is characterized by the gamma (γ) of the
amplifier (Figure 14-3). A linear amplifier has a gamma of
1.0. When gamma is greater than one, the contrast between
the brighter regions of the image is expanded. When
gamma is less than one, the contrast in the darker regions
of the image is enhanced.
With a nonlinear amplifier, the output signal is related
to the input signal according to the following function:
FIGURE 14-3 Nonlinear amplification of the electrical signal that represents intensities.
Although it is possible to adjust knobs and turn switches
to create an image that has little relationship to reality, this
is not the goal of analog image processing. Remember back
to the time I discussed aberrations (in Chapters 2 and 4). An
optical image produced by a single lens contains chromatic
and spherical aberrations. These aberrations are mitigated by
adding additional lens elements to correct the aberrations produced by the original imaging lens of the objective. Moreover,
the objective lens can be considered an analog computer that
diffracts the light coming from the specimen imperfectly
and turns points in the specimen into Airy disks at the image
plane. Therefore, if we used only a single lens to make an
image, we would have a distortion of reality. The distortions
of reality can be corrected either optically or electronically.
Both types of corrections are not “cheating” as long as we
take the advice given in Plato’s Allegory of the Cave (see
Chapter 1), act more like the line than the squiggle in The Dot
and the Line (Juster, 1963), and understand the relationship
between the object and the image. This is the reality of distortion. Using an analog image processor to correct an image
is much like using an equalizer with a stereo to recreate
the sound of the recorded music in a living room or car.
We can use an analog image processor to produce a
pseudo-relief image by differentiating the input signal
(Figure 14-5). Differentiating the video input signal will
brighten one side and darken the other side of the image
of an object with gradients in light absorption. The image
will look like those produced by using oblique illumination,
differential interference contrast, Hoffman modulation
contrast, or single-sideband edge enhancement optics.
221
Chapter | 14 Image Processing and Analysis
White level
Black
level
FIGURE 14-4
Examples of complex processing of the electrical signal that represents intensities.
V
V
dV
dt
dV
dt
Time
FIGURE 14-5 Taking the first derivative of the electrical signal produces a pseudo-relief image.
d2V
dt2
The fidelity of the video signal that emerges from
an analog camera depends on the size of the object; the
smaller the object, the less faithful is the video scan, and
signals that should look like square waves appear as sawtooth waveforms. We can use a sharpening filter to sharpen
an image with an analog image processor. This works by
taking the second derivative of the signal, inverting it, and
adding the inverted, second derivative signal back to the
original signal. This produces an image that more faithfully represents the object (Figure 14-6).
Operational amplifiers or op-amps, combined with
a few electronic parts can be used to control the gain,
gamma, offset, and polarity of the video signal. Operational
amplifiers can also be used to differentiate and integrate
the video signal. Op-amps are high gain amplifiers (Figure
14-7). They are relatively simple integrated circuits that
contain approximately 24 transistors, 11 resistors, and a
capacitor.
I will present a few simple cases in order to describe
how op-amps can modify the video signal voltage. An
op-amp has two input terminals and one output terminal.
d2V
dt2
Time
FIGURE 14-6 Taking the second derivative of the electrical signal and
subtracting it from the original signal sharpens the image.
VInput
Voutput
Op - amp
FIGURE 14-7 An operational amplifier.
222
Light and Video Microscopy
An op-amp can be treated as a black box that obeys two
golden rules (Horowitz and Hill, 1989):
●
●
The output of an op-amp does whatever is necessary to
make the voltage difference between the inputs zero. It
does this through a feedback circuit.
The two inputs of an op-amp draw no current.
I will describe how an op-amp can work as an inverting
amplifier (Figure 14-8) using the golden rules and Ohm’s
Law (E IR).
Since B is at ground, Rule I1 says that the amplifier
will do everything necessary to make the input voltage A,
which is connected to the feedback loop, the same voltage as ground (i.e., 0 V). This means that the voltage drop
across resister R1 (the input voltage, Vin) is cancelled by
the voltage drop across the resistor R2 (the output voltage,
Vout). In order for VA to be equal VB, Vout must have the
opposite sign of Vin.
Vin /R1 Vout /R 2 0
Vout /R 2 Vin /R1
Thus the amplifier gain (VoutVin) is given by the following
relation:
gain Vout /Vin R 2 /R1
If R2 and R1 were equal, then the gain would be 1
and the output would be inverted. If R2 were twice as large
as R1, the gain would be 2, if R2 were half as large as R1,
the gain would be 0.5.
Figure 14-9 is an example of a noninverting amplifier.
Again by Golden Rule I, Vin must equal VA; but, what does
VA equal? VA comes from a voltage divider as shown in
Figure 14-10. According to Kirchhoff’s current rule, there
can be no “build-up” of current at a connection. Thus the
current at VA must equal the current coming from Vout.
I VA /R1 Vout /[(R1 R 2 )]
We can now solve for VoutVA, which is:
Vout /VA (R1 R 2 )/ R1
and since VA Vin, according to Golden Rule I,
gain Vout /Vin (R1 R 2 )/R1
gain Vout /Vin 1 (R 2 /R1 )
As long as R2 R1, the gain of the noninverting
amplifier is given by R2/R1.
When the output of the op-amp and the negative () terminal is connected with a wire, then R2 0, R1 infinite,
and we get an amplifier with unity gain (Figure 14-11). Such
an amplifier can also be used to cause a slight delay in the signal. Since an electric field travels almost at the speed of light,
a current moving through a wire takes approximately 3 ns to
travel 1 m. It takes more time for a signal to travel through
an op-amp than through a wire the length of an op-amp.
When a video signal is split into two, and one signal is subtracted from the other after one is passed through an amplifier of unity gain, a pseudo-relief image will result (O’Kane
et al., 1990). Using combinations of op-amps, resistors,
and capacitors hooked together in various combinations, we
can get the derivative of a signal (Figure 14-12) where
Vout RC (dVin /dt)
Vout
R2
R2
R1
VIn
A
VA
VOut
B
R1
FIGURE 14-8 An operational amplifier configured to function as an
inverting amplifier.
VIn
VIn
VOut
VA
FIGURE 14-10 An equivalent circuit.
A
R2
R1
FIGURE 14-9 An operational amplifier configured to function as a
noninverting amplifier.
VOut
VIn
FIGURE 14-11 An operational amplifier configured as an amplifier
with unity gain.
223
Chapter | 14 Image Processing and Analysis
or we can get the integral of a signal
R
Vout (1/RC)Vin dt constant
R
Vin
using the combination shown in Figure 14-13. We can convert a logarithmic signal to a linear signal using a logarithmic converter (Figure 14-14). We can obtain the absolute
value of an input signal using an active full-wave rectifier
circuit (Figure 14-15). We can filter the signal with a low
pass filter (Figure 14-16), a high pass filter (Figure 14-17),
or a bandpass filter (Figure 14-18).
One or more video signals can be added together or
subtracted from one another using adder (Figure 14-19)
and subtractor (Figure 14-20) connections, respectively.
Analog image processing can be used to lower the contrast-limited limit of resolution of the light microscope
proposed by Lord Rayleigh to the diffraction-limited limit
of resolution proposed by Ernst Abbe. The only circuitry
needed to reduce the limit of resolution to the limit imposed
by diffraction is a gain (contrast) and offset (brightness)
control (Figure 14-21).
We can appreciate better and deeper how the optical
elements in a microscope “process an image” after we
R
FIGURE 14-15
of the input.
R
R/ 2
Vout
Operational amplifiers used to return the absolute value
C1
R1
R2
Vin
C2
Vout
R
R
FIGURE 14-16
Operational amplifier configured as a low pass filter.
C
Vin
R1
Vout
Vin
C1
C2
Vout
R2
FIGURE 14-12 An operational amplifier configured as a differentiator.
(K – 1)R
C
R
Vin
R
FIGURE 14-17
Vout
Operational amplifier configured as a high pass filter.
R2
FIGURE 14-13 An operational amplifier configured as an integrator.
C1
R1
Vin
Vout
C2
R3
C1
D1
R
Q1
Vin
FIGURE 14-18
R1
Operational amplifier configured as a band pass filter.
Io
Q2
B
Vout
V1
V2
R3
R2
1.0 k 15 k
FIGURE 14-14 Operational amplifiers configured as a logarithmic
converter.
V3
R1
R2
R3
R4
Vout
FIGURE 14-19 An operational amplifier configured as an adder connection.
224
Light and Video Microscopy
R2
V1
V2
R1
VOut
R1
R2
FIGURE 14-20 An operational amplifier configured as a subtractor
connection.
Use
offset
Increase
gain
FIGURE 14-21 Beating the Rayleigh criterion using the offset and gain
controls of an analog image processor.
understand the analogous process of signal conditioning by
analog components.
DIGITAL IMAGE PROCESSING
Just as analog image processing put the power and versatility of electrical amplifiers at our disposal for image
enhancement, digital image processing puts the power and
versatility of computers at our disposal for image enhancement and image analysis (Fleagle and Skorton, 1991). A
computer is an extremely powerful instrument and its image
processing capabilities are almost limitless, especially if
the user is able to program. In order to use a computer for
image processing, we must use a digital camera or digitize
the analog output from a video or analog CCD camera.
I will describe how to do digital image processing using two widely available digital image-processing
programs—Image Pro Plus and NIH Image J. Image Pro
Plus is a commercial digital image processor produced by
Media Cybernetics Inc. (www.mediacy.com), and Image J
is available from the National Institutes of Health as freeware (http://rsb.info.nih.gov/ij/). The National Institutes
of Health also produces a program known as NIH Image,
which can be used directly with a Macintosh computer
(www.rsb.info.nih.gov/nih-image/). A PC-compatible version that can be used with a frame grabber board from
Scion Corp is available free from Scion Corp (http://
scioncorp.com/index.html). Many other commercial programs are available for image processing and for performing
specialized techniques, including fluorescence resonance
energy transfer (FRET), fluorescence recovery after photobleaching (FRAP), fluorescence in-situ hybridization
(FISH), ratio-imaging, three-dimensional reconstruction,
tracking movement, deconvolution, and more. The processes described in this chapter will be found in most commercial image software packages. The commands will
have different, although similar names.
A digitizer in general converts an analog signal into
an array of numbers, where the array of numerical values
represents the spatial distribution of intensities in the optical image (Figure 14-22). The digitizer produces a discrete
value for each pixel that represents the light intensity at
each point in the optical image. The discrete number is
known as the gray value of the pixel. Digitizers produce
binary–coded gray values. The number of shades of gray is
known as the bit-depth. The bit-depth produced by a digitizer equals 2n, where n is the number of bits in the analogto-digital converter. The greater the number of bits in the
analog-to-digital converter, the more faithful is the image
in terms of shades of gray, but the longer it takes to digitize
each pixel. The number of colors that can be produced by a
color digitizer is known as the color-depth and is given by
2n, where n is the number of bits in the digitizer.
The numerical value of the brightness of each pixel can
be viewed using the BITMAP ANALYSIS command in the
Image Pro Plus processor. The length of the analog video
signal that must be sampled before the digitizer is able
to convert the information stored in the amplitude of the
video signal into an integer defines the size of a pixel. If
the digitizer is fast, the length of the video signal that must
be sampled is reduced and the spatial resolution of the
digitizer is improved. If the digitizer is slow, the length of
the video signal that must be sampled is increased and the
spatial resolution is worsened. The greater the bit-depth or
color-depth of a digitizer, the slower the digitizer. It is currently possible to have great spatial resolution and colordepth, but only if the images are produced at a rate of less
than 30 frames/second, which we perceive as real time.
According to sampling theory, the sampling interval
must be at least twice as fast as the smallest variation in
the analog signal that we want to resolve. This is known as
the Nyquist criterion (Shotton, 1993; Castleman, 1993). It
will be nice when 20 million pixels can be sampled in 1/30
second with 24-bit color-depth. For this to occur, the digitizer must be fast enough to digitize each pixel in 1.7 nanoseconds. This is equivalent to a throughput of 6 108 Hz
or 600 MHz.
Once the image is digitized it must be stored in an
active digital image memory known as a frame buffer.
Image processing boards, known as frame grabbers, typically have more than one frame buffer so that images can
be added to or subtracted from each other in real time.
Before an image is digitized, it is imperative to make sure
that the video signal that enters the digitizer has not saturated. This can be tested with the SIGNAL command in the
Image Pro Plus digital processor.
The SNAP command digitizes a single video frame
and places it in a frame buffer. The signal-to-noise ratio in
the digital image can be increased with the INTEGRATE
command, which gives an average value for each pixel in
the frames that it sums. The INTEGRATE command also
allows us to sum a given number of frames, but divide the
Chapter | 14 Image Processing and Analysis
225
FIGURE 14-22 The formation of a digital image.
summed pixel values by any smaller number of frames,
so that under low light conditions, the digital image processor acts as an integrator. There is a limit to the number
of frames that can be integrated when imaging a moving
specimen. A moving specimen will appear more and more
blurry as more and more frames get summed.
It is still possible to increase the signal-to-noise ratio
in a moving object by using the AVERAGE SEQUENCE
function. This function averages a number of frames, stores
the average as an image, then averages the same number
of frames again to make the next image. The AVERAGE
SEQUENCE is a good way to visualize movement. Digital
image processors are also capable of performing RUNNING
AVERAGES. With this function every time a new frame is
added to the average image of N frames, the oldest stored
image is lost. Although the RUNNING AVERAGEd image
may have the same number of frames as the AVERAGE
SEQUENCEd image, the RUNNING AVERAGE image
contains information from the last video frames and the
movement of the object will appear smooth, whereas the
AVERAGE SEQUENCE will show “jumping movement”
because n frames will be averaged, then the next n, then the
next n, and so on, and the object appears to jump from average position to average position. The running average is useful when smooth path data of a moving object is desired.
ENHANCEMENT FUNCTIONS OF DIGITAL
IMAGE PROCESSORS
I will describe a few functions of the Image J and the Image
Pro Plus software. In each description, the first command is
from Image J and the second command is from Image Pro
Plus. Other image processing programs will have similar
functions and command names. If you download the Image
J software and the accompanying sample images, you can
perform the image processing operations described in this
chapter while reading.
The function of a digital image processor is, in part, to
reverse the degradation process that takes place in the optical system of the microscope. However, the reversal of the
degradation process is made difficult because, as a consequence of diffraction and unintentional spatial filtering,
identical images can be formed by different objects. Thus we
must really understand the object and the imaging system in
order to use digital image processing to give a more faithful representation of the object. Similar signal processing
techniques can be used to our advantage when using chemical
techniques such as optical spectroscopy. In this case, digital
processing of the data is superior to using a chart recorder
in that the digital processing can compensate for instrument
artifacts, increase the signal-to-noise ratio through averaging,
decompose complex signals into their component parts, and
increase the ability to resolve overlapping peaks.
The signal-to-noise ratio in the image can be improved
by reducing the glare in the microscope, which can come
from many sources. The glare that cannot be removed
optically can be removed digitally using background subtraction. Background subtraction is handy when doing
fluore-scence microscopy—we can sharpen the wanted
information by eliminating the out-of-focus fluorescence. In order to remove the out-of-focus light, we can
slightly defocus the specimen and capture an image using
the
SUBTRACT
BACKGROUND/BACKGROUND
CORRECTION command. Then refocus the specimen,
capture an image, and subtract the background image from
the specimen plus the background to get a clean defect-free
image. This function is also valuable when doing polarization light microscopy to eliminate the background light that
passes through the analyzer because of the depolarization
226
of light by the round surfaces of high numerical aperture
objective lenses. First, we capture an image in the absence
of a specimen and then subtract this image from the one
that includes the specimen.
Typically, the contrast of biological specimens is
extremely poor and the variation in gray levels in neighboring pixels is limited. The IMAGE ADJUST/CONTRAST
ENHANCEMENT commands vary the contrast and
brightness of the image manually. The pixel value of the
enhanced image is related to the pixel value of the original
image in the following manner:
enhanced pixel value m(original pixel value)γ b
where m is the linear change in contrast, γ is the nonlinear
change in contrast, and b is the brightness. Changing these
values digitally accomplishes the same goals as changing
these values with an analog image processor as described
earlier. The brightness of each of the colors that make up a
color image can be adjusted individually using the ADJUST
COLOR BALANCE/CONTRAST ENHANCEMENT
commands. The mathematical equation that transforms the
input values of a frame to the output values is known as a
look-up table (LUT). Look-up tables can be used irreversibly before or reversibly after an image has been saved.
The image should be adjusted so that the full bit-depth
is utilized and gray level values between black (0) and
white (2n) are used to make up the image. The ENHANCE
CONTRAST/BEST FIT commands allow us to stretch out
the gray scale in the image so that the darkest object detail
becomes black and the brightest object detail becomes
white. This increases the variations in brightness of the
image. When only a limited number of gray levels are
used, there is a high probability that a point in the image
will have the same brightness as the neighboring points,
and the image contrast will be low. Consequently, we
may not be able to resolve two neighboring points. This
is how increasing the range of intensities in the image can
increase the contrast. The distribution of gray values can
be plotted using the HISTOGRAM/DISPLAY RANGE
commands. The bit-depth of the image can be reduced to
1-bit to produce a binary image using the THRESHOLD/
THRESHOLD commands. A white-on-black image can
bring out different details than the same specimen presented as a black-on-white image. We can produce either
kind of image with the INVERT/INVERT IMAGE commands. The human eye is more sensitive to variations in
color than it is to variations in gray levels. Therefore, the
LOOKUP TABLES/PSEUDOCOLOR commands are used
to change the gray scale to a pseudo-color display.
The Image Pro Plus system has a TEST STRIPS command, which allows one to obtain an optimum image relatively quickly, much like a photographer used to do in a
darkroom. The TEST STRIPS command automatically
produces a series of images with differing brightness, contrast, or gamma as well as images where any of the two
functions are varied simultaneously.
Light and Video Microscopy
Up to this point, I have discussed point operations
where the gray value of each output pixel is directly related
to the gray level value of the input pixel. Point operations
do not change the spatial relations of the image—they
affect only the contrast and brightness. On the other hand,
spatial filtering modifies the value of a pixel based on the
values of the neighboring pixels. Spatial filtering allows
us to eliminate the high spatial angular wave numbers,
which might represent noise, or the low spatial angular
wave numbers that might represent out-of-focus light that
could obscure the details of interest (Shaw, 1993). In fact,
if we do spatial filtering on an image of a diffraction grating, we can repeat Abbe’s experiment in which he changed
the image of the grating by masking spots in the diffraction
pattern (see Chapter 3). The Image J and Image Pro Plus
systems perform spatial filtering in two ways: by operating
on the diffraction plane, using Fourier mathematics and the
FFT/FFT commands, and by operating on the image plane
using spatial convolutions and the FILTERS/FILTERS
commands.
The Fast Fourier Transform (FFT) command performs
spatial filtering by transforming distance between points
in an image into a series of sinusoidal terms with increasingly larger spatial angular wave numbers and smaller
amplitudes. The image processing programs represent the
Fourier transform as a diffraction pattern, with the smallest spatial angular wave numbers closest to the origin and
the largest spatial angular wave numbers farthest from
the origin. In the Image J system, we eliminate regions
of interest in the Fourier Transform using an area selection tool. Once we select a spot that represents the spatial
angular wave number that we wish to eliminate, we mask
the spot using the FILL command. Once all the unwanted
spots are removed from the Fourier Transform, we use the
INVERSE FFT command to create the spatially filtered
image. In the Image Pro Plus system, LOW PASS, HI
PASS, SPIKE CUT, and SPIKE BOOST commands eliminate or enhance any desired spatial angular wave number.
We then perform an INVERSE FFT on the Fourier transform to produce the spatially filtered image (Figure 14-23).
A pseudo-relief image, similar to those obtained using
oblique illumination, differential interference contrast
optics, or Hoffman modulation contrast optics can be rendered from a relatively transparent object using spatial filtering. First, we perform a FFT on the image. We then mask
the left half, the right half, the top half, or the bottom half
of the Fourier transform, and perform an INVERSE FFT to
get a pseudo-relief image. We can produce a dark-field-like
image by masking the central spot of the Fourier transform
and then performing an INVERSE FFT. Spatial filtering
offers unlimited opportunities to mimic optical processes
that introduce the desired contrast into an image.
Spatial filtering can be done with the Image J and Image
Pro Plus software on the image plane using convolution
filters. Convolution filters are arrays of numbers. For example
a 3 3 smoothing or low pass filter, which blurs the image
227
Chapter | 14 Image Processing and Analysis
FIGURE 14-23
Nonideal
Fourier
transform
Imaging
lens
Specimen
Ideal
Fourier
transform
Non-linear
filter
Image
Use Fourier transforms to correct for the degradation of the image produced by the optical system itself.
Convolution
kernel
C
B
A
F
E
D
I
H
G
4
4
9
8
6
5
8
7
6
5
7
Image
3
2
1
3
2
1
9
FIGURE 14-24 The convolution filtering process.
by making a target pixel more like its neighbors, looks
like so:
3 3 sharpening or high pass filter, which sharpens an
image by accentuating the differences between a target
pixel and its neighbors looks like so:
1/9
1/9
1/9
1/9
1/9
1/9
1
1
1
1/9
1/9
1/9
1
8
1
1
1
1
The SMOOTHING/LO-PASS filter is overlaid on the
image to be filtered. The values in each of the nine pixels
in the image that coalign with the nine cells of the convolution kernel are multiplied by the corresponding value
in the kernel. Then the nine products are summed and this
sum is divided by the sum of the nine numbers in the kernel, which in the preceding kernel equals unity. The original
value of the pixel in the center is replaced with the value of
the sum of the products divided by the sum of the numbers
in the kernel (Figure 14-24). The kernel is moved over the
entire image, so that each pixel gets to be the target pixel.
The result of spatial filtering with a low pass filter is the
loss of high spatial angular wave number information. The
subtraction of an image, which has been spatially filtered
with a low pass filter, from itself, brings out the highlights
in an image. It is one way to rid an image taken in a widefield fluorescence microscope of the annoying out-of-focus
fluorescence.
The SHARPENINGHI-PASS filter commands enhance
the high spatial angular wave numbers in an image. A
Pseudo-relief images, reminiscent of those produced
by oblique illumination, differential interference contrast
microscopy, or Hoffman modulation contrast microscopy,
can be produced from bright-field images by using the
SHADOWS/HORIZONTAL EDGE commands. These
commands produce a pseudo-relief image, using convolution kernels that perform the first spatial derivative of the
target pixel with respect to the x-axis. The convolution kernels look like so:
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
228
Light and Video Microscopy
or convolution kernels that perform the first spatial derivative of the target pixel with respect to the y-axis with convolution kernels that look like so:
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
Image J and Image Pro Plus have many different convolution kernels that let us selectively enhance any given
detail. Both programs let us create original convolution
kernels. An interactive Java-based tutorial in the use of
convolution kernels can be found at the Molecular Expressions web site (http://micro.magnet.fsu.edu/primer/java/
digitalimaging/processing/kernelmaskoperation/).
Many image enhancement programs use the “point
spread function” to estimate how the optical system converts a point of light in the object to an Airy disk on the
image plane. The image that we observe in the microscope
is a composite image composed of the geometric image
and an inflated image due to diffraction. Once the point
spread function is known, all the light that is diffracted
(i.e., convoluted) into the diffraction rings above, below,
and in the plane of the point can be eliminated (i.e., deconvoluted) from the regions outside the point and put back
into the point. In this way, the point becomes brighter, the
surround becomes darker, and the resolution and contrast
are maximized and the depth of field is minimized.
The point spread function is determined by considering what a point should look like in the image plane as a
result of geometrical optics and in the absence of diffraction. The point spread function may be different in regions
close to the optical axis and farther away. It is possible to
image a test pattern composed of an array of points, and
then have the computer minimize the difference between
the brightness of the pixels in the real image and the predicted image. The deconvolution function minimizes this
difference. The computer can store these functions for each
point on the image plane and the deconvolution can then
be used to eliminate the diffraction artifacts introduced into
the image by the limitations of the optical system. Many
commercially available software packages are capable of
doing deconvolutions.
to get real values for spatial measurements, the image processor must be calibrated using a stage micrometer and
the CALIBRATE/SPATIAL CALIBRATION commands.
Once the analysis system is calibrated in two dimensions,
we can use a number of tools to measure the lengths and
areas of regular or irregular objects. In the Image Pro Plus
system, intensities at a point, along a line, or in various
regions of interest (ROI) can be determined with the LINE
PROFILE command. The INTENSITY CALIBRATION
command allows us to convert the intensities into absolute
units. Plug-ins for Image J that allow us to measure intensities along a line, intensities in various regions of interest
(ROI), and the change in intensity over time are available
at http://rsb.info.nih.gov/ij/plugins/index.html.
Plug-ins for Image J and macros in Image Pro Plus
can be programmed to automatically count, measure, and
analyze objects and detect how the positions of the objects
change from frame to frame.
Digital image processing can be used to determine
a multitude of parameters in a living cell simultaneously
(Waggoner et al., 1989; Conrad et al., 1989). For example,
one can correlate the distribution of proteins labeled with
different fluorescent probes (e.g., for actin, myosin, and
tubulin), or visualize fluorescently labeled actin at the
same time one visualizes, with other fluorescent probes,
the local [Ca2] and pH, two factors that affect the polymerization of actin. To do so, one must capture a number of
separate images taken with different excitation or emission
wavelengths. A small amount of chromatic aberration
in the objective lens would cause the excitation of different wavelengths to focus at slightly different depths in the
sample and the different emission wavelengths to focus at
slightly different image planes.
A digital image processor can be used to bring the
images produced by different colors into register in the
image plane by adding multipally-stained stained beads to
the sample so that all the captured images contain a few
beads (Figure 14-25). The center of mass of the beads is
1
5
Center of mass
4
ANALYSIS FUNCTIONS OF DIGITAL
IMAGE PROCESSORS
3
Digital image processors are very good at making quantitative measurements of counts, length, duration, and intensity, and thus can be used to analyze an image. In order
2
FIGURE 14-25 Using multipaly-stained beads to put in register images
from multiply stained specimens.
229
Chapter | 14 Image Processing and Analysis
determined by the image-processing program and used
to align the different images so that they are in the same
register with the same magnification. Multiple spectral
parameter imaging is a powerful tool for studying dynamic
processes that involve many things in live cells.
THE ETHICS OF DIGITAL IMAGE
PROCESSING
As a final project, one of my students presented what
I thought was his project on mitosis. He showed the rest
of the class and me digital images of cells going through
mitosis and described the process of mitosis and the
mechanisms that brought them about. The images and
the presentation on mitosis were beautiful. As he ended
his presentation, he stunned us when he told us that the
presentation was not about mitosis at all, but about the ethics of digital image processing. He told us that the cells he
showed us were mature cells that no longer divided. He
had “cut” chromosomes and mitotic figures from images
of other dividing cells and flawlessly “pasted” them into
the nondividing cells using Adobe Photoshop.
Throughout this book, I have discussed the relationship
between the image and reality using examples from sensory
psychology, Greek philosophy, geometric optics, physical
optics, Fourier optics, all kinds of microscopy, as well as
examples from analog and digital image processing. When
studying microscopy, I have discussed the reality of distortion and the distortion of reality throughout each step in the
process of forming an image (Figure 14-26). As presented
in the last two chapters, the invention of transistors used
to build analog and digital image processors by William
Shockley, John Bardeen, and Walter Brattain has been an
enormous benefit to microscopists (Riordan and Hoddeson,
1997; Shurkin, 2006). Nevertheless, like any new technology, digital image processing presents many ethical challenges. There are digital image processing techniques that
are appropriate, inappropriate, or questionable, and digital
imaging techniques should not be used as a substitute for
correctly aligning the microscope. To ensure honesty and to
protect your reputation, always archive the original unprocessed image and state any techniques used that may be
questionable (Rossner and Yamada, 2004; Pearson, 2005;
Couzin, 2006; Editorial, 2006a, 2006b, 2006c; MacKenzie
et al., 2006). The rapidity in which an image can be obtained
using digital techniques should not inadvertently lead you
to think that a single image is representative of the specimen. As Simon Henry Gage (1917, 1941) wrote nearly a
century ago, the “image, whether it is made with or without
Analog
processor
Vout
Vin
Analog to
digital converter
Vout
ADC
Video camera
Light sensitive elements
12
3
1
24 200
221 155
Frame
grabber
(Tube lens)
Input
look up
table
Aperture plane
Experiences
character
brain, eyes
Objective
Output
look up table
LUT
Observer
Reality
Speciman plane
Digital
monitor,
printer,
optical
disk, etc
Sub-stage condenser
Aperture plane
Analog
monitor
Light source [filters, etc]
FIGURE 14-26 The distortion of reality and the reality of distortion.
DAC
Digital to
analog converter
Additional
digital image
processing
Fourier (FFT, IFT)
spatial filtering
Convolution kernels
Deconvolution
kernels
230
the aid of the microscope, must always depend upon the
character and training of the seeing and appreciating brain
behind the eye.” In the end, character and training is important in relating the image to reality.
It has been my pleasure to share my class with you. I
will end this book with the words Francesco Maurolico
(1611) used to end Photismi de Lumine: “Farewell most
penetrating Reader! If you find the time, push these investigations further: or if, fortunate man [and woman], you stumble upon something better, generously share it with us.”
Light and Video Microscopy
Helpful Web Sites on Digital Image
Processing
Fred’s ImageMagick Scripts: http://www.fmwconcepts.com/imagemagick/
index.php
McMaster Biophotonics Facility: http://www.macbiophotonics.ca/imagej/
index.html
Ethics of Digital Image Processing
www.swehsc.pharmacy.arizona.edu/exppath/micro/digimage_ethics.html
WEB RESOURCES
Animation of The Dot and the Line made by Chuck Jones: http://www.
youtube.com/watch?v=OmSbdvzbOzY
Commercial Digital Image Processors
BD Biosciences: http://www.scanalytics.com/
Media Cybernetics: http://www.mediacy.com/
Microscope Vision and Image Analysis: http://www.mvia.com/IASoftware/
ia_software.html
Molecular Devices: http://www.moleculardevices.com/home.html
Volocity: http://www.improvision.com/products/velocity/
Free Publications
The field of digital imaging is changing rapidly. Links to free publications
that report on digital microscopy are given here:
Microscopy Today: http://www.microscopy-today.com/
Microscopy & Analysis: http://www.microscopy-analysis.com/
Advanced Imaging: http://www.advancedimagingpro.com/
Biophotonics International: http://www.photonics.com/bioPhotonicsHome.aspx
BioTechniques: http://www.biotechniques.com/
The Spectrum: http://www.bgsu.edu/departments/photochem/research/
spectrum.html
Chapter 15
Laboratory Exercises
LABORATORY 1: THE NATURE OF LIGHT
AND GEOMETRIC OPTICS
The Spectral Composition of Light: The
Decomposition and Recombination of
White Light
Observe the sky light through red, yellow, green, and blue
plastic filters. Describe and explain your results.
Observe a narrow beam of sunlight through a prism. How
does the prism split the light? Why does the round sun
appear as an elongated ellipse?
Observe light from a tungsten lamp, the fluorescent room
light, a hydrogen lamp, and a sodium lamp with a
spectroscope. Describe and explain your observations.
Gas lamps are available from Arbor Scientific (http://
www.arborsci.com/detail.aspx?ID927).
Observe white stripes on black cards and black stripes on
white cards using the water-filled prism. How does the
image of the line depend on the thickness of the line
and the background color? The water-filled prism is
available from Carolina Biological Supply (http://www.
carolina.com/product/physicalscience/physics/light/
waterprism.do?sortbybestMatches).
Using three light sources, one with a red filter, one with a
green filter, and one with a blue filter, shine the light
on a white screen. Vary the intensity of each color to
create magenta, cyan, yellow, and white. The color
addition set is available from Arbor Scientific http://
www.arborsci.com/detail.aspx?ID419).
Light Travels in Straight Lines
1. Use the laser to prove to yourself that light travels in a
straight line through air. Fill a Plexiglas tank with water
and a scattering agent. Allow the laser beam to strike
the tank perpendicular to the surface. Does light still
travel in a straight line as it goes from air to water?
2. Can you find conditions in which light does not travel
in a straight line as it propagates from air to water?
The scattering tank and solution are available from
Industrial Fiber Optics (http://www.i-fiberoptics.com/
laser-kits-projects-detail.php?id2450).
Light and Video Microscopy
Copyright © 2009 by Academic Press. Inc. All rights of reproduction in any form reserved.
Demonstration of the Inverse Square Law
1. Use a quantum radiometer to measure the intensity of a
candle, a tungsten light bulb, a fluorescent lamp, and a
laser at various distances from the source.
2. Graph and describe your results. Do your data support
the inverse square law? Why or Why not? The quantum
radiometer is available from Li-cor Biosciences (http://
www.licor.com/env/Products/Sensors/rad.jsp).
3. How do you think Benjamin Thompson (1794)
determined the inverse square law before the invention
of the quantum radiometer?
Geometrical Optics: Reflection
1. Demonstrate that the angle of reflection equals the
angle of incidence by placing the edge of a frontsurfaced mirror on the floor and the back against a
wall. Shine a laser on the center of a mirror so that the
incident and reflected beams are superimposed. Using
a felt-tip pen, mark the point where the laser beam
strikes the mirror.
2. Mark the position of the aperture of the laser on the
floor with a piece of tape. Measure the distance (y, in
m) from the aperture to the mirror with a tape measure.
3. Move the laser as far as possible (3 m) to the right of
the original position in 0.05 m steps. At each position,
called distance x, aim the laser at the spot on the mirror
and measure how far the reflected beam is from the
original laser position (distance x).
4. Calculate the angle of incidence using the relation tan
θ x/y. To get the angle of incidence in degrees, make
sure your calculator is set for degrees, then input x,
divide it by y, and press tan–1. To calculate the angle
of reflection use the relation tan θ x/y. Graph your
results.
5. Do your data support the Law of Reflection? The laser
is available from Industrial Fiber Optics
(www.i-fiberoptics.com).
6. Using the laser and the setup just used, distinguish
between specular and diffuse reflection. Aim the laser
at a back surface mirror, paper, wood, and metal placed
where the mirror was placed. Observe the light that
is reflected from these surfaces by holding a piece of
231
232
Light and Video Microscopy
glossy white paper at the spot where you expect to find
the most reflected light. Describe the appearance of the
reflected light.
7. Make a beam splitter based on the phenomenon of
partial reflection. Pass the laser beam through a clean
microscope slide that is positioned perpendicular (90°)
to the beam. Then orient the microscope slide so that
it is 45° relative to the beam. Notice that some light is
transmitted and some is reflected. Observe the relative
intensity of the transmitted and reflected light.
Geometrical Optics: Refraction
1. Add water to the refraction tank until it is one-half full
(Figure 15-2). Start with air (ni 1) in the incident
medium and water (nt 1.3330) in the medium of
transmission. Vary the angle of incidence and measure
the angle of refraction.
2. Do your results confirm the Snell-Descartes Law (ni
sin θi nt sin θt)? The refraction tank is available from
Arbor Scientific (http://www.arborsci.com/detail.
aspx?ID934).
3. When the incident medium is air, the Snell-Descartes
Law reduces to nt sin θt sin θi or nt sin θi/sin θt.
Mirror on far
wall of room
θr
θi
Measure the Critical Angle of Reflection
1. Using the refraction tank, lower the light so that the
incident medium is composed of water and the medium
of transmission is composed of air. Do your results still
confirm the Snell-Descartes Law (ni sin θi nt sin θt)?
2. When the angle of transmission is greater than 90
degrees, the light is reflected back into the water
instead of entering the air. Determine the critical angle
that results in total internal reflection at a water/air
interface. How does this angle compare with the
calculated critical angle 1/ni sin θi?
3. Orient a glass prism so that the incident light is totally
reflected. Let your finger approach the air/glass
interface where the light is totally reflected. You can
see the evanescent wave jump from the glass to your
finger.
4. Optical light guides (fiber optics) use total internal
reflection to transmit light long distances along a cable
with very little loss to the outside. Illuminate one end
of a light guide with the laser and slowly bend the light
guide until it is no longer able to confine the laser light.
Why does the light exit the light guide?
5. Read a newspaper through a light guide that scrambles
the image and one that transmits the image faithfully.
How do you think the two types of light guides are
constructed?
Refraction through Lenses
Screen
Laser
FIGURE 15-1
Assuming the validity of the Snell-Descartes Law, find
the refractive index of the water.
Setup for proving the law of reflection.
Air
Water
1. Put a double convex lens in a black bottom Plexiglas
scattering tank that contains water and a scattering
medium. Let the laser light propagate along the
principal axis.
2. Raise and lower the laser so that the laser light is
parallel to the principal axis. Can you find the focus of
the lens? Do you see spherical aberration?
3. Repeat with a double concave lens. How would your
results differ if the refractive index of the medium was
greater than the refractive index of the lens?
4. The scattering tank and scattering solution are available
from Web-tronics (http://www.web-tronics.com/opel.
html\).
Measure the Refractive Index of a Liquid
FIGURE 15-2
Setup for demonstrating the Snell-Descartes Law.
1. Use a hand-held refractometer to measure the refractive
index of distilled water (0% sucrose), a 2.5% (w/v)
sucrose solution, a 5.0% (w/v) sucrose solution, a
7.5% (w/v) sucrose solution and a 10.0% (w/v) sucrose
solution. Graph and explain your results.
233
Chapter | 15 Laboratory Exercises
2. Determine the refractive index of a 2.5% (w/v) aqueous
solution of bovine serum albumin (BSA). How does
the value of the protein solution compare with the
values of the four sucrose solutions? Explain. In your
own words, describe what the index of refraction of a
material is.
LABORATORY 2: PHYSICAL OPTICS
In Laboratory 1, we experimented with geometrical optics,
treating light as if it traveled as corpuscles in straight lines.
However, we noticed that the inverse square law did not
hold for all the light sources because some sources produce
coherent light. Coherent light is defined as light composed
of waves that maintain a constant phase difference between
each other. These waves can interfere with one another. In
this laboratory, we will see that light does not necessarily
travel in straight lines, and that its behavior is consistent
with the wave theory of light.
Observation of the Diffraction Patterns of
Opaque Rectangles
1. Set up a laser and a lens or two on an optical bench
so that a slip of card approximately 1 cm in width is
illuminated with plane waves (Figure 15-3). View the
far-field or Fraunhöfer diffraction pattern of the slip
of card. Then insert a second lens between the object
and the screen so that an image of the object is in focus
on the screen (Figure 15-4). Describe the Fraunhöfer
diffraction pattern and the image.
2. Repeat using slips of cards of various widths from 1 cm
to 1 mm. Describe the Fraunhöfer diffraction patterns
and the images.
3. How do they change as the width of the card decreases?
Did you see what Newton missed?
Observation of Diffraction Patterns of
Objects of Various Shapes
1. Set up a laser and a lens or two on an optical bench so
that an object is illuminated with plane waves (Figure
15-3). View the far-field or Fraunhöfer diffraction
pattern of the tip of a needle and the head of a pin
positioned side by side on a screen. Then insert a
second lens between the object and the screen so
that an image of the object is in focus on the screen
(Figure 15-4). In the presence of the second lens, the
Fraunhöfer diffraction pattern will be in focus at the
back focal plane of this lens, and can be viewed with a
piece of ground glass. The focal lengths of the lenses
will be determined by the geometry of the setup and
the size of the room. The test objects are available in
the physical optic lab sold by Industrial Fiber Optics,
Inc. (www.i-fiberoptics.com).
2. After removing the second lens from the optical path,
view the near-field or Fresnel diffraction patterns, of
the tip of the needle and the head of the pin, 5 cm and
10 cm behind the objects. Draw the diffraction patterns.
Draw the far-field or Fraunhöfer diffraction patterns
of the tip of the needle and the head of a pin that are
projected on the screen. Describe the relationship
between the objects and their diffraction patterns.
3. Insert the second lens in the optical path. Describe the
image of the objects on the screen. Use a ground glass
to view the diffraction pattern at the back focal plane of
the second lens. Describe this diffraction pattern.
4. Repeat this experiment, replacing the needle and pin
with the edge of a razor blade, a square aperture, and a
circular aperture. Describe the object, image, Fresnel,
and Fraunhöfer diffraction pattern of each of the
objects.
The Effect of Slit Width on the
Diffraction Pattern
Laser
Object
FIGURE 15-3
Setup for studying far-field diffraction.
1. Observe the Fraunhöfer diffraction pattern produced
by a slit made from two parallel razor blade edges
1 cm apart. Gradually move the edges closer together
and observe what happens to the diffraction pattern.
Describe your observations.
Back focal
plane
Laser
Object
FIGURE 15-4
Fourier
plane
Setup for observing and operating on the diffraction pattern in the back focal plane.
Screen
234
Light and Video Microscopy
2. Observe the diffraction pattern formed by two slits
that are separated by d 5.8 105 m. How many
diffraction orders can you see? Do you see the same
number when the room lights are on? What can you say
about resolution and contrast?
3. Measure the distance between the slits and the screen
(D, in m). Measure the distance between two distant
diffraction spots and divide by the number of spaces
between the spots (x, in meters). If the wavelength
(λ) of the laser is 632.8 109 m, then the distance
between the slits is given by:
d (λ )(D/x)
4. Repeat this experiment for the second pair of slits that
are 4.5 105 m apart, the third pair of slits that are
7.5 105 m apart, and the fourth pair of slits that are
10 105 m apart. Can you confirm that the distances
between the two slits are correct? If you did not know
the wavelength of the laser, but did know the distance
between two slits, you could determine the wavelength
of the laser from the formula.
Observation of Images and Fraunhöfer
Diffraction Patterns of Slits and Grids
1. Observe the images and Fraunhöfer diffraction patterns
of various objects, including single slits with various
widths and coarse and fine grids. Vary the orientation
of the various objects.
2. Describe the relationships between the object,
Fraunhöfer diffraction pattern, and the image.
Observation of the Fourier Transform
of an Object
1. For this section, note the distinction between spatial
angular wave number and the angular wave number of
the illuminating light waves.
2. Use a slide of a person’s head as an object. View the
image. View the diffraction pattern formed at the back
focal plane of the second lens.
Spatial Filtering
1. Use a slide with a circular aperture as a mask. Using
the slide of a person’s head as an object, place the mask
at the back focal plane of the second lens. Block out
the higher diffraction orders with the mask. How does
this affect the image?
2. In the back focal plane of the second lens, vary the
position of the mask and describe the influence of the
mask’s position on the image.
3. Repeat this experiment using a grid as an object.
Describe the diffraction pattern formed at the back focal
plane of the second lens. Use either a circular aperture
or a slit as a mask. Draw and describe the image that is
formed on the screen when:
● Only the central dot of the diffraction pattern is
allowed to pass.
● Only one noncentral dot of the diffraction pattern is
allowed to pass.
● Nine central spots of the diffraction pattern are
allowed to pass.
● The central vertical row of spots of the diffraction
pattern is allowed to pass.
● The central horizontal row of spots of the diffraction
pattern is allowed to pass.
● A diagonal row of spots of the diffraction pattern is
allowed to pass.
4. What generalizations can you make about the
relationship between the diffraction pattern and the
image?
LABORATORY 3: THE BRIGHT-FIELD
MICROSCOPE AND IMAGE FORMATION
Illuminate a Specimen with Köhler
Illumination Using a Microscope with a
Mirror and a Separate Light Source
Establish Köhler Illumination:
1. Put a stained prepared slide on the stage.
2. Position a lamp with a coil filament so that the field
diaphragm is about 9 inches from the microscope
mirror. Tilt the lamp housing until an enlarged image of
the filament is centered on the mirror.
3. Using the 10x objective and a low magnification
ocular, move the concave mirror until the light is seen
passing through the sub-stage condenser to the slide.
Focus perfectly on the object. Adjust the mirror slightly
to make the light central.
4. Rack up the sub-stage condenser until it is nearly
touching the slide. Close the aperture diaphragm. Then
focus the collecting lens of the lamp until a sharp,
enlarged image of the filament is seen on the closed
aperture diaphragm.
5. Close down the field diaphragm and focus the
sub-stage condenser up or down until a sharp image of
the field diaphragm on the lamp appears in the plane
of the specimen. You may have to move the mirror
slightly to keep the image of the field diaphragm in the
center of the field.
6. Take out an ocular and observe the light in the
microscope tube. Open up the aperture diaphragm until
the light fills approximately 80 percent of the back
focal plane of the objective lens.
7. Open the field diaphragm on the lamp until the light
just fills the field.
8. Observe the prepared specimen.
235
Chapter | 15 Laboratory Exercises
Illuminate a Specimen with Critical
Illumination Using a Microscope with a
Mirror and a Separate Light Source
1. Put a stained prepared slide on the stage.
2. Remove the sub-stage condenser.
3. Position a lamp with a ribbon filament bulb so that the
field diaphragm of the lamp is about 9 inches from
the microscope mirror. Tilt the light source and the
microscope vertically so that the rays from the light
source strike the concave mirror surface at a 90-degree
angle relative to the optical axis.
4. Using the 10x objective and a low magnification ocular,
move the mirror until the ribbon filament is focused on
the specimen. Adjust the mirror slightly to make the
light central.
5. Observe the stained prepared specimen.
Establish Köhler Illumination
on the Olympus BH-2
1. Make a thin hand section of a piece of cork, as Robert
Hooke did in 1665. Put it in a drop of lens cleaner on a
microscope slide and cover it with a #1½ cover glass.
The lens cleaner helps eliminate air bubbles. Focus on
the specimen with the coarse and fine focus knobs.
2. Close the field diaphragm and focus an image of the
field diaphragm on the specimen plane by raising or
lowering the sub-stage condenser.
3. Open the field diaphragm so that it almost fills the field
and center it with the centering screws on the sub-stage
condenser.
4. Open and close the aperture diaphragm so that you
optimize resolution and contrast. Remove the ocular
and look down the microscope tube.
5. At the position where the resolution and contrast are
optimal, the light will fill about 80 percent of the width
of the optical tube (Abramowitz, 1985, 1989). All
microscope work from here on will be done with the
room lights off. You can use a flashlight to find things,
prepare specimens, and write in your notebook.
Observe the Diffraction Pattern of a Ruled
Grating with the Olympus BH-2
1. Use a piece of exposed and processed Polaroid Instant
35 mm color slide film as a diffraction grating. Observe
the film with the microscope and notice that it is made
out of thousands of thin red, green, and blue lines. We
will examine the diffraction patterns of this specimen
in the back focal plane of the objective.
2. Insert a green interference filter on top of the field
diaphragm. This filter blocks out the image of most
of the red and blue lines of the grating. Set up Köhler
3.
4.
5.
6.
7.
illumination using a 10x objective and focus the
specimen.
Close the aperture diaphragm as far as possible to
produce axial illumination. You may also need to lower
the sub-stage condenser to produce axial illumination.
Remove an ocular and insert the centering telescope.
Focus the centering telescope on the diffraction pattern.
Do not change the specimen focus.
Make a drawing of the observed diffraction pattern and
identify the zeroth, first, and second orders. Turn the
specimen.
What is the relationship of the orientation of the
diffraction pattern with respect to the long axis of the
grating? How would you expect the diffraction pattern
to change if the lines of the grating were closer together?
Compare the diffraction pattern of the same grating
produced by a 10x objective lenses with numerical
apertures of 0.25 and 0.30.
Observe the Effect of the Numerical
Aperture of the Objective on Resolution
1. Get a slide of the diatom Pleurosigma. Set up
Köhler illumination. Focus on the silica cell wall
of Pleurosigma with the 100x SPlan Apochromatic
oil immersion objective lens equipped with an iris
diaphragm. Put immersion oil on the slide and the top
of the substage condenser.
2. Insert the green interference filter in the light path.
Observe the diffraction pattern in the back focal
plane of the objective using the centering telescope.
Describe the diffraction pattern and compare it with
the image observed with the ocular. Remove the green
interference filter. Describe the diffraction pattern and
image produced by white light.
3. Reduce the numerical aperture of the objective by
closing the iris diaphragm in the objective. Close
the iris diaphragm until the first- and higher-orders
diffracted light are eliminated. Compare the diffraction
pattern to the image of the specimen. Increase the
aperture of the iris diaphragm in the objective and
observe its influence on the diffraction pattern and the
image.
4. Vary the opening of the field diaphragm. How does
this affect the diffraction pattern and the image?
What effect does the size of the opening of the field
diaphragm have on glare?
Lens Aberrations
There are a number of possible aberrations of objective lens
and these all can be corrected, but at a price. In this exercise,
we will test a number of lenses in a series for various aberrations to see whether the correction is worth the cost.
236
1. To test objective lenses for chromatic aberration, place
a slide of carbon dust on the microscope stage. Using
white light, focus on the carbon particles and note the
color fringes above and below the plane of perfect
focus. The following effects will occur, depending on
the type of objective:
Achromat: Pronounced color fringes. Above the focus,
yellow-green, below the focus, red or purple. The wider
the fringes, the poorer the lens is corrected for color.
Fluorite or semi-apochromat: Narrow color fringes
of green and red. The narrower the width of the color
fringes, the better the lens.
Apochromat: No color fringes above and below the
focus.
2. To test objective lenses for spherical aberration, place
an Abbe Test Plate on the microscope stage (Slayter,
1957; Fletcher 1988).
3. Find the cover glass thickness marked on the test plate
that is optimal for the objective lens being tested (0.17).
Search for a minute, circular, brilliant spot of light in the
film that shows several diffraction rings when in focus.
4. To perform the star test, focus above and below the
plane of perfect focus with the fine focus knob. With
an ideal objective that is free from spherical aberration,
the concentric rings should be perfect concentric
circles with equal spacing and brilliance and the rings
should be identical at equal distances above and below
the focus. If the downward rings are plainer than the
upward rings, or the upward rings are plainer than the
downward downward, the lens has spherical aberration.
The greater the symmetry, the better is the correction
for spherical aberration.
5. To test the effect of cover glass thickness on spherical
aberration of the objective lenses, move the Abbe
test plate to regions that have a cover glass thickness
greater than optimal and less than optimal.
6. At each cover glass thickness, perform the star test by
checking the symmetry of the diffraction rings as you
over-focus and under-focus.
7. To test the objective lenses for flatness of field, place a
stained prepared slide on the stage. Is the center of the
image and the edge of the image in focus at the same
time?
8. To test the objective lenses for distortion, place a
specimen of a very fine grid, like the kind used for
electron microscopy, on the microscope stage. Are all
the lines parallel? Is the image of the grid distorted? Is
there pincushion or barrel distortion?
Measurements with a Microscope
1. To measure the length of an object, insert an
ocular micrometer in the ocular and place the stage
micrometer on the stage. Carefully focus the stage
micrometer. Both the stage micrometer and the ocular
Light and Video Microscopy
micrometer will be in focus and sharply defined. Turn
the ocular so that the lines of the eyepiece are parallel
to each other.
2. Determine how many intervals on the ocular
micrometer correspond to a certain distance on the
stage micrometer and then calculate the length that
corresponds to one interval of the ocular micrometer.
For example, if 35 intervals correspond to 200 μm
(0.2 mm), then one interval equals (200/35) 5.7 μm.
This value is specific for each objective. Calibrate
the ocular micrometer for each objective on your
microscope. Put the calibration in a convenient place in
your laboratory notebook.
3. Find the field of view number on the ocular. Divide
the field of view number by the magnification of the
objective to get the diameter (in mm) of the field
of view. Remember to divide this distance again
by the magnification introduced by any additional
intermediate pieces. List the diameter of the field for
each objective next to their calibration.
4. Measure the length of Pleurosigma. Pleurosigma is
___________ μm long.
Many simple experiments that demonstrate the optical
properties of the light microscope can be found in Quekett
(1848, 1852), Wright (1907), Gage (1891, 1894, 1896,
1917, 1925, 1941), Belling (1930), and Oldfield (1994).
Numerous suggestions of good microscopic objects can
be found in Hogg (1898), Clark (1925), Beavis (1931),
Popular Science Staff (1934), and Ealand (no date).
LABORATORY 4: PHASE-CONTRAST
MICROSCOPY, DARK-FIELD MICROSCOPY,
RHEINBERG ILLUMINATION, AND
OBLIQUE ILLUMINATION
In this lab, we will observe transparent, nearly-invisible
specimens under the microscope. We will use Gold Seal
microscope slides and Gold Seal #1½ cover glasses, which
are available from Ted Pella (http://www.tedpella.com/).
Keep the lids closed so the slides and cover glasses remain
dry and dust-free.
Phase-Contrast Microscopy
1. Before you obtain cells to view with qualitative
phase-contrast microscopy, put a drop of water on a
microscope slide so that the cells you will obtain will
remain hydrated.
2. Make a peel of the epidermis from the convex side of
the bulb scale by cutting out a 2 cm 2 cm piece of a
bulb scale that is four or five bulb scales deep into the
onion. Snap the bulb scale so that most of it breaks in
237
Chapter | 15 Laboratory Exercises
Onion
epidermis
for examination
FIGURE 15-5 How to make an epidermal peel form the convex side of
an onion scale.
3.
4.
5.
6.
7.
two (Figure 15-5). The epidermal layer will not break
clean. Pull this layer back with forceps and place it on
a drop of water on a microscope slide.
To make a peel of the epidermis on the concave side of
the bulb scale, remove a bulb scale that is four or five
layers deep within the onion. Make a checkerboard
pattern of cuts with a razor blade on the concave side of
the bulb scale. Pick up several 3 mm × 3 mm squares of
epidermal tissue with forceps, and place the epidermal
tissue sections on the drop of water.
Set up Köhler illumination in the Olympus BH-2
microscope. Observe an onion epidermal cell with
bright-field optics using the 10x phase-contrast
objective lens. Make sure that the condenser ring is
in the 0 position. The cells are virtually invisible and
the contrast is best when the specimen is slightly
defocused.
Turn the sub-stage condenser turret to the “10” position
to observe the cells with phase-contrast microscopy.
In general, the number on the turret matches the
magnification of the objective lens. Center the phase
ring in the sub-stage condenser turret by removing one
ocular and inserting the centering telescope. Focus the
centering telescope so that the phase ring and the phase
plate are in focus. Use the phase annulus centering
screws to center the phase ring and align it with the
phase plate. Remove the centering telescope and
replace the ocular. Repeat for the 40x phase objective
(Abramowitz, 1987).
Observe the onion epidermal cells with the 40x PL
phase-contrast objective. Are the epidermal cells on
the convex side different from the epidermal cells
from the concave side? Can you see the structure in
the nucleus? Can you see mitochondria moving, even
dividing? Can you see the peripheral endoplasmic
reticulum?
Document your observations with photographs.
When you take photomicrographs, make a note of
the specimen identity, the type of objective you use,
its numerical aperture, its magnification, the total
magnification, and the type of microscopy (e.g., phasecontrast). Also, note the camera and/or film type and
the exposure adjustment. How do you set the exposure
adjustment?
8. If the specimen is completely distributed throughout
the bright background, set the exposure adjustment
knob to 1x. If the specimen covers approximately
25 percent of the bright background, set the exposure
adjust to 0.5x, to make the exposure longer. If the
specimen covers less than 25 percent of the bright
background, set the exposure adjust to 0.25x to make
the exposure even longer.
9. Look at the pollen tubes of periwinkle (Catharanthus
roseus) that have been growing on modified
Brewbaker-Kwack medium for about two hours.
Compare the images obtainable with the 40x positive
and the 40x negative phase-contrast objectives.
Which structures and processes show up best with
the negative phase-contrast objective lens? Which
structures and processes show up best with the positive
phase-contrast lens? Do you see any halos?
10. Document your observations with photographs.
11. To make 10 ml of modified Brewbaker-Kwack
Medium, mix together 3 g sucrose, 1 mg boric acid,
2 mg MgSO4 7H2O, 1 mg KNO3, 3 mg Ca(NO3)2 4H2O and 58 mg 2-(N-morpholino) ethanesulfonic
acid (MES). Add 7 ml distilled water and titrate to pH
6.5 with 1 N NaOH. Bring up to 10 ml with distilled
water.
12. To practice quantitative phase-contrast microscopy,
we will use the Olympus BH-2 microscope to
measure the refractive index of the cytoplasm in
endoplasmic drops made from Chara.
13. To make a 100 ml aqueous solution of artificial
cell sap (ACS), add 0.596 g KCl, 0.147 g CaCl2,
0.175 g NaCl, and 0.203 g MgCl2. Take three 1 ml
aliquots of ACS and make a 2% (w/v in ACS) bovine
serum albumin (BSA) solution, a 4% (w/v ACS)
bovine serum albumin solution, and a 6% (w/v
ACS) bovine serum albumin solution. Measure the
refractive indices of these solutions with a hand-held
refractometer, and graph the refractive index vs. the
concentration of bovine serum albumin.
14. Gently dry an internodal cell of the alga, Chara
corallina with toilet paper. As soon as the cell gets a
matte finish, cut one end off the cell and squeeze the
cell contents into a drop of artificial cell sap (ACS), a
drop of 2% BSA in ACS, a drop of 4% BSA in ACS,
and a drop of 6% BSA in ACS.
15. Using the 40x PL objective lens, and a double
counter, count the number of endoplasmic drops
that are darker than the surround or lighter than the
surround and plot the percentage of cells that are
darker than the background vs. the refractive index of
the medium.
16. Find the refractive index where 50 percent of the
endoplasmic drops would be dark. This gives
the percent bovine serum albumin that will make
the average droplet invisible. Find the refractive
238
index from your graph that is equivalent to this
concentration of bovine serum albumin. This is the
refractive index of the cytoplasm in the endoplasmic
drops.
17. The refractive index of the cytoplasm in the
endoplasmic drops is: ___________.
18. Your own cheek cells provide a readily available
specimen that can be used for aligning a phasecontrast microscope at a moment’s notice. You may
want to observe your cheek cells.
Dark-Field Microscopy
1. Focus on the diatoms on a diatom exhibition slide or a
diatom test plate. These slides are available from Klaus
D. Kemp, Microlife Services (http://www.diatoms.co.uk/pg.
htm). Raise the dark-field condenser on the Olympus
BH-2 microscope so that it almost touches the bottom of
the slide.
2. Turn the sub-stage condenser turret to DF. Open the
field diaphragm only until all the specimens in the
field are evenly illuminated, and observe the diatoms
(Abramowitz, 1991). Do some of the diatoms appear
colored? Why? How is the image influenced by putting
water or immersion oil between the top lens of the
condenser and the bottom of the slide? Document your
observations with photographs.
3. If the specimen is completely distributed throughout
the black background, set the exposure adjustment
knob to 1X. If the black background is half-filled with
the specimen, set the exposure adjustment knob to
2X, so that the exposure is twice as fast. If the black
background is only 25 percent filled with the specimen,
set the exposure adjustment knob to 4X, so that the
exposure is four times as fast. If the black background
is sparsely dotted (25%) with specimens, set the
exposure adjustment knob at 4X and turn the ISO dial to
a higher number, to get an even shorter exposure.
4. Put a drop of pond water, a drop from a soil-water
mixture, a drop of pepper-water or a drop of hay
infusion on a microscope slide and cover with a cover
glass. Observe the animalcules that Leeuwenhoek saw
300 years ago. If you have a slowly moving organism
in the preparation, document your observations with
photographs.
Rheinberg Illumination
1. You can make Rheinberg filters using colored theatre
gels manufactured by Rosco International (http://www.
rosco.com/). Choose a color for the outer part of the
filter and cut an 18 mm 18 mm square of this color.
Punch a 3 mm hole in the center of the colored filter
with a cork borer, and insert two or three layers of the
color you want for the central stop in this hole.
Light and Video Microscopy
2. The central color will give the color to the background.
The color of the outer region will give the color to the
specimen. Tape the colored filters to a microscope slide.
3. Hold the microscope slide against the sub-stage
condenser of the Olympus BH-2 and translate the slide
around until the background color at the image plane is
uniform.
4. Tape the microscope slide in place to the sub-stage
condenser. You are ready to view microscopic
specimens on the stage using this quick and dirty form
of Rheinberg illumination.
5. Establish Köhler illumination on your microscope
and observe a drop of pond water. Document your
observations with photography if the specimens are
moving slowly enough.
6. If you would like to make better Rheinberg filters,
make the filters so that the outer diameter of the filter
is the same size as the filter holder at the front focal
plane of the sub-stage condenser on your microscope.
Make the hole for the central stop 1 mm larger than is
necessary to fill the image plane. Place a black ring
around the edge of the central colored spot.
7. Mount the colored filters between two pieces of round
cover glass, using clear mounting medium. The cover
glass should be the same size as the inner diameter of
the filter holder. You can also make tricolor Rheinberg
filters.
Oblique Illumination
1. Put an epidermal peel from the top of a vanilla orchid
on a drop of water on a microscope slide and observe
it with the Olympus BH-2 microscope set up for
Köhler illumination. Then slightly rotate the sub-stage
condenser turret until a pseudo-relief image appears.
The nucleus in each cell will appear as prominent as
they did to Robert Brown (1831), who discovered the
nucleus in the epidermal cells of orchids.
2. Do you remember how difficult it was to see the
nucleus in high school and freshmen biology, before
you knew about oblique illumination? Document your
observations with photographs.
Use of camera lucida (optional)
1. Put a prepared slide in the single ocular microscope
equipped with a camera lucida.
2. Put a piece of blank paper under the mirror, and hold a
pencil over the paper.
3. Look in the ocular; you should be able to see the image
of the specimen and image of the tip of the pencil
simultaneously. If you do not see the pencil tip, put a
piece of white paper on top of the cover glass, and then
translate and rotate the mirror so that you see the pencil
239
Chapter | 15 Laboratory Exercises
tip while looking through the camera lucida. Remove
the paper from on top of the cover glass.
4. To get the correct contrast between the specimen and
the pencil tip, rotate the wheel with neutral density
filters in the camera lucida until the specimen and the
pencil tip can be seen clearly . You may also need to
vary the intensity of the microscope illumination and
the intensity of the light used to illuminate the paper.
5. Trace the image of the specimen on the piece of paper.
LABORATORY 5: FLUORESCENCE
MICROSCOPY
Setting up Köhler Illumination with
Incident Light
Before you begin, set up Köhler illumination for both the
transmitted light and the incident light on the Olympus
BH-2. To set up Köhler illumination for the incident mercury light (Abramowitz, 1993):
1.
2.
3.
4.
5.
6.
7.
8.
Turn on the Hg Lamp
Place a slide on the stage.
Open the shutter slider all the way.
Rotate the iris diaphragm (A) and the field diaphragm
(F) counterclockwise so they are open maximally.
Close the field diaphragm so that you can just see the
edges. Center the field diaphragm by adjusting the
centering screws. Open the field diaphragm.
Center the lamp carefully and gently with the two
lamp centering screws, until the center of the field is
maximally bright.
Adjust the collector lens with the focusing handle until
the field is maximally bright and evenly illuminated.
You may find that you get better contrast with some
specimens and even-enough illumination by focusing
the lamp on the image plane.
Visualizing Organelles with Fluorescent
Organelle-Selective Stains
1. In order to observe the endoplasmic reticulum of onion
epidermal cells, make a stock solution of DiOC6(3) by
dissolving 1 mg of DiOC6(3) in ethanol, and dilute the
stock solution with water (1:1000) to make the working
solution.
2. Prepare several pieces of onion epidermis and mount
them on a drop of staining solution. Wait 5 to 10
minutes. Remove the staining solution with a pipette
and immediately replace it with 0.05% n-propylgallate.
3. Observe the endoplasmic reticulum using the blue
excitation cube. Document your observations with
photographs.
4. To take micrographs of bright fluorescent specimens
scattered over a dark field, typically you will have to
set the exposure meter so that the camera takes shorter
exposures. If the staining is too intense and there is
too much background staining, dilute to working
solution down to 1:50 with distilled water. As a rule, as
you get to know the specimen better, you require less
stain and consequently achieve better selectivity and
contrast.
5. To observe actin microfilaments in onion epidermal
cells, prepare 2 ml of the staining solution by mixing
1.8 ml of Part A with 0.2 ml of Part B. To make 10 ml
of Part A, add 5.5 ml of a 100 mM stock solution of
Piperazine-1,4-bis(2-ethanesulfonic acid) (PIPES)
buffer (pH 7.0), 0.055 ml of a 10 percent stock solution
of Triton X-100 (to permeabilize the cells), 0.55 ml
of a 100 mM stock solution of MgCl2, 0.275 ml of
a stock solution of ethylene glycol tetraacetic acid
(EGTA, pH 7), 0.165 ml of a 100 mM stock solution
of dithiothreitol (DTT), 0.165 ml of a 100 mM stock
solution of phenylmethylsulphonyl fluoride (PMSF),
0.275 ml 200 mM Na phosphate buffer (pH 7.3),
and 0.44 g NaCl. To make 10 ml of 200 mM Na
phosphate buffer (pH 7.3), mix together 2.3 ml of
200 mM monobasic sodium phosphate and 7.7 ml of
200 mM dibasic sodium phosphate. Part B consists of a
3.3 μM stock solution of rhodamine labeled phalloidin
dissolved in methanol.
6. Place several peels of the onion epidermis in the
staining solution for 10 minutes in a warm place (35°
C). Mount the epidermal peels in phosphate-buffered
saline (PBS) that contains 0.05% (w/v) n-propylgallate.
To make PBS, add 0.85 g NaCl, 0.039 g NaH2PO4H2O,
0.0193 g Na2HPO47H2O and enough distilled water to
bring the solution up to 100 ml.
7. Observe the actin microfilaments using the green
excitation cube. Document your observations with
photographs.
Observe Organelles (e.g., Mitochondria
and/or Peroxisomes) in Tobacco Cells
Transformed with Organelle-Targeted
Green Fluorescent Protein (GFP)
1. Make several hand sections of a piece of tobacco leaf
in water or make epidermal peels of the leaf. Place the
sections or peels in a drop of water on a microscope
slide.
2. Using the blue excitation cube, look for the organelles
in the epidermal hairs. Document your observations
with photographs.
3. It is important to shut off the mercury lamp when
you finish with your observations, since the lamp
has a limited lifetime, and may explode if left on for
extended periods when you leave the laboratory. Never
turn a hot mercury lamp back on until it has cooled.
240
Determine the Resolution of Journal Plates
1. Place the 7x Bausch and Lomb measuring magnifier on
a piece of white paper and rotate the lens until the scale
appears in sharp focus.
2. Place the focused measuring magnifier over
micrographs in a variety of scientific journals and
determine the number of dots per mm or dots per inch
(dpi) used to print the micrographs in those journals.
LABORATORY 6: POLARIZED LIGHT
Observation of CuSO4 and Urea
1. Install the polarizing attachments to the Olympus BH-2
microscope. Make sure the polarizer and analyzer are
in the crossed position.
2. Place drops of water on two slides and then add a
few crystals of copper sulfate to one slide and urea to
another. Watch what happens as the crystals dissolve
under the polarizing light microscope with and without
the first order red plate.
3. Describe what happens to the dissolving crystals in
terms of the Michel-Lévy color chart (Delly, 2003).
Observation of Bordered Pits
1. Obtain a lightly stained prepared slide of bordered pits
or make your own slide out of pine.
2. Observe the bordered pits under crossed polars with the
polarized light microscope with and without the firstorder wave plate. Document your observations with
photographs, making sure to document the orientation
of the polarizer, the analyzer and the slow axis (z) of
the first-order wave plate.
3. The cellulose microfibrils that make up the bordered
pit are positively birefringent. How are they oriented in
the bordered pit? Using the Michel-Lévy color chart,
estimate the retardation of the bordered pit.
Observation of the Starch Grains of Potato
1. Grind a chunk of potato in water with a mortar and
pestle. Pipette a drop of the starch grain solution on a
microscope slide and cover with a cover glass.
2. Observe the starch grains under crossed polars with the
polarized light microscope with and without the firstorder wave plate. Document your observations with
photographs, making sure to document the orientation
of the polarizer, the analyzer, and the slow axis (z) of
the first-order wave plate.
3. The starch molecules that make up the starch grains are
positively birefringent. How are the starch molecules
oriented in the grain?
Light and Video Microscopy
4. Using the Michel-Lévy color chart, estimate the
retardation of the starch grain. If you like, prepare a
thin section of the potato to see the starch grains in situ.
Observation of DNA
1. Using forceps, mount thin strands of DNA in a drop of
lens cleaner on a microscope slide.
2. Observe with a polarized light microscope under
crossed polars with and without the first-order wave
plate. Document your observations with photographs,
making sure to document the orientation of the
polarizer, the analyzer, and the slow axis (z) of the
first-order wave plate.
3. The strands of DNA are negatively birefringent. Do
the stands, whose physical axes are parallel to the slow
axis of the first-order wave plate, show additive colors
(blue) or subtraction colors (yellow-orangish)?
4. Put a lot of DNA on the slide and observe retardationdependent colors with and without the first-order wave
plate. Herring sperm deoxyribonucleic acid is available
from Sigma Aldrich (http://www.sigmaaldrich.com/).
Observations of the Orientation of
Microfibrils in the Cell Walls
1. Make a thin transverse hand-section of an
Asparagus root using a razor blade. Mount it in
distilled water.
2. Observe it with a polarized light microscope with and
without the first-order wave plate. Document your
observations with photographs. What can you say
about the orientation of the positively birefringent
cellulose microfibrils?
3. Using the Michel-Lévy color chart, estimate the
retardation of the walls.
4. Make an epidermal peel from the bottom of a vanilla
leaf. Mount it in distilled water.
5. Observe the stomata with a polarized light microscope
with and without the first-order wave plate. Document
your observations with photographs. What can you
say about the orientation of the positively birefringent
cellulose microfibrils in the guard cells?
6. Using the Michel-Lévy color chart, estimate the
retardation of the walls.
Art with Polarized Light (optional)
1. Draw a mosaic-like picture on a piece of paper and
cover it with a piece of glass.
2. Following the pattern drawn on the paper, cover the
glass over each of the mosaic pieces with pieces of
cellulose sheet.
241
Chapter | 15 Laboratory Exercises
3. Place more than one layer in some places and vary the
orientation over other places. Cover the cellulose layers
with another piece of glass and secure the two pieces of
glass together with tape.
4. Observe your art between crossed polars. What happens
when you turn one of the polarizers?
LABORATORY 7: POLARIZING LIGHT
MICROSCOPY
Measuring the Retardation of Cell Walls
Using a de Sénarmont Compensator
(optional)
1. Insert the λ/4 plate into the Zeiss photomicroscope to
make a de Sénarmont compensator.
2. Make an epidermal peel of the leaf of a vanilla orchid.
Mount it in distilled water and observe it with crossed
polars under monochromatic green light.
3. Rotate the analyzer until the walls that are diagonal to
the slow axis of the λ/4 plate are brought to extinction.
4. The retardation of the cell walls is _____________ nm.
Measuring the Retardation of
Stress Fibers Using a Brace-Köhler
Compensator (optional)
1. Make a slide of your cheek cells and observe them in
the Zeiss photomicroscope with crossed polars.
2. Illuminate the cells with monochromatic green
light. Find cells whose birefringent stress fibers are
perpendicular to the slow axis of the λ/30 BraceKöhler compensator.
3. Determine the retardation of the spindle using the
traditional method and the Bear-Schmitt method.
4. The retardation of the stress fibers is ___________ nm
when using the traditional method and __________ nm
when using the Bear-Schmitt method.
Procedure for Testing the Amount of Strain
Birefringence in an Objective (optional)
1. Using the Zeiss photomicroscope, with monochromatic
green light, put a clean slide on the microscope and set
up Köhler illumination for the objective of interest.
2. Close the field diaphragm and set the analyzer to 0.
Turn the polarizer until you get maximal extinction.
3. Replace one of the oculars with a centering telescope
and observe the back focal plane of the objective lens.
You should see a dark, wide, and symmetrical Maltese
cross in the back focal plane of all strain-free objectives.
If you do not see a dark, wide, and symmetrical cross,
then your lens has strain birefringence.
4. Rotate the analyzer. The Maltese cross should open
symmetrically into hyperbolas (in one dimension at a
time). The arms of the hyperbolas should remain dark
until they disappear beyond the field of view.
5. The objective lens is free from lateral and local strain
birefringence if the hyperbola arms remain undistorted
when the objective lens is rotated. The objective lens
is free from radially symmetrical strain birefringence
if the Maltese cross loses contrast and fades away with
minimal change in its shape or position when a BraceKöhler compensator is rotated. If the objective has
radially symmetrical strain birefringence, the cross will
open symmetrically into hyperbolas as it does in strainfree lenses when the analyzer is turned.
LABORATORY 8: INTERFERENCE
MICROSCOPY
Qualitative Image Duplication Interference
Microscopy Using the AO-Baker
Interference Microscope
1. Attach the 40x shearing objective and sub-stage
condenser pair to the microscope. Make a slide of your
cheek cells.
2. Set up bright-field illumination by turning the polarizer
to the OFF position and sliding the λ/4 plate so that
you can see the λ/4 markings.
3. Rotate the analyzer to the unnumbered line position
(where the analyzer is out). Focus the check cells and
set up Köhler illumination.
4. To set up the microscope for interference microscopy,
turn the polarizer to the INT position. Slide the λ/4
plate so that the λ/4 does not show. Rotate the analyzer
to the 90-degree setting when using the 40x SH
objective.
5. Find the astigmatic image of the cheek cell. This is the
region through which the reference wave for the cell
of interest passes. Make sure that there are no cells
or schmootz in this position. The reference wave is
160 μm away from the specimen wave.
6. Remove an ocular and put in the centering telescope.
Examine the back focal plane of the objective. When
using diffuse white light you will see an interference
pattern. This interference pattern will be sharp and
clear if you are focused on a clear portion of the slide.
7. Broaden the first-order red fringe so that it fills the back
focal plane of the objective as uniformly as possible.
You can accomplish this by adjusting the two screws
on the substage condenser screws. The more carefully
you broaden the first-order red fringe and the more
uniformly you illuminate the back focal plane of the
objective, the more dependable your measurements
will be. If the fringe does not cover the entire back
242
Light and Video Microscopy
focal plane of the objective, close down the aperture
diaphragm until the color is uniform. The better
the initial broadening, the better the image. These
adjustments must be made every time you change the
slide.
8. Replace the ocular and view the specimen. It should
be brilliantly colored. Vary the position of the analyzer
and the colors will change. The image duplication
interference microscope converts differences in phase
in transparent specimens into visible differences in
color.
Using the AO-Baker Interference
Microscope to Weigh a Live Nucleus
1. After setting up the microscope as just described, insert
a green (550 107 cm) filter in front of the light
source. Mount some of your cheek cells in a drop of
distilled water.
2. Select a cell. Measure the lengths (in cm) of the major
axis (a) and the minor axis (b) of a nucleus using your
optical micrometer and a stage micrometer. Calculate
the cross-sectional area (A, in cm2) of the nucleus with
the following formula:
A (π / 4) ab
3. Rotate the analyzer until the background is maximally
dark and note the reading of the calibration scale
through the small lens. If the maximally dark area
occurs in the blank area, turn the analyzer in the other
direction until the background is maximally dark again.
This reading is θ1.
4. Turn the analyzer in the counterclockwise direction (so
that the numbers increase) until the nucleus is brought
to extinction. Note this reading on the calibrated scale.
This reading is θ2.
5. Repeat the preceding two steps until you have three
readings for each in order to minimize subjective errors
of judgment in determining where the darkest settings
truly are.
6. Average the three pairs of readings and find an average
θ1 and θ2.
7. To calculate the optical path difference (OPD, in cm),
use the following formula:
OPD = [(θ2 − θ1 )180°] 550 107 cm
8. Calculate the mass (m, in g) of the nucleus using the
specific refractive increment (0.0018 (100 ml/g), which
equals 0.18 cm3/g, and the following formula:
m [(OPD)A]/ 0.18 cm3 /g
9. The average mass of a nucleus is: _____________ g.
Note that DNA accounts for approximately half of the
mass and protein accounts for the other half.
LABORATORY 9: DIFFERENTIAL
INTERFERENCE CONTRAST MICROSCOPY
AND HOFFMAN MODULATION CONTRAST
MICROSCOPY
Differential Interference Contrast
Microscopy
1. Mount cheek cells on a slide and focus on the slide
using bright-field optics and Köhler illumination. Use
the SPLAN objectives.
2. Slide in the polarizer that is attached to the sub-stage
condenser. Slide in the differential interference contrast
beam-recombining prism with the built in analyzer and
first-order wave plate.
3. Rotate the sub-stage condenser turret to the red number
that matches the magnification of the objective lens.
Vary the contrast by turning the knob on the beamrecombining prism. Which color gives the best contrast?
How does the direction of shear influence the image?
4. Optically section the cells. Document your
observations with photographs.
5. Place the Diatom Test Plate with 8 forms on the
microscope. The longest diatom is Gyrosigma balticum,
the one next to that is Navicula lyra, the next one is
Stauroneis phoenocenteron, then Nitzschia sigma,
Surirella gemma, Pleurosigma angulatum, Frustulia
rhomboides, and Amphipleura pellucida. Observe with
the SPLAN 40 objective.
6. Rotate the stage so that the long axes of the diatoms
are either parallel or perpendicular to the direction of
shear. How does the orientation of the diatom affect the
image? Pay particular attention to the dots and striations
in Stauroneis phoenocenteron and Nitzschia sigma.
Hoffman Modulation Contrast Microscopy
1. To use Hoffman modulation contrast optics, remove
the regular sub-stage condenser and replace it with the
Hoffman modulation contrast substage condenser, and
remove the regular objectives and replace them with the
Hoffman modulation contrast objectives. Make a slide of
cheek cells and place the microscope slide on the stage.
2. Rotate the Hoffman modulation contrast substage
condenser turret to the bright-field position (no colored
dot). Set up Köhler illumination using the 10x objective
lens.
3. Remove an ocular and replace it with a centering
telescope. Focus the centering telescope to get a sharp
image of the modulator plate in the back focal plane of
the objective.
4. Move the specimen out of the way so that a clear area
of the slide is visible. Set the Turret to the 10x position
(yellow dot).
243
Chapter | 15 Laboratory Exercises
5. Put the polarizer (called the contrast control filter)
above the field diaphragm. Note that rotating the
polarizer causes a change in brightness of half of the
slit. The region whose brightness changes is called
region 2.
6. Move the slit at the front focal plane of the substage
condenser, using the knurled knob until region 1 of
the slit is superimposed on the gray region of the
modulator plate and region 2 of the slit is in the clear
region of the modulator plate. When the slit is correctly
aligned, region 2 of the slit will be completely black
when the polarizer is rotated to the crossed position.
7. Repeat the slit alignment step for each objective
making sure to match the correct turret position with
each objective. Use the green dot position for the 20x
objective, the blue dot position for the 40x objective, and
the white dot position for the 100x objective. Remove
the centering telescope and replace it with the ocular.
8. Reestablish Köhler illumination. As you view the
specimen, adjust the contrast control filter to get
optimal contrast. The graininess of the image increases
as the contrast increases, so find a good compromise.
Document your observations with photographs.
Seeing “Animalicules” or “Living Atoms” in
Pseudo-Relief
1. Make a slide with a drop of pond water and/or make a
variety of slides, each containing a different organism.
View your slides with differential interference
microscopy and Hoffman modulation contrast
microscopy. Compare and contrast the images obtained
with each method.
2. Take photographs of the organisms that move slowly.
Increasing the viscosity of the sample with Protoslow
or methylcellulose will slow down the organisms.
Samples of the amoeba, Chaos carolinensis; the
ciliates, Blepharisma, Paramecium bursaria, Stentor
and Vorticella; the coelenterate, Hydra; the nematode,
Turbatrix aceti; the rotifer, Brachionus; the tardigrade,
either Milnesium or Hypsibius; and the crustaceans,
Gammarus, Cyclops, Daphnia pulex and Daphnia
magna are available. They can be obtained from Carolina
Biological Supply (http://www.carolina.com/).
LABORATORY 10: VIDEO AND DIGITAL
MICROSCOPY AND ANALOG AND DIGITAL
IMAGE PROCESSING
Making Videos of Moving Microscopic
Objects
1. Remove the semiautomatic camera from the
microscope and replace it with the c-mount adapter.
2.
3.
4.
5.
6.
Attach a video camera to the c-mount adapter. Attach
a coaxial cable with BNC connectors from the VIDEO
OUT terminal of the video camera to the VIDEO IN
terminal in the videocassette recorder (VCR). Connect
the VIDEO OUT on the back of the VCR to the
VIDEO IN terminal of the monitor. Make sure that you
set the IMPEDANCE SELECT switch on the monitor
to 75 ohms.
Turn on the microscope, the video camera, the VCR,
and the monitor. Set the beam splitter so that either 80
or 100 percent of the light goes to the video camera
and 20 or 0 percent goes to the oculars. You may also
use the digital camera to capture images by using
the continuous mode. Plug the digital camera (e.g.,
Nikon 4500 attached to an optical coupler) into a video
capture card (http://www.winnov.com/Home.aspx).
Choose one of the specimens that show motility. For
example, mitosis in Tradescantia stamen hairs, pollen
tube growth in Catharanthus, cytoplasmic streaming
in Tradescantia stamen hairs, onion epidermal cells or
Chara rhizoids, light-induced chloroplast movements
in Elodea or Mougeotia, and the various swimming
movements that occur in the protozoa that live in pond
water.
Choose the type of microscopy that best brings out
the process that you want to study (e.g., bright-field,
dark-field, phase-contrast, polarization, fluorescence,
differential interference microscopy, or Hoffman
modulation contrast microscopy.
Start taping the sequence when you are ready. You
must make a five-minute video for this course on any
specimen or process you like that takes advantage
of the strengths of video microscopy in studying the
movements that occur in microscopic objects. We will
show the videos after we eat dinner at my house, so
they must also be entertaining. You can dub music over
them and add titles. You must write a one- or two- page
paper that describes what organism or process you are
studying and the type of optics and video equipment
you are using.
Remember the x-y rule: Take a sequence that is long
enough before moving the specimen. It is annoying to
the viewer if you take too many short sequences trying
to find a better position. Remember the z rule: It is
also annoying to the viewer if you try to incessantly
improve the focus while recording.
Analog Image Processing
1. Remove the semiautomatic camera from the
microscope and replace it with the c-mount adapter.
Attach an analog CCD camera (e.g., Dage-MTI CCD
72) to the c-mount adapter. Notice the specifications of
the camera. What do the specifications mean?
244
2. Display the gray level test pattern generated by the
camera. Adjust the brightness and contrast of the
monitor so that all the gray levels are clear.
3. Turn on the Olympus BH-2 microscope, the camera
control box, the computer, and the monitor. Set the
beam splitter to the 80/20 position so that 80 percent of
the light goes to the video camera and 20 percent goes
to the oculars.
4. Set up the bright-field microscope with Köhler
illumination. Focus with the SPLAN 40 lens. The cells
should be visible when the iris diaphragm is closed
and invisible when the iris diaphragm is open and the
resolution is maximal. Keep the iris diaphragm most of
the way open.
5. Adjust the manual gain (contrast) and manual black
level (brightness) so that the cheek cells, which are
invisible when looking through the oculars, become
visible on the video monitor. Vary the gain and black
level to maximize the resolving power of the bright-field
microscope. The camera box, which is a sophisticated
analog image processor, has the following controls.
6. The GAIN control affects the amplitude of the video
signal by acting like a linear amplifier. When the GAIN
SWITCH is in the AUTOMATIC position, the camera
automatically tracks and adjusts the whitest portion
of the image to an internally preset value. When
the switch is in the MANUAL position, the camera
maintains a fixed gain that is set by adjusting the GAIN
KNOB.
7. The BLACK LEVEL control affects the amplitude of
the video signal by changing the voltage that produces
a black image. When the BLACK LEVEL is on
PRESET AUTOMATIC, the camera automatically
sets the darkest level to an internally preset value.
The VARIABLE AUTOMATIC setting automatically
adjusts the image to the black level set by the BLACK
LEVEL KNOB. When this switch is on VARIABLE
MANUAL, the camera maintains a fixed black
reference that’ is set by adjusting the BLACK LEVEL
knob.
8. The GAMMA control affects the amplitude of the
video signal by acting like a nonlinear amplifier.
Turning the gamma from 1.0 to 0.45 increases the
contrast of the low light details in the specimen and
decreases the contrast of the brighter details. The
POLARITY switch changes black to white and white
to black by passing the signal through an inverting
amplifier.
9. The camera box has other analog image processing
capabilities. The STRETCH switch gives additional
gain to low light level signals by turning on a nonlinear
amplifier. The BANDWIDTH control increases the
speed of the amplifier so you get better resolution at
the cost of more noise. The ENHANCE knob is used to
sharpen the edges of the specimen.
Light and Video Microscopy
10. What happens to the image of the cheek cells as
you vary the black level and gain? What happens to
the image of the cheek cells when you change the
polarity? What happens to the image of the cheek
cells as you vary the gamma? What effect does
varying the bandwidth have on the image?
Digital Image Processing
1. Attach a digital camera (e.g., Hitachi KP-D50 color
digital camera) to the Integral flashpoint 128 frame
grabber board in the computer. Start the Image Pro
Plus software.
2. Go to the Acquire menu and explore the various
options. Then capture an image with the SNAP
command.
3. Close the Acquire menu and open the File menu.
Save the unenhanced image using the SAVE
command.
4. Open the Enhance menu and click DISPLAY
RANGE to see the distribution of pixel brightness.
Close the DISPLAY RANGE window and click
CONTRAST ENHANCEMENT. Experiment with
the brightness, contrast, gamma, and invert controls.
View the image before and after the enhancement
and look at the graph of the lookup table, which
relates the output intensity to the original intensity.
Keeping the CONTRAST ENHANCEMENT
window open, go to the EQUALIZE command in the
Enhance menu, and experiment with the BEST FIT
command. Notice how the image and the lookup table
changes.
5. Acquire another image and save it. Defocus the
specimen or move it out of the way, and capture
another image and save it.
6. Go to the Process menu and click the BACKGROUND
CORRECTION command. Subtract the background
image from the image of the specimen.
7. Experiment with spatial filtering using Fourier
transforms and convolution kernels. First go to the
Edit menu and convert any color image to a blackand-white image, using the CONVERT TO command.
8. Then go to the Process menu and click the FFT
command. Click the Forward FFT command to do a
Fourier transform on the image. Observe the Fourier
transform. Using the SPIKE CUT command and the
ASYMMETRICAL option, remove selected Fourier
spots, and then click INVERSE FFT. How does the
image produced by the inverse Fourier transform
compare with the original image?
9. Also experiment with the LO-PASS, HI-PASS, and
SPIKE-BOOST commands. Close the Process menu.
10. After experimenting with Fourier transforms, try
spatial filtering with convolution filters. In the Process
245
Chapter | 15 Laboratory Exercises
menu, click FILTERS, ENHANCE, and LO-PASS.
How does the image look?
11. Click UNDO and then click HI-PASS. How does
the image look now? Experiment with various
convolution kernels, varying the size, strength, and
number of passes.
12. Focus the microscope on a stage micrometer. Then
capture and save an image of the stage micrometer.
13. Pull down the Measure menu. Click CALIBRATION,
SPATIAL, and IMAGE. Drag a line between two
distant bars on the stage micrometer and type the
actual distance. The program will respond with the
number of pixels/micrometer for the magnification
used. Then click the MEASUREMENT command,
select the line tool, and begin measuring lengths in
one of your images. Experiment with the various
MEASUREMENT and CALIPER tools.
14. Pull down the Macros menu and follow the
commands given to get a feeling for what the Image
Pro Plus digital image processor can do.
15. Copy all your saved images onto a memory stick. You
will have to print them yourself.
COMMERCIAL SOURCES FOR LABORATORY
EQUIPMENT AND SPECIMENS
Arbor Scientific: http://www.arborsci.com/detail.aspx? ID934
Carolina Biological Supply: http://www.carolina.com/
Edmund Scientific: http://scientificsonline.com/
Industrial Fiber Optics, Inc: http://www.i-fiberoptics.com/
Li-cor Biosciences: http://www.licor.com/
Pasco: http://www.pasco.com/
Ted Pella: http://www.tedpella.com/
Web-tronics: http://www.web-tronics.com/
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