Basics of Polarizing Microscopy

Basics of Polarizing Microscopy
Basics of
Polarizing Microscopy
1.Properties of polarized light
1.1 Polarized light
Polarized light
Transverse wave light whose vibration possess
direction is called polarized light. Light from an
Linearly polarized light
ordinary light source (natural light) that vibrates in
random directions (Fig. 1.1) is called nonpolarized
Circularly polarized light
light. In contrast, while light with vertical vibration
that travels within a single plane (Fig. 1.2a) is called
linearly polarized light, circularly polarized light (Fig.
Elliptically polarized light
1.2b) and elliptically polarized light (Fig. 1.2c) are
types of light in which the vibration plane rotates
Polarizing plate
The vibration direction of light is perpendicular to
the progressing light. The vibration direction of
natural light points to all the directions.
Fig. 1.1 Natural light (nonpolarized light)
Polarizing filter
Polarizing prism
Crossed nicols
Parallel nicols
a. linearly polarized light
b. circularly polarized light
c. elliptically polarized light
Each figure on the left-hand side shows decomposition of each polarized light into two mutual
perpendicular linearly polarized light.
Fig. 1.2 Types of polarized light
A polarizing plate (polarizing filter) or polarizing
prism is often used as the device to change natural light to linearly polarized light (see 1.7).
Configuring the primary and secondary polarizing
devices in the orthogonal directions of each
transmitting linearly polarized ray will cut the light.
Such state in which the primary light polarizing
device is the polarizer and the secondary device
is the analyzer is called crossed nicols. Parallel
nicols is the state in which the analyzer is rotated
to make the direction of the transmitting linearly
polarized light match with the polarizer, and the
amount of light transmittance is maximized. (Fig.
Fig. 1.3 a) crossed nicols and b) parallel nicols
P: polarizer A: analyzer
1.2 Polarization by reflection
When light reflects off the surface of water and
glass, its reflectance varies with the direction of
Component P
polarization (Fig. 1.4a). Comparing the two oscillation components, Component P is parallel to the
Component S
plane of incidence and has 0 reflectance while
Brewster angle
Component S is perpendicular to the plane and
has higher reflectance. The 0 reflectance of
Component P is caused by the existence of an
angle of incidence, known as the Brewster angle.
In other words, the reflected light at this angle is
linearly polarized, and can be cut out with a polar-
q1: Brewster angle
: Angle of incidence
Fig. 1.4 a) Difference of reflectance is due to vibration direction of light
izing plate. In photography, a polarizing filter is
Double refraction
Ordinary ray
used in order to remove reflection from the surface of water and glass (Fig. 1.4b). The Brewster
Extra ordinary ray
angle against the surface of water (n =1.33) and
the surface of glass (n =1.52) is 53°07' and 56°40',
Optical axis
b) Effectiveness of polarizing filter (left: without filter right: with filter)
1.3 Double refraction
An object whose image passes through a calcite
CaCO3 crystal appears doubled (Fig. 1.5a). This
phenomenon is called double refraction or birefringence, which occurs when light that is
launched through a crystal material is divided into
two linearly polarized light rays having mutually
crossing vibration directions, and then refracted.
Among these two light rays, the one that follows
the law of refraction is called an ordinary ray, while
the other one is called an extraordinary ray. Their
Fig. 1.5a. Double refraction phenomenon due to calcite
speed and index of refraction differ from one
Ejection light of
linearly light
Ejection ray of
linearly polarized
A crystal that refracts in such way is called an
anisotropy. Light passing through an anisotropy is
generally divided into ordinary and extraordinary
rays, but toward a certain direction called optical
axis, they travel together. When that happens, the
double refraction phenomenon does not occur.
(see 1.4).
C : optical axis
Fig. 1.5b. Double refraction phenomenon due to diagram
1.4 Optically uniaxial crystal
Optically uniaxial crystal
Anisotropy can be divided into an optically uniaxial
crystal and an optically biaxial crystal accordinng
Optically biaxial crystal
to the optical properties. An optically uniaxial crystal has one optical axis while an optically biaxial
Principal section
crystal has two axes. A material classification in
optically isotropic
isoaxial system crystal
tetragonal system crystal
optically uniaxial crystal
hexagonal system crystal
optically anisotropy
terms of optical properties is as follows:
rhombic system crystal
optically biaxial crystal
Optically positive crystal
monoclinic system crystal
triclinic system crystal
Optically negative crystal
Optical character
Index surface
Principal refractive
The optical axis and the direction of a beam of
light determine the vibration direction of extraordi-
•: vibration direction of
ordinary ray
(perpendicular to
principal section)
- : vibration direction of
extra ordinary ray
(within principal section)
The principal section
is surface of space.
nary and ordinary rays in an optically uniaxial crystal, and the section containing both rays is called
the principal section. The ordinary rays oscillate
vertically through the principal section while the
extraordinary rays oscillate within the principal
section (Fig. 1.6).
Fig. 1.6 Vibration direction of ordinary rays and extraordinary rays of an optically uniaxial crystal
Optically uniaxial crystals can be divided into two types:
optically positive crystals, in which the index of refraction
of extraordinary rays is greater than that of ordinary rays,
c : optical
and vice versa, called optically negative crystals
(hereafter, positive crystals and negative crystals). For
instance, rock crystals belong to positive crystals,
whereas calcite and sapphires belong to negative
crystals. Positive and negative crystals can also be said to
possess a positive or negative optical character,
The index of refraction of extraordinary rays varies with
the direction of progression of light rays. Figure 1.7 shows
the index surface for optically uniaxial crystals with a) a
a. positive crystal
b. negative crystal
(The ellipse is exaggerated)
Fig. 1.7 Index surface of an optically uniaxial crystal
positive crystal, and b) a negative crystal. The index
surface expresses the index of refraction toward the
direction of progression of ordinary rays and extraordinary
rays in terms of the distance from the origin. As shown in
the diagram, the index of refraction of extraordinary rays
inclined by q from the optical axis is ne. The index of
refraction of extraordinary rays reaches a maximum or
minimum perpendicularly along the direction of the optical
axis. The indices of refraction of the ordinary and
extraordinary rays in this direction, w and e, respectively,
are called principal refractive indices. The principal
refracive indices for significant crystals are given in table
Crystal name
rock crystal (quartz)
Table 1.1 Principal refractive indices of significant crystals (wavelength = 589.3 nm)
1.Properties of polarized light
In double refraction, the vibration direction of light with
faster progression is called the X' direction, while the
slower progression is called the Z' direction. As for the
vibration direction, the positive crystals represent the
OP : Direction of
optical axis
2 : optical axial
direction of extraordinary rays, whereas the negative
Phase difference
and compensator of a polarizing microscope (see 3.2.8),
the Z' direction is displayed for investigating the vibration
are both extraordinary rays whose speed differs according to the direction of its progression. See Fig. 1.8 for the
index surface of optically biaxial crystals. a, b, and g show
Direction of arrows express the
vibration direction.
Fig. 1.8 Section of refractive index of an optically biaxial crystal
the principal refractive indices of optically biaxial crystals.
The angle that constitutes the two optical axes (2 ) is
called the optical axial angle.
1.5 Retardation
After being launched into an anisotropy. phase
differences will occur between the ordinary and
extraordinary rays. Fig. 1.9 shows the relationship
between the direction of the optical axis and double refraction. In cases (a) and (b) in Fig. 1.9, relative surges and delays, i.e., phase differences, d,
will occur between the two rays. On the contrary,
no phase difference can be seen in Fig. 1.9c
because light rays advance in the direction of the
optical axis.
The phase difference for extraordinary and ordinary rays after crystal injection is given next.
l indicates the light wavelength, d the thickness of
double refraction properties. n e and n o are the
refraction indices of extraordinary and ordinary
rays, respectively.
Here, the optical path difference R is called retardation and can be expressed as follows.
R is the value of the deviation of two light rays in a
double refraction element, converted to mid-air
distance; it is expressed in a direct number (147
nm, etc.), a fraction or the
( /4, etc.) of the used wavelength.
mu l t i p l e
Z' direction
Optical axial angle
crystals express that of the ordinary rays in the
Z'direction of optically uniaxial crystals. In the test plate
direction of the light for specimens. Generally, even optically biaxial crystal will separate in two rays, and yet they
X' direction
o : ordinary ray
e : extraordinary
: Direction of
optical axis
Fig. 1.9 Relationship between direction of optical axis and double refraction of a crystal
1.Properties of polarized light
1.6 Optical strain
Optical strain
When stress is applied to an isotropic body such
as glass or plastic, optical strain occurs, causing
the double refraction phenomenon, and that is
called photoelasticity. By observing the optical
strain of various materials by means of polarization, the stress distribution can be estimated (Fig.
Glan-Thompson prism
Nicol prism
1.7 Light polarizing devices
Fig. 1.10 Optical strain of plastic
As stated in 1.2, a polarizing plate and polarizing prism are
generally used as the polarizing devices to convert natural
light into linearly polarized light. Their respective features
are given below.
(1) polarizing plate
A polarizing plate is a piece of film by itself or a film
being held between two plates of glass. Adding salient
iodine to preferentially oriented macromolecules will
allow this film to have dichroism. Dichroism is a phenomenon in which discrepancies in absorption occur
due to the vibration direction of incident light polarization. Since the polarizing plate absorbs the light oscillating in the arranged direction of the macromolecule,
the transmitted light rays become linearly polarized.
Despite its drawbacks of 1) limited usable wavelength
band (visible to near infrared light), and 2) susceptibility
to heat, the polarizing plate is inexpensive and is easy
to enlarge.
(2) polarizing prism
When natural light is launched into a crystal having
double refraction, the light proceeds in two separate,
linearly polarized lights. By intercepting one of these
express direction of
optical axis
two, the linearly polarized light can be obtained; this
kind of polarizing device is called a polarizing prism,
and among those we find Glan-Thompson prism (a)
and Nicol prism (b).
A polarizing prism has higher transmittance than a
polarizing plate, and provides high polarization characteristics that cover a wide wavelength band. However,
its angle of incidence is limited and it is expensive. In
addition, when used in a polarizing microscope, this
prism takes up more space than a polarizing plate and
may cause image deterioration when placed in an
image forming optical system. For these reasons, a
polarizing plate is generally used except when brightness or high polarization is required.
Fig. 1.11 Polarizing prism )
(a. Glan-Thompson prism b. Nicol prism)
2.Fundamentals of polarized light analysis
2.1 Anisotropy in crossed nicols
Light does not transmit in a crossed nicols state,
but inserting an anisotropy between a polarizer
and an analyzer changes the state of the polarized light, causing the light to pass through. When
Extinction position
Diagonal position
the optical axis of a crystal with difference of d is
placed between the crossed nicols at an angle of
q to the polarizer's vibration direction, the intensity
of the injected light is expressed as (2.1).
A : direction of progression of analyzer
P : direction of progression of polarizer
C : direction of optical axis of anisotropy
Fig. 2.1 Anisotropy between crossed nicols
Io is the intensity of transmitted light during parallel
nicols, and R is the retardation (equation (1.2)).
With this equation, the change in brightness during the rotation of an anisotropy and of the interference color from retardation can be explained.
2.1.1 Change in brightness when rotating anisotropy
As the equation 2.1 signifies, at certain four positions, (90 degrees apart from each other), the
anisotropy appears black as its optical axis
matches with or becomes perpendicular to the
vibration direction. Such positions are called the
extinction positions. The brightest position, also
known as the diagonal position, is at a 45°. The
drawings in Fig. 2.2 represent the change in
brightness from extinct to diagonal position and
vice versa, while rotating the body.
A : vibration direction
of analyzer
P : vibration direction
of polarizer
Fig. 2.2 Extinction position and diagonal position of anisotropy
2.1.2 Interference color in anisotropy
Interference color
By equation (2.1), when the phase difference d of an
anisotropy is 0, 2 , 4 , (retardation R 0,
,2 ,
represents a single color wavelength) the intensity of the transmitted light is 0, or the body appears
pitch dark. On the other hand, when the body seems
brightest, d is p, 3p, 5p,. (R is /2, 3 /2, 5 /2,
…)This gap in light intensity attributes to the phase difference created between the ordinary and extraordinary rays after passing through an anisotropy, next
through an analyzer, and eventually to have interference.
Interference color chart
The first order
Sensitive color
Fig. 2.3 shows the transmittance of light when a
wedge-shaped quartz plate, having double refraction is
placed in the diagonal position in crossed nicols. In the
case of single color light, the intensity of transmitted
light creates light and dark fringes. As the phase difference of an ordinary and extraordinary rays vary according to the wavelength, so does the transmittance at
each wavelength. (See formula 1.1).
When observing the wedge-shaped quartz plate of Fig.
2.3 under white light, interference destroys some
wavelengths and reinforce others. As a result, by
superimposing the wavelength of visible light, the color
appears. This is called interference color.
(Transmitted light intensity)
quartz plate
expresses the direction of optical axis
Fig. 2.3 Transmittance of wedge-shaped quartz plate
The relationship between retardation amount of
anisotropy and interference color is shown by the
interference color chart. By comparing the interference color of the anisotropy with the interference
color chart, the retardation of the anisotropy can be
estimated. A vertical line is drawn on the interference color chart to show the relationship between
double refraction (n e -n o ) and the thickness of
anisotropy. This is used to find out the thickness d
of specimens or the double refraction (ne-no). from
Fig. 2.4 Color Chart
The visible colors in the color chart from zero order
black to first order purplish-red are called the first order
colors. The first order purplish-red is extremely vivid,
and the interference color changes from yellow, red to
blue just by the slightest retardation. This purplish-red is
called a sensitive color. Colors between the first order
red and second order red are called second order
colors, such as second order blue, second order
green. The higher the order of colors gets, the
closer the interference color approaches white.
2.Fundamentals of polarized light analysis
Figure 2.5 shows the transmittance curve of the
interference color in relation to retardation around
the sensitive color, and is calculated from equation (2.1). In the sensitive colors, green light can-
a) R=400 nm
The light within the range from green
to purple is transmitted, and appears
yellow with a mixed color.
not be transmitted and thus appears as purplishred (Fig. 2.5b). If retardation is reduced from
sensitive colors, then a wide-range mixed color
light from green to red turns up, observed as yellow, as shown in Fig. 2.5a; increased retardation,
contrarily, brings out a blue interference color.
(Fig. 2.5c.)
b) R=530 nm (sensitive color)
The low number of green portions
results in purple and red light to
transmit, and is seen as purplish red.
c) R=650 nm
The strong transmitting light of blue
and purple emphasizes the blue
Fig. 2.5 Retardation and transmittance curve
2.2 Superimposing anisotropy
Now we consider two anisotropy overlapping one
another; one with the vibration directions of their
slower light rays (Z' direction) in the same direction (Fig. 2.6a), and the other perpendicularly. (Fig.
Fig. 2.6 Superimposing anisotropy
a:addition b:subtraction
When the Z' directions of two anisotropy overlap,
pointing the same direction, the vibration direc-
mined from the changes in the interference
color when the anisotropy overlap. Shifting of
tions of the slower polarized light match. The total
retardation is equivalent to the numerical sum of
the interference color toward the increase of
retardation is addition, and vice versa for sub-
the retardations.
traction. Both addition and subtraction are the
R=R1+R2 (R1, R2 denote the retardations of anisotropy 1 and 2)
This state is called addition (Fig 2.5a). In contrast
determinants for judging Z' direction. (To be
discussed further in 4.1.3) Knowing the Z'
the phase difference after passing through one
anisotropic element is cancelled out by the other
direction helps determine the optical character
of elongation (see 2.3) In addition, when the
phase difference. As a result, the total retardation
anisotropy overlap with one at the extinction
is the difference between the two anisotropy
position and the other at the diagonal position,
the total retardation becomes equivalent to
This state is called subtraction (Fig 2.5b). Whether
the retardation of the anisotropy at the diagonal position.
the state is addition or subtraction can be deter-
2.Fundamentals of polarized light analysis
Optical character of elongation
Some anisotropy are elongated in some direction as the
narrow crystals and fibers in rock would be. The relation-
Slow length
ship between the direction of elongation and Z' direction
can specify the optical character of elongation (zone
Fast length
Phase plate
character). When the Z' direction matches the direction of
elongation, it is said to have a slow length, and when the
z' direction crosses the direction of elongation, then it has
a fast length).
Tint plate
This optical character does not coincide with the positive
and negative attributes of uniaxial and biaxial crystals. The
Quarter-wave plate
optical character of elongation is fixed for anisotropy such
Half-wave plate
2.3 Optical character of elongation
as crystals (e.g., uric acid sodium crystals of gout), and, by
using a polarizing microscope, can be distinguished from
optical character of
elongation is positive
optical character of
elongation is negative
Fig. 2.7 Optical character of elongation
pseudo gout crystals (see 4.1.3).
2.4 Phase plate
A phase plate is used in the conversion of linearly
polarized light and circularly polarized light, and in
(tint plate, quarter-wave plate, and half-wave
plate) are made. When using a quarter-wave
the conversion of the vibration direction of linearly
polarized light. A phase plate is an anisotropy which
plate, a diagonally positioned optical axis
direction can convert incident linearly polarized
generates a certain fixed amount of retardation, and
light into circularly polarized light and vice versa
based on that amount, several types of phase plate
(Fig. 2.8).
linearly polarized light
circularly polarized light
1/4 wave plate
Conversion of linearly polarized light into circularly polarized light
circularly polarized light
linearly polarized light
1/4 wave plate
Conversion of circularly polarized light into linearly polarized light
Fig. 2.8 Quarter-wave plate conversion of linearly polarized light into circularly polarized light
A half-wave plate is mainly used for changing the
vibration direction of linearly polarized light, and for
plates, half-wave plates, and tint plates are
usually thin pieces of mica or crystal sand-
reversing the rotating direction of circularly polarized and elliptically polarized light. Quarter-wave
wiched in between the glass.
3. Polarizing microscopes
3.1 Characteristics of a polarizing microscope
A polarizing microscope is a special microscope that uses
polarized light for investigating the optical properties of
specimens. Although originally called a mineral microscope because of its applications in petrographic and
mineralogical research, in recent years it has now come
to be used in such diverse fields as biology, medicine,
polymer chemistry, liquid crystals, magnetic memory,
and state-of-the-art materials. There are two types of
polarizing microscopes: transmitted light models and
incident light models. Fig. 3.1 shows the basic construction of a transmitted light polarizing microscope.
Observation tube prism
Eyepiece with crosshair
Image formation lens
Bertrand lens
Test plate, compensator
Centerable revolver
Strain-free objective
Rotating stage
Polarizing condenser
Transmitted light illuminator
Fig. 3.1 External view and construction of a transmitted light polarizing microscope (BX-P)
Polarizing microscope
Polarizing condenser
As seen in Fig. 3.1, compared to a typical microscope, a polarizing microscope has a new con-
a Bertrand lens for observing the pupil of the
objective, a test plate, a compensator, and an
Rotating stage
struction with the following added units: a polarizing condenser that includes a polarizer, a rotating
eyepiece with crosshair. An incident light
polarizing microscope like the one shown in
stage that allows the position of the specimen to
Fig. 3.2 is used for the observation of metallic
be set, a strain-free objective for polarized light, a
centerable revolving nosepi ece that allows opti-
and opaque crystals.
Strain-free objective
Centerable revolver
cal axis adjustment for the objective, an analyzer,
Bertrand lens
Test plate
Eyepiece with crosshair
Observation tube prism
Eyepiece with crosshair
Image formation lens
Bertrand lens
Half mirror
Incident light illuminator
Centerable revolver
Strain-free objective
Rotating stage
Fig. 3.2 External view and construction of an incident light polarizing microscope
3. Polarizing microscopes
3.2 Constituents of a polarizing microscope
3.2.1 Polarizer and analyzer
Among the essentials for polarized light observation, for a transmitted light polarizing microscope,
the polarizer should be placed below the condenser and the analyzer should be above the
objective. For an incident light polarizing microscope, the polarizer is positioned in the incident
A:Vibration direction of analyzer
light illuminator and the analyzer is placed above
the half mirror.
P:Vibration direction of polarizer
The polarizer is rotatable 360° with degree gradations indicated on the frame. The analyzer can
also rotate 90° or 360°, and the angle of rotation
can be figured out from gradations as well. As fig.
3.3 shows, the vibration direction of a polarizer
Fig. 3.3 Vibration direction of light polarizing devices
should go side to side relatively to the observant,
and go vertically for an analyzer. (ISO/DIS 8576)
3.2.2 Polarizing objective (strain-free objective)
A polarizing objective differs from ordinary objectives in a respect that it possesses a high lightpolarizing capability. A polarizing objective can be
distinguished from ordinary ones by the label P,
PO, or Pol. Objectives which have the label DIC or
NIC signify their use for differential interference,
and yet have improved polarization performance.
The polarizing objectives can easily be adopted
for bright field observation, too.
There are two factors which determine the level
of the objectives' polarizing performance: 1) the
turbulence of polarizing state, caused by the antirefraction coating of lenses, or the angle of incidence influencing the refraction on the lens surface, and 2) a lens strain such as an original lens
strain, newly created from the junction of the
lenses, or from the connection of frame and
lenses etc. An objective lens for polarization is
designed and manufactured to have low turbulence by refraction in the polarizing state on the
lens surface and to have low lens strain.
Fig. 3.4 Polarizing objective
(ACH-P series and UPLFL-P series)
3.2.3 Polarizing condenser
Polarizing condenser
A polarizing condenser has the following three
characteristics: 1) built-in rotatable polarizer, 2) top
Cross moving device
lens out construction when parallel light illumination at low magnification is required, and 3) strain-
Rotating stage
free optical system, like the objectives.
Universal stage
Bertrand lens
Fig. 3.5 Polarizing condenser (U-POC)
3.2.4 Polarizing rotating stage
As illustrated in 2.1.1, rotating an anisotropy between
crossed nicols changes the brightness. For this reason, in
polarized light observation, the specimen is often rotated
to the diagonal position (the position where the
anisotropy is brightest). In other words, rotatability of the
polarizing stage and centerability are fundamental (see
360° angle gradations are indicated in the area
surrounding the rotating stage, and, using the vernier
scale, the angle can be measured to an accuracy of 0.1°.
A cross moving device is also equipped exclusively for
moving specimens.
A universal stage with multiple rotating axes may also be
used to enable the observation of specimen from many
3.2.5 Bertrand lens
A Bertrand lens projects an interference image of
the specimen, formed in the objective pupil, onto
the objective image position (back focal length). It
is located between the analyzer and eyepiece for
easy in and out of the light path. See 4.2 for how
to use the lens.
Fig. 3.6 Polarizing rotating stage (U-SRP)
3. Polarizing microscopes
3.2.6 Centerable revolving nosepiece
The optical axis of the objective changes slightly
according to the lens. Since the stage needs to
Centerable revolving nosepiece
be rotated for polarizing observation, the objective and the optical axis of the tube must coincide
Eyepiece with crosshair
exactly with one another. In order for the optical
Test plate
axis to completely match even when the lens'
magnification is changed, a revolver with optical
centering mechanism is installed in each hole.
(see 3.3).
Fig. 3.7 Centering revolving nosepiece (U-P4RE)
3.2.7 Eyepiece with crosshair
This is an eyepiece with a diopter correction
mechanism which has a built-in focusing plate
containing a crosshair. By inserting the point pin
into the observation tube sleeve, the vibration
direction of the polarizer and analyzer can be
made to agree with the crosshair in the visual
Fig. 3.8 Crosshair
3.2.8 Test plate and compensator
The test plate is a phase plate used for verifying
the double refractivity of specimens, determining
the vibration direction of pieces, and for retardation measurement; a quarter-wave plate (R=147
nm) or a tint plate (R=530) are some examples.
direction shown on the test plate indicates
the Z' direction.
The compensator is a phase plate that can
change and measure the retardation. See
Chapter 5 for more details.
Fig. 3.9 Test plate with compensator
Orientation plate
3.3 Preparation for polarizing microscope observation
In polarized light microscopy, always perform the
optical adjustments, e.g. centering of the rotatable stage, adjusting the optical axis of objective
lens and vibration direction of a polarizer, before
the observation.
(1) Adjusting the stage
In a polarizing microscope, the stage is often
rotated during observation. Thus, it is necessary that centering of the rotatable stage is in
alignment with the optical axis of the objective.
Insert a standard objective (normally 10x) into
the optical path and rotate the stage.
Manipulate the two stage centering knobs to
bring the center of a circle, which is traced by
Fig. 3.10 Centering adjustment of the stage
a point on a specimen on the stage to align
with the intersection of the crosshair of the
eyepiece. (Fig. 3.10).
(2) Adjusting the optical axis of the objective
For stan dard objectives, as explained in (1)
orientation plate
above, the centering of the rotating stage
aligns with the optical axis of the objective. For
objectives with other magnifications, the centerable revolving nosepiece adjusts the centering of the objective optical axis.
orientation plate
crosshair in an
For objectives other than 10x, insert the objective into the light path. Then, rotate the stage
and turn the screw of the centerable revolving
nosepiece to make the optical axis align with
the rotating center of the stage.
standard plane
(3) Adjusting the polarizer
When the calibration of the polarizer is 0°, the
vibration direction must correctly align with the
crosshair in the visual field. To do this, an orientation plate, which is a crystal specimen
whose optical axis is parallel to the standard
plane, is used. If the vibration direction of the
polarizer is not in alignment with this optical
axis, the orientation plate appears bright. In
order to darken it, adjust the polarizer and
analyzer and fix them at the position where
the standard plane of the orientation plate is
parallel with the horizontal line of the crosshair
(Fig. 3.11). For some polarizing microscope,
Make it parallel
the analyzer is already built into the mirror unit
Fig. 3.11 Adjustment by the orientation plate
and its vibration direction is controlled.
3.Polarizing microscopes
Observation of an anisotropy by a polarizing
microscope is generally done with illumination of
lower NA but without the top lens of the ordinary
condenser lens. This observation is called ortho-
One nicol
scopic observation. In order to investigate the
optical properties of a crystal, etc., interference
fringes that appear on the exit pupil of the objective can be observed during polarizing light observation. This observation method is called conoscopic observation. Provided below are the
orthoscopic and conoscopic observation meth-
a) Vitamin crystal
4.1 Orthoscopic observation
Among the observation methods of a polarizing
microscope, the orthoscopic observation is the
one in which only the roughly vertical light is
exposed to the specimen surface (i.e., low illumi-
b) Optical pattern of liquid crystal
nation light of NA), and the optical properties are
observed only in that direction. In orthoscopic
observation, the Bertrand lens is removed from
the light path, and either the top lens of the condenser lens is out, or the aperture diaphragm is
There are two orthoscopic observations, one is
crossed nicols and the other is one nicol. In
crossed nocols, the polarizer and analyzer are
both used to be crossed, while in one nicol, only
the polarizer is used.
c) Rock
4.1.1 Observation of anisotropy via crossed nicols
The most commonly used observation method in
polarizing microscope is crossed nicols observation to inspect the double refractive structures in
biology, rock minerals, liquid crystals, macromolecule materials, anisotropic properties such as
emulsions, and stress strain.
d) Emulsion
Fig. 4.1 Example of anisotropy observation via crossed nicols
4. Observation method for polarizing
4.1.2 General principles of interference colors and retardation
Retardation testing is conducted for investigating
an optical anisotropy. Retardation R is expressed
specimen diagonally in crossed nicols,
observe the interference colors, then com-
by the equation (1.2) as d (ne -no), the product of
the width of anisotropy and double refraction. By
pare it with the interference color chart given
in 2.1.2. However, a high degree of accuracy
using this equation, the specimen's double refrac-
cannot be expected from the retardation
tion can be calculated from the value of thickness
d, giving a hint as to what the anisotropy may be.
value derived in this way; measurement is
restricted to the range of bright colors, from
If, on the other hand, the value for double refraction is already given, then the thickness d will be
primary order to secondary order. This is why
figured out. Furthermore, through the computation of optical strains, the analysis of stress can
be used in order to perform accurate measurements.
a compensator as outlined in Chapter 5 must
possibly be made.
In order to determine the retardation, set the
4.1.3 How to use a test plate
The test plate for a polarizing microscope is used as
(1) Sensitive color observation
Use of a tint plate in polarization observation of
anisotropy with small retardation enables observation at bright interference colors. In the neighborhood of sensitive colors, the retardation changes,
and the interference colors alter accordingly but
only more sharply and dramatically. Because of its
sensitivity, any minute retardation can be detected
through interference colors.
(2) Measurement of optical character of elongation
As stated in 2.3, measuring the optical character of
If the test plate is put in, the interference color shifts to
higher order. (addition)
The Z' direction matches the direction of elongation.
The optical character of elongation is positive.
elongation for anisotropic elements elongated in a
certain direction enables to identify the unknown
anisotropy. Determining the optical character of
elongation is performed while using the test plate
and compensator to observe changes in the interference colors (Fig. 4.2).
(a) Set the anisotropy in the diagonal position. Look
over the interference color of the specimen in
the interference color chart.
(b) Insert the test plate into a slot and observe the
changes in the interference colors. If the color
converts to higher order, then the Z' direction of
the anisotropy matches the Z' direction of the
test plate. If it changes to lower order, the Z'
Z' direction
test plate
If the test plate is put in, the interference color
shifts to lower order. (subtraction)
The Z' direction is perpendicular to the direction of
The optical character of elongation is negative.
direction is perpendicular to that of test plate.
Relationship between the direction of elongation
and Z' direction of the anisotropy helps determine the optical character of elongation.
Fig. 4.2 Determination of the optical character of elongation
4.1.4 One nicol observation
One nicol observation, in which the analyzer is
removed from the optical path, leaving the polar-
izer inside, is mainly used to observe rock minerals. In crossed nicols observation, the anisotropy
Becke line
appears colored by the interference colors.
However, because interference colors do not
emerge with only one nicol, the specimen can be
seen in more natural, original color. Besides
inspecting the shape, size, and color of the specimen, investigation of plechroisms by rotating the
stage and observing the changes in colors can be
To estimate the index of refraction of crystals
such as minerals, Becke line is often utilized. The
Becke line is a bright halo visible between the
crystal and the mounting agent when the aperture stop of the condenser lens is closed (Fig.
4.3). The Becke line is clearly visible when the difference of the index of refraction of the mounting
agent and the crystal is large; it becomes dim
when the difference is smell.
Lowering the stage (or raising the objective)
moves the Becke line to a higher index of refraction, and raising the stage (or lowering the objec-
Fig. 4.3 Becke line
tive) moves the line to a lower index of refraction.
By changing the mounting medium while observ-
When the index of refraction of the crystal is
ing the Becke line, the medium having the same
index of refraction with the crystal can be deter-
ing agent:
mined, and in turn, the crystal's index of refraction
b) Becke line with a slightly raised stage
can be deduced.
In the opposite case, the location of the Becke line
greater than the index of refraction of the mounta) Becke line with a slightly lowered stage
is contrary to what is seen in Fig 4-3.
4.2 Conoscope
Conoscopic observation is used to obtain the
information necessary for identifying crystals such
as rock minerals in uniaxial and biaxial measurement as well as in measurement of the optical
axis angle.
4.2.1 Conoscopic optical system
Among many observation methods using a polarizing
microscope, the one which studies the pupil surface of
the objective (back focal plane) with a condenser lens
installed is called conoscopic observation. The purpose of conoscope is to view the interference fringes
Conoscopic projection image
(observed with eyepieces)
created from the light rays that travels through the
specimen through multiple angles, and thus enables
the inspection of various optical properties of the
specimen in different direction at the same time. In
order to gain the best result, the objective lens with NA
Bertrand lens
Conoscopic image
of high magnification is required.
Objective lens
e:extra ordinary ray
o:ordinary ray
The Conoscopic optical system is shown in Fig. 4.4.
The linearly polarized light that passes through the
polarizer is converged by the condenser and travels
through the specimen at various angles. After that, the
linearly polarized light will be divided into ordinary and
Condenser lens
extraordinary rays in the crystal, will proceed parallel to
each other after passing through the crystal, then possess the optical properties that are peculiar to the
specimen, and the retardation dependent of the angle
of incidence.
The two rays meet on the pupil surface of the objective and their polarization direction is adjusted by the
analyzer, causing an interference. These interference
fringes are called the conoscopic image. First interference fringes, created by the rays parallel to the microscope optical axis, emerge at the center of the conoscopic image. The light rays which was launched at an
angle relative to the optical axis creates the second
interference fringes, which then appear in the periphery of the image.
The conoscopic image can be easily studied by
removing the eyepiece. However, because the interference fringes will become rather small, an auxiliary
lens called a Bertrand lens projects the pupil surface of
the objective onto the original image position, and
enlarges it through the eyepiece.
Fig. 4.4 Conoscopic optical system
4. Observation method for polarizing microscope
4.2.2 Conoscopic image of crystals
Conoscopic images of uniaxial crystals differ from
those of biaxial crystals. A flake that has been cut
vertically by uniaxial optical axis can be viewed as
a concentric circle with penetrated black cross
(isogyre). This cross center is the optical axis
direction of the uniaxial crystal.
As shown in Fig. 4.5b, if an image has two centers
of the interference fringes, then the image is for a
biaxial crystal. By studying the style of a
conoscopic image, the distinction between
uniaxial crystals and biaxial crystals, the optical
a) Uniaxial crystal conoscopic image (calcite)
axis direction, the optical axis angle of biaxial
crystals, and the positive and negative crystals
can be attained.
b) Biaxial crystal conoscopic image (topaz)
Fig. 4.5 Conoscopic images
4.2.3 Determination of positive and negative crystal using a test plate
The use of a test plate in the conoscopic image
enables to distinguish positive and negative crystals. In
the case of uniaxial crystals, the vibration direction of
the extraordinary rays oscillates inside the principal
section (the surface including the vibration direction of
the rays and the optical axis), and ordinary rays oscillate
perpendicularly to the principal section. For positive
crystals, the index of refraction of extraordinary rays is
greater than that of the ordinary rays, and vice versa for
negative crystals.
As a result, in uniaxial crystals cut perpendicularly by the
optical axis, the Z' direction of the conoscopic image
appears as shown in fig. 4.6a. Inserting the test plate
into the optical path for a positive crystal changes the
interference colors in the direction in which the first
quadrant and third quadrant are added. As for a negative crystal, the interference colors move in the direction in which the second quadrant and the fourth
quadrant are added. Observing the changes in the
interference colors upon inserting the test plate helps
determine whether it is a positive crystal or a negative
Figure 4.6b shows a conoscopic image of the uniaxial
crystal when the sensitive color test plate is inserted
into the light path. Observing the changes in the interference colors around the optical axis determines
whether the crystal is positive or negative.
positive crystal
negative crystal
positive crystal
negative crystal
Z' direction
of test plate
Fig. 4.6
a) The Z' direction of the uniaxial crystal conoscopic image
b) Changes while the sensitive color test plate
is present in the light path
5. Compensator
For strict measurement of the retardation of
anisotropy, a device called a compensator, com-
tion vary, thus it is necessary to choose the
most suitable compensator for the application.
posed of a phase plate that can change the retardation, is used. Depending on the compensators,
This chapter describes the principles and
measurement methods of various compen-
measurement methods and measurable retarda-
5.1 Types of compensators
The accurate retardation measurement can be
obtained by canceling the retardation created
measuring ranges and applications are given
from specimens, and by reading the calibration
marked at the point. Most typical compensators'
Measuring Range**
Main Applications
0-11000nm(0-20 )
0-1640nm(0-3 )
• Substances with high retardation such as crystals,
LCDs, fibers, plastics, teeth, bones, and hair.
•Retardation measurement of optical strain
•Determination of the Z' direction of anisotropy
• Retardation measurement of crystals, fibers, living
organisms, etc.
•Retardation measurement of optical strain
•Emphasizing contrast for the observation of fine
retardation textures
• Determination of the Z' direction of anisotropic
•Retardation measurement for thin film and glass
• Emphasizing contrast for the observation of fine
retardation textures
• Determination of the Z' direction of anisotropy
quartz wedge
• Retardation measurement of rock crystals
• Determination of the Z' direction of anisotropy
Table 5.1 Measuring range and applications of various compensators
* Compensator names are Olympus brand names
** The measuring range of the compensator is that of an Olympus compensator
(compensator measuring ranges vary with manufacturers)
The Z' direction (
direction) is printed on the compensator to facilitate distinguishing the Z' direc-
tion of anisotropy as well as test plate. (see 4.1.3).
Detailed information on each compensator is given next.
5.2 Berek compensator
A Berek compensator is a kind of a prism which
measures retardation with a calcite or magnesium
Berek compensator
fluoride crystal cut perpendicular to the optical
axis. (Fig. 5.1)
Turning the rotating dial on the compensator
inclines the prism relative to the optical axis,
lengthens the optical path, and increases the difference between the index of refraction of the
ordinary rays and extraordinary rays (ne-no), which
in turn increases retardation as shown in Fig. 5.2.
Fig. 5.1 Berek compensator
:prism tilting angle
C :optical axis
prism tilting angle
Fig. 5.2 Angle of prism inclination and retardation of Berek compensator
To measure the retardation of specimen, tilt the
Here, C is calculated as follows:
prism to move the black interference fringes or a
dot to the desired location, then read the
calibration from the rotation dial (at this point, the
retardation of the compensator and that of the
specimen become equivalent).
Use the attached conversion table to determine
the retardation R from the angle that is read out.
The table is deriven from calculation using the
following equation.
: refraction indices for ordinary rays and
extraordinary rays
d: prism thickness of the compensator
Two kinds of Berek compensators are available
from Olympus: U-CTB with a large double refrac-
range than conventional Berek compensators.
The typical interference fringes when using a
tance calcite prism, and U-CBE with a calcite
magnesium prism. U-CTB has a wider measuring
Berek compensator are shown below.
a) diagonal position
b) while measuring retardation
Fig. 5.3 Berek compensator interference fringes when measuring minerals inside rocks
a) U-CBE
b) U-CTB
Fig. 5.4 Berek compensator interference fringes when measuring fibers
(The above diagram is from a positive fiber. When it is negative, the interference fringes are reversed for U-CBE and U-CTB.)
5. Compensator
5.3 Sénarmont compensator
A Sénarmont compensator is a combination of a
highly accurate quarter-wave plate and a rotating
configuration of the Se
énarmont compensator
is shown in Fig. 5.6.
1/4 Wave plate
Sénarmont compensator
Fig. 5.5 Sénarmont compensator (quarter-wave plate)
Fig. 5.6 Sénarmont compensator configuration
The rays exited from the specimen whose retardation is measured are elliptically polarized light.
Specimen retardation determines the state of this
elliptically polarized light. This light becomes linearly polarized when it passes through a
Sénarmont compensator (quarter-wave plate).
The linearly polarized light at this time is rotated
more than when no specimen is present. The
retardation of the specimen determines the
extent of the rotation. The rotation angle q is the
position at which the specimen is darkened when
a) diagonal position
the analyzer is rotated. The retardation R is calculated from the rotation angle q by the following
Since the quarter-wave plate used in the
Sénarmont compensator is normally designed for
a 546 nm wavelength, the
= 546 nm narrow
band interference filter must be used.
An example usage of the Sénarmont compensator is shown in the picture below.
b) while measuring retardation
Fig. 5.7 Measurement of muscle with Sénarmont compensator
Sénarmont compensator
Bräce-köhler compensator
5.4 Bräce-köhler compensator
A Br¨åce-köhler compensator is a compensator
for measuring fine retardation. (see Fig.5.9) To
center. Turning the dial will rotate the prism.
change the retardation, rotate the small mica
prism with low retardation with optical axis in the
Vibration direction of analyzer
Zero position of compensator
Vibration direction
of polarizer
optical axis
Fig. 5.8 Bräce-köhler compensator
Fig. 5.9 Bräce-köhler compensator prism (rotation direction)
The value of retardation R using a Bräce-köhler
compensator can be found from the equation
below, using the rotation angie q.
) (5.3)
R=R0 • sin (2 •
R 0 is a constant value individually attached to
each product. An example usage of the Bräceköhler compensator is shown in Fig 5.10.
A Bräce-köhler compensator is also used to
increase contrast in polarized light observation,
diagonal position
besides retardation measurement. When using a
Bräce-köhler compensator to observe a sample
with an extremely small retardation, an increase
or a decrease of retardation results in stressing
the differences in brightness between the place
where retardation occurs and its background,
and thus simplifies the observation. The Bräceköhler compensator is particularly effective during
observation in polarized light of the double refractive structure in living organisms.
Two Bräce-köhler compensators are available
from Olympus: U-CBR1 and U-CBR2. U-CBR1 has
a measuring range of 0-55 nm (
CBR2 has 0-20 nm (
/10), and U-
while measuring retardation
Fig. 5.10 Measurement of a film with Bräce-köhler compensator
5. Compensator
5.5 Quartz wedge
A quartz wedge is shown in Fig. 5.12. Moving the
quartz wedge can alter the retardation because
Quartz wedge
the retardation continually changes in the direction of the wedge.
Instructions on how to measure the sample retardation is provided next. Moving the quartz wedge
toward the long-side direction makes the black
fringes appear when the sample retardation and
compensator retardation cancel out each other.
At this point, remove the specimen, secure the
quartz wedge, and determine the retardation by
comparing the observable interference color with
the interference color chart. The result obtained in
this manner lacks accuracy. Besides measuring
Fig. 5.11 Quartz wedge
retardation, the quartz wedge is also used for
determining the Z' direction.
optical axis
Quartz wedge
Direction of
optical axis
to space)
moving direction
Fig. 5.12 Quartz wedge prism
An example of measuring quartz wedge retardation is shown below.
a) diagonal position
b) while measuring retardation
Fig. 5.13 Measurement with a mineral crystal quartz wedge.
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