2
Acquiring Images
The quality of image analysis results depends to
a great extent on the quality of the images that
are used. The (in-)famous motto: “garbage in—
garbage out” applies. Trying to recover an
underexposed or otherwise corrupted image is
an enormous effort. Moreover, the very process
of image restoration can be considered a form of
tampering with the original image, because it
introduces information that may not have been
there in the first place. When compared to the
little extra time spent when taking the picture,
having to restore input images constitutes an
extremely poor return on investment. We therefore want to spend an entire chapter on how to
acquire good images for image analysis.
With a view towards image analysis, three
aspects deserve particular attention: (1) A correct analysis of shapes and preferred orientations
requires high spatial resolution. This is obtained
by choosing equipment with high resolving
power and by focusing under appropriate f-stop
or condenser settings. Correct digitization, i.e.,
conversion of the continuous image coordinates
to discrete raster coordinates is important also.
(2) Correct estimates of size and volumes
depends on magnification. The scale should be
constant throughout the image; if it varies it
should be known such that the image can be
rectified. (3) Correct identification of phases
and segmentation depend very sensitively on
image contrast, given that colors and gray values
should have the same ‘meaning’ everywhere in
the image. To achieve this, the illumination and
the background have to be constant.
Most of the images that are going to be
analyzed in this book come from microscopic
and macroscopic sources: photomicrography
and photomacrography. Proceeding form the
largest scale to the smallest we will discuss a
number of methods of image acquisition keeping
in mind (1) best resolution, (2) constant magnification and (3) even illumination. Note, however,
that this chapter does not serve as an introduction
to photography, photomacrography or microscopy techniques—it merely highlights certain
aspects that are important for image analysis.
2.1
Photography
One of the most common source for images is
photography. We begin with pictures that are
taken in the field, at the outcrop, using normal
lenses or macro lenses for close-ups. Very few
people still use photographic film, but the geometrical and optical aspects of picture taking are
the same for film and digital cameras. We will
discuss photographic optics first and talk about
specific aspects of digital cameras later in this
chapter. For a more thorough introduction to
optics, a textbook (e.g., Hecht and Zajac, 2003)
should be considered.
2.1.1
Field Photography
Field photographs are mostly used for illustration or
reference. However, under certain circumstances,
R. Heilbronner and S. Barrett, Image Analysis in Earth Sciences,
DOI 10.1007/978-3-642-10343-8_2, # Springer-Verlag Berlin Heidelberg 2014
15
16
2
Acquiring Images
Fig. 2.1 Photographs of outcrops. (a) Outcrop showing ductile shear zone, pocket knife for scale; note, uneven surface
producing uneven lighting in spite of diffuse day light conditions; (b) soil profile of rendzina (Image courtesy Christine
Alewell); picture taken with flash; note central perspective and even illumination; (c) snow profile; picture taken in
transmitted light; scale is missing
and in particular if they are flat, they may also
be used as input for image analysis. However, no
matter if the images are going to be used as
illustrations or for image analysis, a few points are
worth considering when acquiring them: (1) locality, (2) lighting, (3) perspective, and (4) scale.
First, with digital storage space being cheap
and plentiful, it is worth taking a number of extra
pictures at a scale large enough to show the entire
outcrop. Using a series of shots one can then zoom
in on the actual area of interest. Such overview
pictures are often helpful to position and orient
close-ups; they also present a record of the
sampling site, showing, for example, if the detail
images are representative samples or not. If the
camera does not have a GPS device, it may even
be worth taking a picture of the topographic or
geological map showing the location to make sure
that the images can be geo-referenced later on.
Next, the lighting situation has to be considered. Direct sunlight is not recommended because
between light and shadow more contrast is created
than any film or chip can reproduce; diffuse
lighting is best (Fig. 2.1). Direct sunlight should
only be used if features of the surface topography
such as fractures, cleavage, weathering etc. are to
2.1
Photography
17
Fig. 2.2 Photomacrography in the field. (a) Glacially polished outcrop; (b) detail of ductile shear zone; (c) foliated
granitic rock (light) with highly stretched enclaves (dark); (d) fault rock, tip of pencil for scale (Image courtesy Holger
Stünitz). Note central perspective and diffuse lighting conditions
be emphasized; in these cases, oblique or grazing
sunlight is best. Diffuse lighting is given if the day
is overcast (Fig. 2.1a) or—on a sunny day—if the
outcrop faces away from the sun. For smaller
outcrops, a flash can be used (Fig. 2.1b). A special
situation is given for snow, where homogenous
illumination can be generated by digging a trench
and viewing the snow in transmission (Fig. 2.1c).
When photographing smaller details (Fig. 2.2),
indirect lighting is easily obtained by blocking the
direct sun with a field note book or ones own
body. When lighting is poor, additional light can
be guided to the scene by using a reflector such as
a white piece of paper or the aluminum back of
the writing pad (Fig. 2.2d). Again, a flash could
be used, but pictures taken with a flash should be
checked immediately: it is often difficult to anticipate the effect of the flash when the picture is
taken at close range.
Finally, if the picture is to be used for analysis, a central perspective should be used, i.e., the
viewing direction should be normal to the surface, as is approximately the case for all outcrops
shown in Figs. 2.1 and 2.2 with the exception of
Fig. 2.1a. Keeping the magnification constant
across the image also implies that distortions
are avoided. Last but not least, a scale or an
object of known size should be placed somewhere in the picture (Figs. 2.1 and 2.2). For
completeness sake, one may consider taking
two images, one with and one without the scale.
2.1.2
Photomacrography
In photography, the image is produced by the
geometric projection of a scene on the image
plane. Regular photographic cameras are designed
18
2
for situations where objects are large and at a large
distance (compared to the focal length of the
camera). The distance between an object and
the lens, g, and the distance between the lens and
the film or chip, b, are related to the focal length, f,
of the lens through a simple geometric relation:
1 1 1
¼ þ
f b g
B b
¼
G g
a
(2.1)
1 mm
The magnification, m, is the ratio between
image size, B, and object size, G:
m¼
Acquiring Images
b
(2.2)
from which it follows that the distance, b,
between the lens and the image (film or chip) is
b ¼ ðm þ 1Þ f
1 mm
(2.3)
In field photography, objects are typically
much larger than the image. In other words,
m 1 and the image distance, b, is on the
order of the focal length, f, which is of the order
of ~50 mm for film cameras, or ~10–30 mm for
digital cameras. Focusing is achieved by adjusting
the image distance, i.e., moving the objective.
Photomacrography covers the range of
magnifications between field photography, where
m 1, and photomicrography, where m > 1
(see later). For a 1:1 magnification, b ¼ g and
B ¼ G, and the image distance, b ¼ 2f. For
increasing magnifications (m > 1), the objective
has to be moved to increasing distances, b, from
the image plane and this can only be performed by
using a specially designed macro lenses or by
introducing a bellows between the camera and
the objective. While it is possible to acquire
photomacrographs in the field, better results are
generally obtained in the lab, where the camera
and the light sources can be mounted in a fixed
position and the specimen can be fixed as well.
Coarse grained rocks are typical objects for
photomacrography and polished sections of such
rocks can be used for image analysis. The
polished surface of an oolithic limestone is
shown in Fig. 2.3a. The image has been acquired
Fig. 2.3 Two dimensions? (a) Polished surface of
oolithic limestone; (b) acetate foil replica of surface
shown in (a). Arrows point to identical sites
using a reprographic unit. The sample was placed
in a shallow tray and covered with a thin film of
water to enhance the color contrast. The light
sources were placed at 45 on either side.
The ooides can be recognized as ‘swimming’ in
a completely transparent calcite cement. Due to
the transparency it is possible to see particles that
do not intersect the surface but lie a few mm below
it. In other words, the image does not show a
perfectly two-dimensional section but the projection of the top layer (0–2 mm) of the rock. As we
will learn later (in Chaps. 11 and 12), the extrapolation from 2-D to 3-D is easier if the image
represents a truly 2-D sample such as provided,
for example, by an acetate foil (Fig. 2.3b).
An acetate foil is a replica made by pressing
the softened foil onto the cleaned and etched
polished surface and letting it dry again. Such a
foil shows the microscopic topographic details of
the surface roughness without intruding into the
rock. Areas with roughness (microcrystalline
layers of ooides) appear white; smooth areas (crystal faces of calcite cement) appear dark (Fig. 2.3b).
2.3
Light Microscopy
Images made from surface replicas are much
closer representations of 2-D section. Grains that
lie below the surface—and that are visible through
the transparent cement (Fig. 2.3a)—are not
represented on the surface replica (arrows on the
right of Fig. 2.3a, b). Other grains appear much
larger on the polished surface than on the replica
(arrow on the left). In other words, if a grain size
analysis were to be made using the polished section, the size of the ooides and the density of the
packing would probably be overestimated. Therefore, for the analysis of particles that are suspended
in a transparent matrix, surface replicas should be
used because they are easier to analyze and interpret than polished sections.
2.2
Optical Scanners
Another option for acquiring images of a polished
surface at a magnification, m ¼ 1, is to use a
flatbed scanner. Best results are obtained if the
surface is wetted and put into optical contact
with the glass of the scanner. (To avoid major
cleaning sessions, water should be used instead
of glycerin.) A black towel screens off all stray
light and creates a uniform (black) background
(Fig. 2.4). Acetate foils can also be scanned, but
as they are usually warped they need to be
weighted down (often requiring rather heavy
weights to accomplish an acceptable flatness). A
black paper should be placed between replica and
weight, and reflective mode should be used.
Thin sections can also be scanned with a slide
scanner (normally used for 35 mm photographic
slides), provided that a special holder is available
that allows the thin section to be inserted into the
slide scanner. Fitting the holder with parallel or
crossed polarizer foils, plane or cross polarization can be achieved (Fig. 2.5).
The maximum resolution of slide scanners is
usually quite high (4,000 ppi or more), and as a
consequence, the complete scan of a thin section
may easily come out to be an image of 70 MB or
more. A resolution of 4,000 ppi corresponds to a
pixels size of 6.35 μm which, at a 1:1 magnification would imply a resolved length of 6.35 μm. The
truly resolved length, however, may be larger
19
(i.e., the true resolution may be poorer) if the indicated resolution is not the physical one but obtained by software interpolation. Note, also, that the
nominal physical resolution is only achieved if the
focus of the slide scanner can be adjusted to the thin
section. An example of a thin section that has been
recorded with a slide scanner is shown in Fig. 2.6.
2.3
Light Microscopy
The most common source of images for the image
analysis applications discussed in this book is the
optical microscope, and in particular the polarization microscope. The details of polarization microscopy are not explained here—the reader is
referred to standard textbooks and/or to a number
of excellent tutorials that can be found on the
internet (e.g., Molecular Expressions, JOptics,
Microscopy Resource Center, MicroscopyU,
Education in Microscopy and Digital Imaging).
Here, we will only briefly review the type and
quality of the images that are obtained by the
four most commonly used modes of polarization
microscopy.
2.3.1
Modes of Polarization
Microscopy
2.3.1.1 Unpolarized Light or Plane
Polarization
The polarizers are not inserted or only one is
inserted. This situation is called ‘no polarization’
(nopol) and yields an image as shown in Fig. 2.7a.
A nopol image is basically an absorption image
(showing absorption contrast) where optically
opaque regions appear dark and optically transparent parts bright. Absorption contrast is unrelated to the crystallographic orientation of the
mineral grains; rather it is related to the amount
of impurities, inclusions, etc. If the second
polarizer is inserted in an orientation parallel
to the first one, the situation is called ‘parallel
polarization’ (parpol); the parpol image is also
an absorption image, as before. In very few
minerals, pleochroism—a change of contrast or
20
2
Acquiring Images
10 mm
10 mm
2 mm
2 mm
a
b
Fig. 2.4 Acquiring images with a flatbed scanner. (a) Polished surface of oolithic limestone and acetate foil are
scanned on a A4 scanner at its maximum resolution (600 ppi); (b) enlarged details (see frames in (a))
2.3
Light Microscopy
21
a
b
c
d
Fig. 2.5 Acquiring images with a slide scanner. Thin sections are scanned using special slide holders at high resolution
(4000 ppi); white frames in (a) and (b) indicate enlarged details (c) and (d): (a) and (c) consolidated fault rock, plane
polarization; (b) and (d) quartz mylonite, cross polarization
color (i.e., absorption) as a function of crystallographic orientation—may be observed. Otherwise, as in the case of quartz, the nopol and
parpol images are essentially the same.
2.3.1.2 Cross Polarization
The polarizers are inserted at orthogonal
orientations, 0 and 90 . This arrangement is
called cross polarization (crosspol). Here, the
image contrast is due to interference which in
turn depends on the orientation of the optic axes
of the minerals with respect to the microscope
table or image plane (Fig. 2.7b). Crosspol images
show interference contrast that depends on the
birefringence of the mineral, the thickness of the
section and the full orientation (azimuth and
inclination) of the optical axes with respect to
the microscope table (or image plane). Later (in
Chaps. 21 and 22) we will use the interference
contrast to derive crystallographic orientations.
Note that the upper polarizer is sometimes
denoted the analyzer, but we will use the same
term for both of them.
2.3.1.3 Cross Polarization and Wave Plate
Two polarizers are inserted as before (0 and
90 ) and the wave plate, extinguishing at
546 nm, is inserted at 45 with respect to the
polarization direction of the crossed polarizers.
The wave plate (also called a full-wave plate or a
lambda plate) is made from quartz or gypsum.
On its own, the wave plate appears magenta
colored (sensitive tint). The purpose of inserting
a wave plate is to better discriminate the
orientations of the optic axis (compare Chap.
21). The combined optical path length of the
wave plate and the crystals in the thin section
determines the hue and saturation of the resulting
interference colors. If a positive optic axis is
parallel to the fast direction of the wave plate
22
2
a
b
c
d
Acquiring Images
1 mm
Fig. 2.6 Resolution of slide scanner. (a) Entire thin section of foliated granitoid rock in plane polarization; (b) entire
thin section in cross polarization; (c) detail of (a), area in rectangle is shown enlarged in Fig. 2.9; (d) detail of (b)
(or a negative one normal to it), the path lengths
are added and the color appears as first-order
blue. If a negative optic axis is parallel to the
fast direction of the wave plate (or a positive one
normal to it), the path lengths are subtracted and
the color is first-order yellow (Fig. 2.7c). Interference colors will be discussed in more detail in
Chap. 21. In short, crosspol images with the
2.3
Light Microscopy
23
a
b
c
d
Fig. 2.7 Light microscopy. Thin section of quartzite shown in different modes: (a) plain transmitted light; (b) cross
polarization; (c) cross polarization and wave plate; (d) circular polarization
lambda plate inserted also show interference contrast; the color depends on the birefringence of
the mineral, the thickness of the section and the
full orientation (azimuth and inclination) of the
optic axis with respect to the image plane.
2.3.1.4 Circular Polarization
Two polarizers are inserted as before (0 and
90 ) and two parallel quarter-wave plates are
inserted at 45 with respect to the polarization
directions of the polarizers. One is placed
between the thin section and the lower polarizer;
one between the thin section and the upper
polarizer. This situation is called circular polarization (cirpol). Again, the image shows an interference contrast (Fig. 2.7d) and the contrast
depends on the birefringence of the mineral and
the thickness of the section, but only on the
inclination—not the azimuth—of the optic axis
with respect to the image plane.
2.3.2
Illumination
High quality images, crucial for successful image
analysis, require that the thin sections are of high
quality too. Most importantly, they should be
clean and without scratches. They should also
be of uniform thickness from the center to the
edges, so as to avoid artificial interference contrast—the thinner the section, the smaller the
path difference, the lower the interference color
(more on interference colors in Chap. 21).
Even a perfect thin section will give bad results
if the lighting is not perfectly centered and even.
To ensure optimal lighting conditions in the
microscope, the so-called Köhler illumination is
adopted. The procedure is shown schematically
in Fig. 2.8. The last step (stopping down the
condenser) has to be done with great care because,
for visual observation, we tend to stop down the
condenser to very small apertures because we
24
2
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
Acquiring Images
Fig. 2.8 Köhler illumination. Procedure: (1) observe cross hair in eye piece; (2) focus cross hair; (3) observe thin section;
(4) bring image of thin section into same plane of focus as cross hair of eyepiece; (5) start with well focused image; (6) install
appropriate condenser (with numerical aperture matching that of objective) and open condenser diaphragm completely; (7)
close illumination diaphragm; (8) focus image of closed diaphragm by moving the condenser up and down; (9) center image
of illumination diaphragm using condenser screws; (10) open illumination diaphragm until the rim of the opening barely
disappears from the field of view; (11) stop down condenser
prefer high contrast and an increased field of view.
However, the more we stop down, the more we
decrease the optical resolution. A slight stopping
down is fine because it reduces the remaining
aberrations of the optical system and decreases
flare, and so stopping down as described in
Fig. 2.8 (step 10) strikes a balance between not
enough and too much.
2.3.3
Magnification and Resolution
Microscopes are designed for magnified views of
small objects, in other words, magnification,
m 1. Contrary to the photographic cameras,
where m 1, object distances are large and
image distances short, microscopes are designed
for short object distances, g, and large image distances, b. Thin sections are placed very close to
the front of the microscope objective (g 1 mm),
while the image is created at the other end of the
tube (b ¼ 170–200 mm). Focusing is achieved by
adjusting the object distance, g, i.e., by moving
the microscope table while the image distance, b,
is fixed by the length of the tube.
The magnifying power of a microscope objective is engraved as 2.5, 5 etc. on its side.
Multiplied with the magnifying power of the eyepiece (15, 20, etc.) the total magnifying power
of the microscope can be calculated. However, the
precise value for the magnification of a given
objective-eyepiece combination can only be determined by taking a micrograph of a micrometer
scale and determining the number of pixels per μm.
The largest magnifying power that microscope objectives can achieve is 100. Combining this with a 20 magnifying power of an
2.3
Light Microscopy
25
Fig. 2.9 Comparison between slide scanner and low magnification microscopy. (a) Detail of scanned thin section of
foliated granitoid rock (see Fig. 2.6c); (b) same area taken with light microscope, ZEISS NEOFLUAR Epiplan 2.5/
0.075, plane polarized condition, area in frame is shown at higher magnification in Fig. 2.14
eyepiece, for example, this would yield a total
magnification of 2,000. By re-sizing the image
digitally, the magnification could be increased
even further. However, the resulting magnification would be an ‘empty’ magnification because
the larger image does not reveal any new detail;
the resolution would not increase. An example is
given by the thin section shown in Fig. 2.9. An
image has been acquired once using a slide scanner and a second time using an optical microscope with a low-power (2.5) objective.
The magnification in Fig. 2.9a is identical to
that of Fig. 2.9b. Yet, quite obviously, there is a lot
more detail visible in the image taken with the
microscope. The reason for this is the higher
resolving power of the microscope objective. In
general, the resolving power increases with
increasing magnifying power. Still, the resolving
power is a separate quality by which excellent and
not so excellent objectives can be distinguished.
The resolving power is given by the numerical
aperture, a number which is also engraved on the
side of microscope objectives. For example, the
numbers ‘2.5/0.075’ indicate that the magnifying
power is 2.5 and the numerical aperture is 0.075.
Optical microscopes are diffraction-limited
systems and both the lateral resolution and
the depth resolution depend on the numerical
aperture of the microscope objective. The numerical aperture, NA, in turn, depends on the opening angle, u, of the imaging system:
NA ¼ n sinðuÞ
(2.4)
n is the refractive index of the medium. In dry
microscopy n ¼ nair ¼ 1.0. If oil immersion is
used n ¼ noil ¼ 1.5 and NA can be as high as 1.3.
Due to the wave nature of light, the light
emanating from an (infinitely small) point source
does not converge to an (infinitely small) image
26
2
a
Acquiring Images
b
dfield
rAiry
max
f
min
Fig. 2.10 Point spread function (PSF). (a) Lateral resolution in image plane (x-y plane) determined by radius of Airy
disk; (b) depth resolution determined by constant size (magnification) of Airy disk along the z-axis of the optical
system; longitudinal section, f ¼ focal length, direction of optical axis
point. Instead, it creates an extended image featuring a central bright spot with concentric rings
(Fig. 2.10a). The brightness distribution is
described by the point spread function, PSF,
and the central bright spot is the Airy disk. The
radius of the Airy disk, rAiry, depends on the
wavelength of the light and the numerical aperture of the optical system:
rAiry ¼
1:22 λ
2 NA
(2.5)
The lateral resolution is given by the Rayleigh
criterion which says that two points can be
resolved if the distance, d, between them is at
least equal to the radius of the Airy disk.
d¼
1:22 λ
NAobj þ NAcond
(2.6)
Note that d depends on the numerical aperture
of the entire system, i.e., on the NA of the condenser, NAcond, and the NA of the objective,
NAobj. Matching the NA of the condenser to the
NA of the objective, such that NAobj ¼ NAcond,
leads to the smallest value of d, i.e., to the best
resolution. This is the reason for not stopping the
condenser more than is absolutely necessary (see
Fig. 2.8, step 11, and Sect. 2.3.2 on illumination).
The PSF not only extends in the x-y plane of
the image, but also in the third dimension
(Fig. 2.10b) along the axis of the optical system.
Based on the Rayleigh criterion, the depth of
field is given by:
dfield ¼
λ
2 n sin2 ðuÞ
(2.7)
For dry systems this reduces to:
dfield ¼
λ
2 NA2
(2.8)
In summary, both the lateral resolution and the
depth resolution depend on the wavelength and the
numerical aperture of the optical system
(Figs. 2.11 and 2.12). At 550 nm, i.e., the green
wavelength, where the human eye is most sensitive, a low-power objective (2.55 with
NA ¼ 0.075) can resolve points that are 4.47 μm
apart and the depth of field is ~50 μm; while a high
performance dry objective (50 with NA ¼ 0.8)
resolves 0.42 μm, i.e., more than 2,000 lines per
mm, with a depth of field of 1.1 μm. Note that in
the case of a regular thin section (thickness 25
μm), a low-power objective can bring the entire
thin section into focus, from top to bottom,
whereas the high-power objective can resolve a
little more than 4 % of its thickness.
Note that in photography or during observational work at the microscope, when focusing, we
try to create a situation where we can resolve as fine
2.4
Digital Cameras
27
d [µm]
d [µm]
objective @ 550 nm
9.59
4.47
2.24
1.12
0.67
0.42
b
[µm]
d
d
a
[µm]
Fig. 2.11 Lateral resolution. Resolved length, d, as function of wavelength, λ, for different microscope objectives;
values of d at 550 nm wavelength are indicated
numerical aperture
700 nm
550 nm
400 nm
numerical aperture
Fig. 2.12 Depth resolution. Depth of field, dfield, as a function of numerical aperture is shown for three different
wavelengths: (a) logarithmic plot; (b) linear plot
a detail as possible but where we also have as large
a depth of field as possible; the former is obtained
with high-power objectives, the latter with lowpower objectives. However when we consider resolution in three dimensions, we realize that the
smallest resolved volume (given by the lateral resolution and depth of field: d·d·dfield) decreases from
978 μm3 for a 2.5/0.075 objective to 0.194 μm3
for a 20/0.5 objective, by a factor of 5,000!
2.4
Digital Cameras
Very few photographic cameras still use photographic film; in most cases the film is replaced by
an image sensor. Image sensors are typically
CCD (charge-coupled device) or CMOS (complementary metal oxide semiconductor) chips.
In either case, the image is usually generated as
a matrix of square pixels recording brightness.
The spectral sensitivity of an image sensor typically extends from less than 400 nm to more than
1,000 nm (Fig. 2.13a). For color cameras, color
separation is effected by placing a Bayer filter
grid in front of the sensor (see Fig. 2.13b for filter
transmission). Two green filters, one red and one
blue filter are placed across groups of four pixels
as shown in Fig. 2.13c, combining four monochromatic pixels to create one color pixel. As a
consequence, the physical resolution of a color
28
2
Acquiring Images
a
relative sensitivity
SONY ICX285 CCD
400
500
600
700
900
c
1000
nm
d
relative sensitivity
b
800
0
R
1
G
0
B
1
6.45 µm
400
500
600
700 nm
Fig. 2.13 Example of image sensor. (a) Spectral sensitivity of CCD image sensor without filter; (b) spectral sensitivity
of CCD image sensor with Bayer filters for red, green and blue pixels; (c) recording color through Bayer filter, typical
width of pixel is 6–7 μm, position of two green, one red and one blue filter in the even (0) and odd (1) columns and rows
of the chip are indicated; (d) rendition of color as three color channels (RGB) in color images and three fluorescent spots
on the monitor
sensor is decreased by a (linear) factor of 2 compared to an unfiltered, monochromatic sensor.
Full resolution is restored through interpolation
(de-mosaicking) in the course of calculating the
three color channels (Fig. 2.13d).
When matching an image sensor to an optically
produced image, the size of the pixels on the
sensor and optical resolution of the optical system
have to be matched. The Nyquist sampling theorem requires that the sampling frequency should
be twice the highest frequency of the image.
Translating this to the spatial resolution of optical
systems, the pixel size should be < 0.5 dm
(resolved length times magnification). Table 2.1
shows the comparison of the μm/pixel recorded at
Table 2.1 True size represented by one pixel in image
compared to resolved length of objective; values
measured for Axiocam camera and ZEISS Axioplan
microscope; note that the true pixels size is approximately
one half of the resolved length
objective
no. of
pixels
true
length
[µm]
true size resolved
of pixel
length
[µm]
[µm]
2x
205
500
2.44
4.47
5x
79
100
1.27
2.24
10x
156
100
0.64
1.12
20x
155
50
0.32
0.67
50x
158
20
0.13
0.42
2.5
Electron Microscopy
29
Fig. 2.14 Scanning electron microscopy. (a) Micrograph of polished surface of foliated granitoid rock (Image courtesy
Rüdiger Kilian), backscatter electron contrast (BSE) showing different mineral phases: white ¼ biotite, very light
gray ¼ K-feldspar, light gray ¼ muscovite, gray ¼ plagioclase, dark gray ¼ quartz; (b) same area taken with optical
microscope, circular polarization (see Fig. 2.9b): here contrast is mainly due to orientation of crystals with respect to
polarizers
Fig. 2.15 Transmission electron microscopy. (a) Free dislocations in quartz, bright field contrast (Image courtesy John
Fitz Gerald); (b) Chlorite, lattice planes, high resolution image (Image courtesy Andreas Kronenberg)
various magnifications with the Axiocam camera
of a ZEISS microscope. The table shows that the
Nyquist criterion is fulfilled at all scales.
that they are uncovered. However, for TEM analysis special sample preparation is necessary.
2.5
2.5.1
Electron Microscopy
For higher resolution and higher magnification,
electron microscopy is used. In scanning electron
microscopy (SEM), spatial resolution is limited
by the excitation volume for secondary or backscattered electrons. In transmission electron
microscopy (TEM), the resolution is limited by
the wavelength of the electron beam.
For SEM, it is possible to use the same thin sections that are used for light microscopy, provided
Scanning Electron Microscopy
(SEM)
In SEM analysis the surface of a sample is scanned
with an electron beam and the intensity of secondary electrons is recorded producing an image
where the brightness reflects surface topography.
If a back-scattered electron (BSE) detector is used,
the brightness reflects atomic number. SEM/BSE
images of polished sections show different mineral
phases with different shades of gray (Fig. 2.14a).
30
2
Comparison with a micrograph taken under
circular polarization shows that the SEM/BSE
micrograph is a truly 2-D section, whereas the
light micrograph shows a projection of a 25 μm
thick volume of rock. In the SEM/BSE micrograph, grain boundaries appear as linear traces;
in the light micrograph, they are seen projected
and if they are oblique to the thin section surface
they appear as wide strips. The second difference
is the contrast: in the BSE/SEM micrograph contrast reflects composition; in the light micrograph, the contrast reflects a combination of
mineral composition and crystallographic orientation. SEM/BSE micrographs constitute excellent input for image analysis.
2.5.2
Transmission Electron
Microscopy (TEM)
Image formation in a TEM is analogous to that in
light microscopy, and TEM micrographs are occasionally used for image analysis. For periodic
Acquiring Images
structures, such as crystals, contrast is always
some form of phase contrast. Under bright field
conditions, defect structures such as dislocations
may be seen (Fig. 2.15a); direct resolution reveals
lattice planes (Fig. 2.15b).
References
Web Pages
Education in Microscopy and Digital Imaging http://
zeiss-campus.magnet.fsu.edu
JOptics http://www.ub.edu/javaoptics/index-en.html
Microscopy Resource Center http://www.olympusmicro.
com
MicroscopyU http://www.microscopyu.com
Molecular
Expressions http://micro.magnet.fsu.edu/
primer
Textbooks
Hecht E, Zajac A (2003) Optics, 4th edn. AddisonWesley, Amsterdam
http://www.springer.com/978-3-642-10342-1