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Differential Interference Contrast (DIC) Microscopy
C H A P T E R
11 Differential Interference Contrast (DIC) Microscopy In Chapter 10, 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 (DIC) microscopy. Color Plates 14 through 18 and 40 through 42 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 (Fig. 11.1). 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, 1994). The Zeiss Jena interference microscope uses a Mach-Zehnder-type interferometer to separate and recombine the specimen wave and the reference wave (Fig. 11.2). 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 appears in the aperture plane. An image of the specimen propagates through each arm of the interferometer. If the two arms of the interferometer were identical, the specimen would be invisible in the image plane. There is a tilting plate in one arm that is used to laterally separate or shear the two images perpendicular to the length of the slit. A rotating plate in the same arm is able to add additional optical path length into the image in that arm. The additional axial separation results in a colored image when the two laterally and axially separated images recombine at the image plane.
Light and Video Microscopy https://doi.org/10.1016/B978-0-12-816501-0.00011-1
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© 2019 Elsevier Inc. All rights reserved.
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
1
dOPL 0 dX
OPL X
Vesicle
Bright
2
Distance
Gray
Distance
Dark
FIG. 11.1 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. Camera Interferometer Eye
Specimen
FIG. 11.2 Diagram of the Zeiss Jena interference microscope.
Jerzy (Georges) Nomarski was able to create a transmitted light differential interference contrast microscope using a single prism (Wollaston or Nomarski) to laterally and axially separate the two images formed from orthogonally polarized light. The lateral separation was perpendicular to the length of the slit. A pseudo-relief or shadow cast image was formed when the two orthogonally polarized images were recombined by an analyzer (Fig. 11.3; Pluta, 1994). This optical configuration is very practical and economical in that it only requires one prism; however, the slit reduces the substage condenser aperture and consequently the resolving power of the microscope and the ability to optically section. This was remedied by removing the slit and introducing a second Wollaston or Nomarski prism. The differential interference microscope based on polarized light has a certain similarity with the polarizing microscope and the image duplication interference microscope based on polarized light (Lang, 1968; Allen et al., 1969; Fig. 11.4). 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 each point in 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 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
DESIGN OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST MICROSCOPE
299
FIG. 11.3 Diagram of the Nomarski differential interference microscope using a slit and a single prism. Modified from Pluta, M., 1994. Nomarski’s DIC microscopy: a review. Proc. SPIE. 1846 (May 3) 10. https://doi.org/10.1117/12.171873 (Phase Contrast and Differential Interference Contrast Imaging Techniques and Applications).
Analyzer Compensator
+
Wollaston prism
Objective Calcite prism
l/2 plate Calcite prism
Sub-stage condenser
+ Wollaston prism
Polarizer
Polarizing
Image duplication
Differential interference contrast
FIG. 11.4 A comparison of a polarizing microscope, an image duplication interference microscope, and a differential interference contrast microscope.
10–500 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.
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
Eye Analyzer Eye Wollaston prism (calcite)
Interference fringes
Analyzer
Nomarski prism Objective Substage condenser Wollaston prism (calcite)
Specimen Interference fringes
Interference fringes
Objective (Ob) Specimen
Polarizer
Substage condenser Interference fringes
Nomarski prism
Polarizer
FIG. 11.5 Differential interference microscopes comprised of negatively birefringent calcite Wollaston prisms (left) or positively birefringent quartz Nomarski prisms (right).
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 (Fig. 11.5). 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 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 (Fig. 11.6). 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
INTERPRETATION OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
A
B
C
D
0l
l/4
0l
l/4
Wollaston prism
o e o e
o e
oe
301
All waves are in phase
FIG. 11.6 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
l/4
B
0l
C
l/4
D
l/2
Beam recombiner
Specimen o e o e
o e
o e
FIG. 11.7 Formation of a differential interference contrast image. The two members of each pair of waves have been laterally separated and axially separated.
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 so that the ordinary ray is retarded relative to the extraordinary ray (Fig. 11.7). 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 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 0λ 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 O-ray, which is perpendicular to the ordinary wave front, as they emerge from the first Wollaston or Nomarski prism.
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
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 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 first-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 substage condenser to the position where the prism matches the objective. Some microscope manufacturers provide a single wave recombiner that works 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 bright-field microscope. Imagine that the object retards a plane wave that is moving in an upward direction (Fig. 11.8). 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 (Fig. 11.9). 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 (Fig. 11.10). 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.
Wave front emanating from specimen
Specimen Incident wave front
FIG. 11.8
Wave fronts approaching and leaving a transparent specimen.
FIG. 11.9 Allow a laterally separated pair of waves to propagate through specimen.
INTERPRETATION OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
l/2
303
l/4
0l
FIG. 11.10
Axially separate the pair of laterally separated waves that propagate through the specimen.
0l l/4
FIG. 11.11
0l l/4
0l
Without axial separation of the two waves, the contrast in the image of a vesicle will be symmetrical.
Gray
Bright Gray
Black
l/4
Gray l/4
l/2 0l
FIG. 11.12
l/4
With axial separation of the two laterally displaced waves, the image of the specimen will be asymmetrical and appear to have relief.
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 (Fig. 11.11). 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 (Fig. 11.12). 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 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 and the
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
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
FIG. 11.13 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.
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 pseudorelief 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 (Fig. 11.13). For example, consider a cell with a vacuole (n ¼ 1.33) and a mitochondrion (n ¼ 1.5) in a cytoplasm with a refractive index of n ¼ 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.
INTERPRETATION OF A REFLECTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
305
8 7
1 2 (3) 4 1. Rotating polarizer 2. l/4-plate 3. Additional l-plate 4. Wollaston prism
FIG. 11.14
5. Objective 6. Specimen 7. Half-silvered mirror 8. Analyzer
5
6
Diagram of a reflected light differential interference microscope.
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. 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 12).
DESIGN OF A REFLECTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST MICROSCOPE Reflected light differential interference contrast microscopy reveals surface contours by changing differences in height into variations in intensity or color (Pluta, 1994). It is used in biology, medicine, microelectronics, and other disciplines. Reflected light differential interference microscopy is based on the same principles as transmitted light differential interference microscopy (Fig. 11.14). 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 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 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.
FIG. 11.15
Gray
Dark
Gray
Bright
Gray
Dark
Bright
Dark
Bright
11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
Dark
306
Contrast is generated in a reflected light interference contrast microscope as a result of differences in microtopography.
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 (Fig. 11.15). 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.
11 Differential Interference Contrast (DIC) Microscopy In Chapter 10, 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 (DIC) microscopy. Color Plates 14 through 18 and 40 through 42 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 (Fig. 11.1). 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, 1994). The Zeiss Jena interference microscope uses a Mach-Zehnder-type interferometer to separate and recombine the specimen wave and the reference wave (Fig. 11.2). 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 appears in the aperture plane. An image of the specimen propagates through each arm of the interferometer. If the two arms of the interferometer were identical, the specimen would be invisible in the image plane. There is a tilting plate in one arm that is used to laterally separate or shear the two images perpendicular to the length of the slit. A rotating plate in the same arm is able to add additional optical path length into the image in that arm. The additional axial separation results in a colored image when the two laterally and axially separated images recombine at the image plane.
Light and Video Microscopy https://doi.org/10.1016/B978-0-12-816501-0.00011-1
297
© 2019 Elsevier Inc. All rights reserved.
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
1
dOPL 0 dX
OPL X
Vesicle
Bright
2
Distance
Gray
Distance
Dark
FIG. 11.1 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. Camera Interferometer Eye
Specimen
FIG. 11.2 Diagram of the Zeiss Jena interference microscope.
Jerzy (Georges) Nomarski was able to create a transmitted light differential interference contrast microscope using a single prism (Wollaston or Nomarski) to laterally and axially separate the two images formed from orthogonally polarized light. The lateral separation was perpendicular to the length of the slit. A pseudo-relief or shadow cast image was formed when the two orthogonally polarized images were recombined by an analyzer (Fig. 11.3; Pluta, 1994). This optical configuration is very practical and economical in that it only requires one prism; however, the slit reduces the substage condenser aperture and consequently the resolving power of the microscope and the ability to optically section. This was remedied by removing the slit and introducing a second Wollaston or Nomarski prism. The differential interference microscope based on polarized light has a certain similarity with the polarizing microscope and the image duplication interference microscope based on polarized light (Lang, 1968; Allen et al., 1969; Fig. 11.4). 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 each point in 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 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
DESIGN OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST MICROSCOPE
299
FIG. 11.3 Diagram of the Nomarski differential interference microscope using a slit and a single prism. Modified from Pluta, M., 1994. Nomarski’s DIC microscopy: a review. Proc. SPIE. 1846 (May 3) 10. https://doi.org/10.1117/12.171873 (Phase Contrast and Differential Interference Contrast Imaging Techniques and Applications).
Analyzer Compensator
+
Wollaston prism
Objective Calcite prism
l/2 plate Calcite prism
Sub-stage condenser
+ Wollaston prism
Polarizer
Polarizing
Image duplication
Differential interference contrast
FIG. 11.4 A comparison of a polarizing microscope, an image duplication interference microscope, and a differential interference contrast microscope.
10–500 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.
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
Eye Analyzer Eye Wollaston prism (calcite)
Interference fringes
Analyzer
Nomarski prism Objective Substage condenser Wollaston prism (calcite)
Specimen Interference fringes
Interference fringes
Objective (Ob) Specimen
Polarizer
Substage condenser Interference fringes
Nomarski prism
Polarizer
FIG. 11.5 Differential interference microscopes comprised of negatively birefringent calcite Wollaston prisms (left) or positively birefringent quartz Nomarski prisms (right).
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 (Fig. 11.5). 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 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 (Fig. 11.6). 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
INTERPRETATION OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
A
B
C
D
0l
l/4
0l
l/4
Wollaston prism
o e o e
o e
oe
301
All waves are in phase
FIG. 11.6 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
l/4
B
0l
C
l/4
D
l/2
Beam recombiner
Specimen o e o e
o e
o e
FIG. 11.7 Formation of a differential interference contrast image. The two members of each pair of waves have been laterally separated and axially separated.
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 so that the ordinary ray is retarded relative to the extraordinary ray (Fig. 11.7). 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 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 0λ 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 O-ray, which is perpendicular to the ordinary wave front, as they emerge from the first Wollaston or Nomarski prism.
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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 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 first-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 substage condenser to the position where the prism matches the objective. Some microscope manufacturers provide a single wave recombiner that works 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 bright-field microscope. Imagine that the object retards a plane wave that is moving in an upward direction (Fig. 11.8). 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 (Fig. 11.9). 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 (Fig. 11.10). 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.
Wave front emanating from specimen
Specimen Incident wave front
FIG. 11.8
Wave fronts approaching and leaving a transparent specimen.
FIG. 11.9 Allow a laterally separated pair of waves to propagate through specimen.
INTERPRETATION OF A TRANSMITTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
l/2
303
l/4
0l
FIG. 11.10
Axially separate the pair of laterally separated waves that propagate through the specimen.
0l l/4
FIG. 11.11
0l l/4
0l
Without axial separation of the two waves, the contrast in the image of a vesicle will be symmetrical.
Gray
Bright Gray
Black
l/4
Gray l/4
l/2 0l
FIG. 11.12
l/4
With axial separation of the two laterally displaced waves, the image of the specimen will be asymmetrical and appear to have relief.
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 (Fig. 11.11). 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 (Fig. 11.12). 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 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 and the
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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
FIG. 11.13 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.
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 pseudorelief 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 (Fig. 11.13). For example, consider a cell with a vacuole (n ¼ 1.33) and a mitochondrion (n ¼ 1.5) in a cytoplasm with a refractive index of n ¼ 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.
INTERPRETATION OF A REFLECTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST IMAGE
305
8 7
1 2 (3) 4 1. Rotating polarizer 2. l/4-plate 3. Additional l-plate 4. Wollaston prism
FIG. 11.14
5. Objective 6. Specimen 7. Half-silvered mirror 8. Analyzer
5
6
Diagram of a reflected light differential interference microscope.
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. 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 12).
DESIGN OF A REFLECTED LIGHT DIFFERENTIAL INTERFERENCE CONTRAST MICROSCOPE Reflected light differential interference contrast microscopy reveals surface contours by changing differences in height into variations in intensity or color (Pluta, 1994). It is used in biology, medicine, microelectronics, and other disciplines. Reflected light differential interference microscopy is based on the same principles as transmitted light differential interference microscopy (Fig. 11.14). 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 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 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.
FIG. 11.15
Gray
Dark
Gray
Bright
Gray
Dark
Bright
Dark
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11. DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY
Dark
306
Contrast is generated in a reflected light interference contrast microscope as a result of differences in microtopography.
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 (Fig. 11.15). 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.