White light differential interference contrast microscope with a Sagnac interferometer Sanjib Chatterjee* and Y. Pavan Kumar Raja Ramanna Centre for Advanced Technology, Department of Atomic Energy, Indore 452013, India *Corresponding author: [email protected] Received 4 September 2013; revised 11 December 2013; accepted 11 December 2013; posted 16 December 2013 (Doc. ID 197015); published 10 January 2014
A new technique for producing a white light differential interference contrast (DIC) image using a lateral shearing, rotation phase shifting Sagnac interferometer (SI) is proposed. The SI, placed in the image space after the tube lens of a microscope system with spatially coherent white light Kohler illumination, splits the image forming beam into coherent components with small lateral shear. Phase shifts, between the interfering components, which can be considered as biased phase difference (BPD), are introduced by applying small angular rotation of the SI in its own plane. This variable BPD between the interfering white light components produces a uniform intensity colored background. The object related phase shift, due to the height difference between two close points on the object surface with separation on the order of least resolvable separation of the microscope objective, in addition to the BPD would produce a change in intensity/hue/color against a uniform background due to the BPD. Thus a DIC image is formed and the variable BPD provides an excellent means of improving the contrast of the image. © 2014 Optical Society of America OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (120.3180) Interferometry; (120.5050) Phase measurement; (120.6650) Surface measurements, figure. http://dx.doi.org/10.1364/AO.53.000296
1. Introduction
Surface structure or phase gradient on a smooth test surface does not generally produce enough contrast for visible detection with an ordinary microscope. Differential interference contrast (DIC) is a lateral shearing technique that is used to introduce contrast and sometimes color in the image of the test object/ specimen that lacks contrast. DIC microscopy is a very effective means of observing the phase distribution of a test object/specimen for revealing detailed structures and small phase steps. In a DIC microscope, small phase variations on the test object surface are transformed into intensity variations due to interference of light from two closely separated points on the test object surface. This separation is generally on the order of the resolving power, i.e., 1559-128X/14/020296-05$15.00/0 © 2014 Optical Society of America 296
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the least resolvable separation of the microscope objective (MO). In a Nomarski-DIC [1–5], a modified Wollaston prism called a Nomarski prism (NP) splits up a linearly polarized incident ray of light into angularly separated orthogonal linearly polarized extraordinary (e) and ordinary (o) rays that intersect each other at a plane outside the exit face of the NP. This ray intersection plane (IP) is adjusted to coincide with the back focal plane of the MO. Thus the extraordinary and ordinary rays become parallel to each other in the space between the MO and the test surface, and the rays strike the test surface at closely separated points. After suffering reflection on the test object surface, the reflected e and o rays pass through the MO and again intersect each other at its back focal plane, which coincides with the IP, and the rays are recombined by the NP. Due to the symmetrical double pass of the rays through the NP, the optical path difference (OPD) between the extraordinary and ordinary rays remains
plane of the MO, is illuminated by collimated broadband light. The retro-reflected beam, from the smooth test surface, which carries the phase and intensity reflectance information of the test surface, retraces its path through the MO and becomes collimated after passing through the TL. BS1 splits up the image forming beam into reflected and transmitted beam components. The reflected component with nearly half of the intensity of the incident beam travels toward a lateral shearing SI formed by a thin plate beam splitter (BS2) along with two plane mirrors M1 and M2 that are inclined at 45° to each other. The SI produces two identical coherent and laterally sheared WL beam components, shown by the central rays, which interfere to produce a lateral shearing WL interferogram. The phase shifts, between the interfering components, which can be considered as a biased phase difference (BPD), are introduced by applying small angular rotation to the SI in its own plane. For the test surface, MO and TL form a microscope system and thus a magnified image of the test surface is formed at the back focal plane of the TL. The image plane is shown by a dotted line (I). The lateral shear S (between the interfering beam components) introduced by the SI corresponds to a differential lateral shear, S1 S∕M 0.61λa ∕NA (where M is the linear magnification produced by the combination of MO and TL, λa is the mean wavelength of the WL beam, and NA is the numerical aperture of the MO) between the rays reflected from the test surface. Thus the image is actually a lateral shearing interferogram. An imaging lens (IL) transfers this image on to the detector plane of a color CCD camera connected to a personal computer. It is evident that the final image is actually a superposition of interferograms formed by phase shifted wavelength components of the imaging WL beam. Since different wavelength components are incoherent, the resultant intensity in the image plane is due to an incoherent addition of the intensities of
constant for the bundle of image forming rays. This OPD varies linearly with the change in transverse position of the NP with respect to the axis of the microscope system, and the OPD can be called a biased OPD. Thus the total OPD between the extraordinary and ordinary rays can be considered as the sum of the biased OPD, which is variable, and a small OPD due to height variations on the test object surface. The components of the extraordinary and ordinary rays, selected by a linear polarizer, interfere to produce an interference field. The biased OPD produces a uniform intensity field that would be modulated by the object related phase changes proportional to the gradient/slope of the phase variation in the direction of the lateral shear between the extraordinary and ordinary rays on the test object surface. Therefore the biased OPD provides an excellent means of improving the contrast of the image. Reference [6] describes a technique for roughness measurement using a shearing interference microscope. The DIC technique has also been used for characterizing transparent phase objects and biological specimens [7,8]. Reference [9] discusses quantitative phase imaging techniques suitable for biological specimens. We discuss a new white light DIC technique using a rotation phase shifting, lateral shearing Sagnac interferometer (SI). 2. Principle
An optical schematic of the SI-based DIC-microscope system is shown in Fig. 1. A condenser lens system (CL) images a source (S) of white/broadband light (filament of a halogen projection lamp) on the plane of a pinhole (PH) placed at the back focal plane of a telescope objective (TO). The collimated white light (WL) beam from the TO passes through a thin plate beam splitter (BS1) and falls on a tube lens (TL) that focuses the beam at the back focal plane of a MO. Thus a test surface, which is placed at the front focal BS1
TO CL
TL
PH
S
M O
O1
Test surface
BS2 Q3
Q2 Q
O
CCD
P2
P3
IL
P1
M2
I
Q1 P
M1
Fig. 1. Optical schematic of the SI-based white light DIC-microscope system. 10 January 2014 / Vol. 53, No. 2 / APPLIED OPTICS
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I
D BS2
C Q2
Q3
R
O1
Q
O
P3
P2
O2
S
P1
M2 L Q1
M1’ M1
P
B
A Fig. 2. Ray paths in the SI.
the interferograms formed by all the wavelength components. We explain the rotation phase shift introduced by the SI using Figs. 2 and 3. Figure 2 shows the central ray paths in the SI. We use same nomenclature as used in Fig. 1. BS2 splits up an incident ray (IO) into reflected and transmitted components with nearly the same intensities. M1 and M2 are initially adjusted, symmetrically equidistant with respect to BS2, and the initial position of M1 is shown by the dotted line M1’, to make the reflected (OQLO) and transmitted (OLQO) components of the incident beam traverse the same triangular path in opposite directions. A pair of rays (not shown in Fig. 2) with zero lateral shear and zero OPD emerge out in a direction normal to the incident ray IO from the output side of BS2. Lateral shear between the emergent rays can be introduced by linearly translating one of the plane mirrors, say M1, in a direction normal to the plane of the mirror, say by d, from the zero shear position M1’. Therefore the rays (OQQ1Q2Q3) and (OPP1P2P3) emerge from p the output side of BS2 with a lateral shear S 2d. The emergent rays (Q2Q3) and (P2P3), which traverse in a direction normal to the incident ray IO, are parallel to each other and with zero OPD between them. For an object point O, on BS2, virtual images, O1 and O2 (formed by
the counterpropagating rays OQQ1Q2Q3 and OPP1P2P3), lie on the extremities of the emergent rays (Q2Q3) and (P2P3), respectively, and O1O2 S. Since O is an object point on BS2, the positions of O1 and O2 remain constant with respect to the SI. For zero OPD between the emergent rays (Q2Q3) and (P2P3), the line joining O1 and O2 is normal to the emergent ray direction. In Fig. 3, the SI is shown as a black box (ABCD). For a small angular rotation α of the SI in its plane, there is no change in the directions of the emergent rays as the rays suffer an even number of reflections within the SI. The virtual images undergo the same angular shift along with the SI, so that RO1 SO2, and the line O1O2 suffers an angular rotation of α with respect to the normal (O1X) to the invariant emergent ray direction. Therefore, as shown in Fig. 3, an OPD given by O2X O1O2 sin α S sin α is introduced between the emergent beam components due to angular rotation of the SI. The reflected component (OQQ1Q2Q3) (Fig. 2) suffers a phase shift of π during its reflection at Q2. Accordingly the variation in BPD between the emergent beam components, due to small angular rotation of the SI, is given by 2π (1) ϕBλ π S sin α ; λ where λ is the wavelength of light. Thus the zeroth-order fringe due to interference of the emergent beams, for α 0, is dark. It is evident from Eq. (1) that each wavelength component suffers a different amount of biased phase shift for a particular value of α and a band of wavelength components, which satisfy/nearly satisfy destructive interference condition ϕBλ 2n 1π, where n is an integer, cannot be present in the final image. Hence the background color of the final image depends on α. The phase difference due to height difference δ between two close points, on the test surface, separated by differential lateral shear, S1 0.61λa ∕ NA, is given by 2π∕λ2δ, and the total phase difference at each point on the image plane can be written as
I
D C
Q3
R R’
α
S S’
P3
O1
α
O2 X
A B
Fig. 3. Longitudinal shift between the virtual images due to an angular rotation α of the SI shown by ABCD. 298
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Fig. 4. Spectral intensity distribution of the halogen lamp.
2π 2π ϕTλ π S sin α 2δ : λ λ
(2)
The additional phase difference due to height variation on the test surface represented by the third term of Eq. (2) produces a change in intensity/hue/color against a uniform intensity, possibly colored background that can be suitably adjusted for improving contrast.
3. Results and Discussion
An infinity corrected MO (M ≈ 10×, NA ≈ 0.25) is used in combination with a TL of focal length ≈200.0 mm as microscopic system. M1 and M2 of the SI are mounted in tip tilt mirror mounts, and M1 can be linearly translated in a direction normal to its plane by means of a precision translation stage. A lateral shear S 13.5 μm is introduced between the emergent wavefronts from the SI. The SI is also mounted on a precision graduated rotation stage. An OPD ≈ 0.43λ∕deg, where λ ≈ 0.55 μm, can be introduced between the emergent beams by imparting small angular rotation of the SI in its own plane. The spectral intensity distribution of the halogen lamp is shown in Fig. 4. Images obtained using a liquid phase epitaxy (LPE) grown GaAs sample surface, for different values of α, are shown in Figs. 5(a)–5(c). 4. Conclusions
A new technique for producing DIC imaging using a rotation phase shifting SI is proposed. In this technique the SI splits the WL imaging beam into laterally sheared coherent components with adjustable/ variable phase difference. The important advantages of the SI-based technique are as follows: (1) an expensive NP prism is not needed. (2) Beam splitting is not based on polarization and no polarization components are needed. (3) The DIC image is not affected due to spurious birefringence of the optical components and also due to any polarization dependent phase shift introduced by the test surface, i.e., birefringence of the specimen. (4) The SI-based setup is not sensitive to vibration. (5) The setup is simple and low cost. (6) Quantitative measurement can be done by applying phase shifting interferometry and by using a quasi-monochromatic light source or a filtered broadband source of light such as a halogen lamp. (7) The SI-based technique could also be applied in transmission mode, i.e., for biological specimens. Two NPs are needed in a transmission NomarskiDIC microscope, whereas a single SI is required for the proposed technique. (8) Some biological specimens exhibit birefringence and tend to mask the effect of DIC in a common transmission Nomarski-DIC microscope. The proposed SI-based technique could be very useful for obtaining an improved DIC image of such samples. We thank S. S. Negi of our group for his help in setting up the experimental arrangement and for figure drawing. References
Fig. 5. (a)–(c) DIC images obtained for different BPD.
1. G. Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Rad. 16, 9s–13s (1955). 2. D. L. Lessor, J. S. Hartman, and R. L. Gordon, “Quantitative surface topography determination by Nomarski reflection microscopy. 1. Theory,” J. Opt. Soc. Am. 69, 357–365 (1979). 3. J. S. Hartman, R. S. Gordon, and D. L. Lessor, “Quantitative surface topography determination by Nomarski reflection microscopy. 2. Microscope modification, calibration, and planar sample experiments,” Appl. Opt. 19, 2998–3009 (1980). 10 January 2014 / Vol. 53, No. 2 / APPLIED OPTICS
299
4. J. S. Hartman, R. S. Gordon, and D. L. Lessor, “Nomarski differential interference contrast microscopy for surface slope measurements: an examination of techniques,” Appl. Opt. 20, 2665–2669 (1981). 5. S. Chatterjee, “Design considerations and fabrication techniques of Nomarski reflection microscope,” Opt. Eng. 42, 2202–2213 (2003). 6. M. Adachi and K. Yasaka, “Roughness measurement using a shearing interference microscope,” Appl. Opt. 25, 764–768 (1986).
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7. K. Matsuda, M. Namiki, and T. H. Barnes, “A differential interference contrast system incorporating a Murty interferometer and holographic correction,” Opt. Lasers Eng. 9, 35–46 (1988). 8. D. Fu, S. Oh, W. Choi, T. Yamauchi, A. Dorn, Z. Yaqoob, R. R. Dasari, and H. S. Feld, “Quantitative DIC microscopy using an off axis self interference approach,” Opt. Lett. 35, 2370–2372 (2010). 9. M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2012), Chap. 3, pp. 133–179.
A new technique for producing a white light differential interference contrast (DIC) image using a lateral shearing, rotation phase shifting Sagnac interferometer (SI) is proposed. The SI, placed in the image space after the tube lens of a microscope system with spatially coherent white light Kohler illumination, splits the image forming beam into coherent components with small lateral shear. Phase shifts, between the interfering components, which can be considered as biased phase difference (BPD), are introduced by applying small angular rotation of the SI in its own plane. This variable BPD between the interfering white light components produces a uniform intensity colored background. The object related phase shift, due to the height difference between two close points on the object surface with separation on the order of least resolvable separation of the microscope objective, in addition to the BPD would produce a change in intensity/hue/color against a uniform background due to the BPD. Thus a DIC image is formed and the variable BPD provides an excellent means of improving the contrast of the image. © 2014 Optical Society of America OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (120.3180) Interferometry; (120.5050) Phase measurement; (120.6650) Surface measurements, figure. http://dx.doi.org/10.1364/AO.53.000296
1. Introduction
Surface structure or phase gradient on a smooth test surface does not generally produce enough contrast for visible detection with an ordinary microscope. Differential interference contrast (DIC) is a lateral shearing technique that is used to introduce contrast and sometimes color in the image of the test object/ specimen that lacks contrast. DIC microscopy is a very effective means of observing the phase distribution of a test object/specimen for revealing detailed structures and small phase steps. In a DIC microscope, small phase variations on the test object surface are transformed into intensity variations due to interference of light from two closely separated points on the test object surface. This separation is generally on the order of the resolving power, i.e., 1559-128X/14/020296-05$15.00/0 © 2014 Optical Society of America 296
APPLIED OPTICS / Vol. 53, No. 2 / 10 January 2014
the least resolvable separation of the microscope objective (MO). In a Nomarski-DIC [1–5], a modified Wollaston prism called a Nomarski prism (NP) splits up a linearly polarized incident ray of light into angularly separated orthogonal linearly polarized extraordinary (e) and ordinary (o) rays that intersect each other at a plane outside the exit face of the NP. This ray intersection plane (IP) is adjusted to coincide with the back focal plane of the MO. Thus the extraordinary and ordinary rays become parallel to each other in the space between the MO and the test surface, and the rays strike the test surface at closely separated points. After suffering reflection on the test object surface, the reflected e and o rays pass through the MO and again intersect each other at its back focal plane, which coincides with the IP, and the rays are recombined by the NP. Due to the symmetrical double pass of the rays through the NP, the optical path difference (OPD) between the extraordinary and ordinary rays remains
plane of the MO, is illuminated by collimated broadband light. The retro-reflected beam, from the smooth test surface, which carries the phase and intensity reflectance information of the test surface, retraces its path through the MO and becomes collimated after passing through the TL. BS1 splits up the image forming beam into reflected and transmitted beam components. The reflected component with nearly half of the intensity of the incident beam travels toward a lateral shearing SI formed by a thin plate beam splitter (BS2) along with two plane mirrors M1 and M2 that are inclined at 45° to each other. The SI produces two identical coherent and laterally sheared WL beam components, shown by the central rays, which interfere to produce a lateral shearing WL interferogram. The phase shifts, between the interfering components, which can be considered as a biased phase difference (BPD), are introduced by applying small angular rotation to the SI in its own plane. For the test surface, MO and TL form a microscope system and thus a magnified image of the test surface is formed at the back focal plane of the TL. The image plane is shown by a dotted line (I). The lateral shear S (between the interfering beam components) introduced by the SI corresponds to a differential lateral shear, S1 S∕M 0.61λa ∕NA (where M is the linear magnification produced by the combination of MO and TL, λa is the mean wavelength of the WL beam, and NA is the numerical aperture of the MO) between the rays reflected from the test surface. Thus the image is actually a lateral shearing interferogram. An imaging lens (IL) transfers this image on to the detector plane of a color CCD camera connected to a personal computer. It is evident that the final image is actually a superposition of interferograms formed by phase shifted wavelength components of the imaging WL beam. Since different wavelength components are incoherent, the resultant intensity in the image plane is due to an incoherent addition of the intensities of
constant for the bundle of image forming rays. This OPD varies linearly with the change in transverse position of the NP with respect to the axis of the microscope system, and the OPD can be called a biased OPD. Thus the total OPD between the extraordinary and ordinary rays can be considered as the sum of the biased OPD, which is variable, and a small OPD due to height variations on the test object surface. The components of the extraordinary and ordinary rays, selected by a linear polarizer, interfere to produce an interference field. The biased OPD produces a uniform intensity field that would be modulated by the object related phase changes proportional to the gradient/slope of the phase variation in the direction of the lateral shear between the extraordinary and ordinary rays on the test object surface. Therefore the biased OPD provides an excellent means of improving the contrast of the image. Reference [6] describes a technique for roughness measurement using a shearing interference microscope. The DIC technique has also been used for characterizing transparent phase objects and biological specimens [7,8]. Reference [9] discusses quantitative phase imaging techniques suitable for biological specimens. We discuss a new white light DIC technique using a rotation phase shifting, lateral shearing Sagnac interferometer (SI). 2. Principle
An optical schematic of the SI-based DIC-microscope system is shown in Fig. 1. A condenser lens system (CL) images a source (S) of white/broadband light (filament of a halogen projection lamp) on the plane of a pinhole (PH) placed at the back focal plane of a telescope objective (TO). The collimated white light (WL) beam from the TO passes through a thin plate beam splitter (BS1) and falls on a tube lens (TL) that focuses the beam at the back focal plane of a MO. Thus a test surface, which is placed at the front focal BS1
TO CL
TL
PH
S
M O
O1
Test surface
BS2 Q3
Q2 Q
O
CCD
P2
P3
IL
P1
M2
I
Q1 P
M1
Fig. 1. Optical schematic of the SI-based white light DIC-microscope system. 10 January 2014 / Vol. 53, No. 2 / APPLIED OPTICS
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I
D BS2
C Q2
Q3
R
O1
Q
O
P3
P2
O2
S
P1
M2 L Q1
M1’ M1
P
B
A Fig. 2. Ray paths in the SI.
the interferograms formed by all the wavelength components. We explain the rotation phase shift introduced by the SI using Figs. 2 and 3. Figure 2 shows the central ray paths in the SI. We use same nomenclature as used in Fig. 1. BS2 splits up an incident ray (IO) into reflected and transmitted components with nearly the same intensities. M1 and M2 are initially adjusted, symmetrically equidistant with respect to BS2, and the initial position of M1 is shown by the dotted line M1’, to make the reflected (OQLO) and transmitted (OLQO) components of the incident beam traverse the same triangular path in opposite directions. A pair of rays (not shown in Fig. 2) with zero lateral shear and zero OPD emerge out in a direction normal to the incident ray IO from the output side of BS2. Lateral shear between the emergent rays can be introduced by linearly translating one of the plane mirrors, say M1, in a direction normal to the plane of the mirror, say by d, from the zero shear position M1’. Therefore the rays (OQQ1Q2Q3) and (OPP1P2P3) emerge from p the output side of BS2 with a lateral shear S 2d. The emergent rays (Q2Q3) and (P2P3), which traverse in a direction normal to the incident ray IO, are parallel to each other and with zero OPD between them. For an object point O, on BS2, virtual images, O1 and O2 (formed by
the counterpropagating rays OQQ1Q2Q3 and OPP1P2P3), lie on the extremities of the emergent rays (Q2Q3) and (P2P3), respectively, and O1O2 S. Since O is an object point on BS2, the positions of O1 and O2 remain constant with respect to the SI. For zero OPD between the emergent rays (Q2Q3) and (P2P3), the line joining O1 and O2 is normal to the emergent ray direction. In Fig. 3, the SI is shown as a black box (ABCD). For a small angular rotation α of the SI in its plane, there is no change in the directions of the emergent rays as the rays suffer an even number of reflections within the SI. The virtual images undergo the same angular shift along with the SI, so that RO1 SO2, and the line O1O2 suffers an angular rotation of α with respect to the normal (O1X) to the invariant emergent ray direction. Therefore, as shown in Fig. 3, an OPD given by O2X O1O2 sin α S sin α is introduced between the emergent beam components due to angular rotation of the SI. The reflected component (OQQ1Q2Q3) (Fig. 2) suffers a phase shift of π during its reflection at Q2. Accordingly the variation in BPD between the emergent beam components, due to small angular rotation of the SI, is given by 2π (1) ϕBλ π S sin α ; λ where λ is the wavelength of light. Thus the zeroth-order fringe due to interference of the emergent beams, for α 0, is dark. It is evident from Eq. (1) that each wavelength component suffers a different amount of biased phase shift for a particular value of α and a band of wavelength components, which satisfy/nearly satisfy destructive interference condition ϕBλ 2n 1π, where n is an integer, cannot be present in the final image. Hence the background color of the final image depends on α. The phase difference due to height difference δ between two close points, on the test surface, separated by differential lateral shear, S1 0.61λa ∕ NA, is given by 2π∕λ2δ, and the total phase difference at each point on the image plane can be written as
I
D C
Q3
R R’
α
S S’
P3
O1
α
O2 X
A B
Fig. 3. Longitudinal shift between the virtual images due to an angular rotation α of the SI shown by ABCD. 298
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Fig. 4. Spectral intensity distribution of the halogen lamp.
2π 2π ϕTλ π S sin α 2δ : λ λ
(2)
The additional phase difference due to height variation on the test surface represented by the third term of Eq. (2) produces a change in intensity/hue/color against a uniform intensity, possibly colored background that can be suitably adjusted for improving contrast.
3. Results and Discussion
An infinity corrected MO (M ≈ 10×, NA ≈ 0.25) is used in combination with a TL of focal length ≈200.0 mm as microscopic system. M1 and M2 of the SI are mounted in tip tilt mirror mounts, and M1 can be linearly translated in a direction normal to its plane by means of a precision translation stage. A lateral shear S 13.5 μm is introduced between the emergent wavefronts from the SI. The SI is also mounted on a precision graduated rotation stage. An OPD ≈ 0.43λ∕deg, where λ ≈ 0.55 μm, can be introduced between the emergent beams by imparting small angular rotation of the SI in its own plane. The spectral intensity distribution of the halogen lamp is shown in Fig. 4. Images obtained using a liquid phase epitaxy (LPE) grown GaAs sample surface, for different values of α, are shown in Figs. 5(a)–5(c). 4. Conclusions
A new technique for producing DIC imaging using a rotation phase shifting SI is proposed. In this technique the SI splits the WL imaging beam into laterally sheared coherent components with adjustable/ variable phase difference. The important advantages of the SI-based technique are as follows: (1) an expensive NP prism is not needed. (2) Beam splitting is not based on polarization and no polarization components are needed. (3) The DIC image is not affected due to spurious birefringence of the optical components and also due to any polarization dependent phase shift introduced by the test surface, i.e., birefringence of the specimen. (4) The SI-based setup is not sensitive to vibration. (5) The setup is simple and low cost. (6) Quantitative measurement can be done by applying phase shifting interferometry and by using a quasi-monochromatic light source or a filtered broadband source of light such as a halogen lamp. (7) The SI-based technique could also be applied in transmission mode, i.e., for biological specimens. Two NPs are needed in a transmission NomarskiDIC microscope, whereas a single SI is required for the proposed technique. (8) Some biological specimens exhibit birefringence and tend to mask the effect of DIC in a common transmission Nomarski-DIC microscope. The proposed SI-based technique could be very useful for obtaining an improved DIC image of such samples. We thank S. S. Negi of our group for his help in setting up the experimental arrangement and for figure drawing. References
Fig. 5. (a)–(c) DIC images obtained for different BPD.
1. G. Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Rad. 16, 9s–13s (1955). 2. D. L. Lessor, J. S. Hartman, and R. L. Gordon, “Quantitative surface topography determination by Nomarski reflection microscopy. 1. Theory,” J. Opt. Soc. Am. 69, 357–365 (1979). 3. J. S. Hartman, R. S. Gordon, and D. L. Lessor, “Quantitative surface topography determination by Nomarski reflection microscopy. 2. Microscope modification, calibration, and planar sample experiments,” Appl. Opt. 19, 2998–3009 (1980). 10 January 2014 / Vol. 53, No. 2 / APPLIED OPTICS
299
4. J. S. Hartman, R. S. Gordon, and D. L. Lessor, “Nomarski differential interference contrast microscopy for surface slope measurements: an examination of techniques,” Appl. Opt. 20, 2665–2669 (1981). 5. S. Chatterjee, “Design considerations and fabrication techniques of Nomarski reflection microscope,” Opt. Eng. 42, 2202–2213 (2003). 6. M. Adachi and K. Yasaka, “Roughness measurement using a shearing interference microscope,” Appl. Opt. 25, 764–768 (1986).
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7. K. Matsuda, M. Namiki, and T. H. Barnes, “A differential interference contrast system incorporating a Murty interferometer and holographic correction,” Opt. Lasers Eng. 9, 35–46 (1988). 8. D. Fu, S. Oh, W. Choi, T. Yamauchi, A. Dorn, Z. Yaqoob, R. R. Dasari, and H. S. Feld, “Quantitative DIC microscopy using an off axis self interference approach,” Opt. Lett. 35, 2370–2372 (2010). 9. M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2012), Chap. 3, pp. 133–179.
