Abstract

Imaging of phase or optical path length is becoming more important with the development of better imaging systems, computational algorithms, faster computers, and a greater interest in the imaging of transparent objects. Early phase imaging involved qualitative imaging of phase gradients. New computational algorithms can be used to extract some quantitative phase imaging from these techniques. In contrast, new hardware has enabled full-field quantitative phase imaging on a practical and cost-effective scale. We explore a quantitative comparison between two techniques for imaging phase. In the first technique, phase is recovered from a pair of differential interference contrast images, and in the second technique, phase is measured pixel-by-pixel interferometrically. It is shown, experimentally, that the overall results are similar, but each technique has its own advantages and disadvantages.

© 2008 Optical Society of America

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W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

2006 (1)

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

2005 (1)

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

2004 (6)

2003 (1)

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

2000 (1)

B. Zhao and A. Asundi, “Discussion on spatial resolution and sensitivity of Fourier transform fringe detection,” Opt. Eng. 39, 2715-2719 (2000).
[CrossRef]

1999 (2)

1998 (2)

1995 (2)

1993 (1)

1992 (1)

C. J. Cogswell and J. R. Sheppard, “Confocal differential interference contrast (DIC) microscopy including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81-101 (1992).
[CrossRef]

1990 (1)

1987 (1)

1985 (1)

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

Asundi, A.

B. Zhao and A. Asundi, “Discussion on spatial resolution and sensitivity of Fourier transform fringe detection,” Opt. Eng. 39, 2715-2719 (2000).
[CrossRef]

Axelrod, N.

Badizadegan, K.

Balmer, R.

Belectic, J.

Ben-Yosef, N.

Bevilacqua, F.

Boccara, A. C.

F. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 43, 2326-2331 (2004).

Brooks, D. H.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

Chang, C.-C.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

Chim, S. S. C.

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

C. J. Cogswell and J. R. Sheppard, “Confocal differential interference contrast (DIC) microscopy including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81-101 (1992).
[CrossRef]

Conchello, J.

Creath, K.

Cuche, E.

Dasari, R. R.

Deflores, L. P.

Depeursinge, C.

Devaney, A. J.

D. O. Hogenboom, C. A. DiMarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23, 783-785 (1998).
[CrossRef]

C. A. DiMarzio, A. J. Devaney, and S. C. Lindberg, “Optical quadrature interferometry utilizing polarizing optics,” U.S. patent 5,883,717 (16 March 1999).

DiMarzio, C. A.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

D. O. Hogenboom, C. A. DiMarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23, 783-785 (1998).
[CrossRef]

C. A. DiMarzio, A. J. Devaney, and S. C. Lindberg, “Optical quadrature interferometry utilizing polarizing optics,” U.S. patent 5,883,717 (16 March 1999).

Dubois, F.

F. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 43, 2326-2331 (2004).

Feld, M. S.

Francon, M.

M. Francon and S. Mallick, Polarization Interferometers (Wiley, 1971).

Gaudette, T. J.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Herrera, G. E.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

Hogenboom, D. O.

Iwai, H.

Jansson, P. A.

P. A. Jansson, Deconvolution of Images and Spectra (Academic, 1997).

Kino, C. S.

Laevsky, G. S.

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

Lewis, A.

Lindberg, S. C.

D. O. Hogenboom, C. A. DiMarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23, 783-785 (1998).
[CrossRef]

C. A. DiMarzio, A. J. Devaney, and S. C. Lindberg, “Optical quadrature interferometry utilizing polarizing optics,” U.S. patent 5,883,717 (16 March 1999).

Malacara, D.

D. Malacara, Z. Malcacara, and M. Servin, Interferogram Analysis for Optical Testing (Dekker, 2005).
[CrossRef]

Malcacara, Z.

D. Malacara, Z. Malcacara, and M. Servin, Interferogram Analysis for Optical Testing (Dekker, 2005).
[CrossRef]

Mallick, S.

M. Francon and S. Mallick, Polarization Interferometers (Wiley, 1971).

Matthews, H. J.

Newmark, J. A.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

Novak, E.

O'Shea, D. C.

Pluta, M.

M. Pluta, Advanced Light Microscopy: Principles and Basic Properties (Elsevier, 1988).

M. Pluta, Advanced Light Microscopy: Specialized Methods (Elsevier, 1989).

Popescu, G.

Poutous, M.

Preza, C.

Quarles, K. D.

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

Radko, A.

Rajadhyaksha, M.

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

Rockward, W. S.

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

D. C. O'Shea and W. S. Rockward, “Gray-scale masks for diffractive-optics fabrication: II. spatially filtered halftone screens,” Appl. Opt. 34, 7518-7526 (1995).
[CrossRef] [PubMed]

Schmit, J.

Selb, J.

F. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 43, 2326-2331 (2004).

Servin, M.

D. Malacara, Z. Malcacara, and M. Servin, Interferogram Analysis for Optical Testing (Dekker, 2005).
[CrossRef]

Sheppard, C. J. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

C. J. R. Sheppard and H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354-1360(2004).
[CrossRef]

Sheppard, J. R.

C. J. Cogswell and J. R. Sheppard, “Confocal differential interference contrast (DIC) microscopy including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81-101 (1992).
[CrossRef]

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

Snyder, D. L.

Streibl, N.

Suleski, T. J.

Thomas, A. L.

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

Townsend, D. J.

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

Vabre, L.

F. Dubois, J. Selb, L. Vabre, and A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 43, 2326-2331 (2004).

Vaughan, J. C.

Wan, D. S.

Warger, W. C.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

Warner, C. M.

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

Yamamoto, T.

T. Yamamoto, “Coherence theory of source-size compensation in interference microscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier), pp. 295-341.

Zhao, B.

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

B. Zhao and A. Asundi, “Discussion on spatial resolution and sensitivity of Fourier transform fringe detection,” Opt. Eng. 39, 2715-2719 (2000).
[CrossRef]

Appl. Opt. (9)

J. Biomed. Opt. (1)

W. C. Warger, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. 12, 440-446 (2007).
[CrossRef]

J. Microsc. (2)

C. J. Cogswell and J. R. Sheppard, “Confocal differential interference contrast (DIC) microscopy including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81-101 (1992).
[CrossRef]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (3)

Microsc. Microanal. (1)

J. A. Newmark, W. C. Warger, C.-C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the number of cells in preimplantation embryos by using non-invasive optical quadrature microscopy in conjunction with differential interference contrast microscopy,” Microsc. Microanal. 13, 118 (2007).
[CrossRef] [PubMed]

Opt. Eng. (1)

B. Zhao and A. Asundi, “Discussion on spatial resolution and sensitivity of Fourier transform fringe detection,” Opt. Eng. 39, 2715-2719 (2000).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (3)

D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative phase measurements using a quadrature tomographic microscope,” Proc. SPIE 4964, 59-65 (2003).
[CrossRef]

W. C. Warger, J. A. Newmark, B. Zhao, C. M. Warner, and C. A. DiMarzio, “Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy,” Proc. SPIE 6090, 30-41 (2006).

W. C. Warger, J. A. Newmark, C.-C. Chang, D. H. Brooks, C. M. Warner, and C. A. DiMarzio,“ Optical quadrature and differential interference constrast to facilitate embryonic cell counts with fluorescence imaging for confirmation,” Proc. SPIE 5699, 334-341 (2005).
[CrossRef]

Other (9)

freehand is a trademark of the Macromedia Corporation, San Francisco, Calif.

C. A. DiMarzio, A. J. Devaney, and S. C. Lindberg, “Optical quadrature interferometry utilizing polarizing optics,” U.S. patent 5,883,717 (16 March 1999).

D. Malacara, Z. Malcacara, and M. Servin, Interferogram Analysis for Optical Testing (Dekker, 2005).
[CrossRef]

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

M. Pluta, Advanced Light Microscopy: Principles and Basic Properties (Elsevier, 1988).

M. Pluta, Advanced Light Microscopy: Specialized Methods (Elsevier, 1989).

T. Yamamoto, “Coherence theory of source-size compensation in interference microscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier), pp. 295-341.

M. Francon and S. Mallick, Polarization Interferometers (Wiley, 1971).

P. A. Jansson, Deconvolution of Images and Spectra (Academic, 1997).

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Figures (14)

Fig. 1
Fig. 1

Segment of a typical phase object surface profile using a Talystep mechanical profilometer with a stylus tip of 0.4 μm and a shank angle of 60 ° .

Fig. 2
Fig. 2

Optical quadrature configuration.

Fig. 3
Fig. 3

Optical structure and model in the reference path.

Fig. 4
Fig. 4

Optical structure and model in the signal path.

Fig. 5
Fig. 5

Sample illumination and effective illumination NA . (a) Sample is away from the condenser focal plane, NA is the angle, ω. (b) Illustration of the effect of the extended light source on the illumination NA .

Fig. 6
Fig. 6

Phase map in radians measured with OQM. The units of the X and Y are pixels with each pixel representing a distance of 0.71 and 0.75 μm , respectively.

Fig. 7
Fig. 7

Illustration of the optical-path compensation generated by a condenser prism in a DIC system.

Fig. 8
Fig. 8

Illustration of the degree of coherence introduced by a Wollaston prism. (a) Source point S coherently illuminates two points, M O and N O , in the sample plane; (b) source point S also sends two incoherent rays o and e (dashed curves) to the sample plane. M O and N O are illuminated with partial coherent rays. Polarizer and analyzer are not shown in this figure.

Fig. 9
Fig. 9

Polarization changes with a 90 ° rotation of the analyzer. The rectangle represents a Wollaston prism (top view).

Fig. 10
Fig. 10

Illustration of an incoherent ray elimination with a 180 ° phase-shifting method. The sample is a binary grating discussed in Section 2. (a)  X Z image (Z is the optic axis), polarizer and the analyzer is perpendicular. Each pixel in the X direction corresponds to a distance of 0.355 μm . (b)  X Z image taken in the same conditions as in (a) but with a 90 ° rotation of the polarizer. (c) The result of the subtraction of (a) from (b).

Fig. 11
Fig. 11

Example of phase reconstruction of a binary phase grating with DIC images. The units of X and Y are pixels, each representing a distance of 0.355 and 0.375 μm for X and Y, respectively. (a) Original image, (b) image with a 180 ° phase shift relative to (a), (c) subtraction of (b) from (a), (d) recovered phase grating image in radians.

Fig. 12
Fig. 12

Illustration of the degradation of the spatial resolution due to the existence of the polar point of the phase transfer function. The applied Wiener-type filter is like a high-pass filter. The spatial resolution is defined as 1 / L .

Fig. 13
Fig. 13

Example of phase recovery of a binary phase grating with DIC images. The units of the X and Y are pixels, each pixel representing a distance of 1.61 μm . (a) Original image, (b) image with 180 ° phase shift relative to (a), (c) subtraction of (b) from (a), (d) recovered phase grating image in radians.

Fig. 14
Fig. 14

Comparison of the phase measurements with OQM and DIC. (a) Phase map in radians measured with DIC, (b) phase map in radians measured with OQM, (c) phase profile measured with DIC from the phase map shown in (a), (d) phase profile measured with OQM from the phase map shown in (b). The units of X and Y are pixels, each pixel representing a distance of 0.71 and 0.75 μm , respectively.

Tables (1)

Tables Icon

Table 1 Lateral Resolution of the Microscope System.

Equations (11)

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d = λ 2 ( n 1 ) .
Reg r = 1 / | η g r | λ | sin θ 0 | + NA obj - eff ,
E ( X ) = E 0 exp [ i Δ φ ( X ) ] .
U ( X , Z ) = E ( X ) h ( X ) = E 0 cos [ Δ φ ( X ) ] h ( X ) + i E 0 sin [ Δ φ ( X ) ] h ( X ) .
I ( X ) = | U ( X ) | 2 = 0.25 I 0 { [ cos ( Δ φ ) K ] 2 + [ cos ( Δ φ ) K + ] 2 2 cos ( 2 Δ θ ) [ cos ( Δ φ ) K ] [ cos ( Δ φ ) K + ] } + 0.25 I 0 { [ sin ( Δ φ ) K ] 2 + [ sin ( Δ φ ) K + ] 2 2 cos ( 2 Δ θ ) [ sin ( Δ φ ) K ] [ sin ( Δ φ ) K + ] } 0.5 I 0 sin ( 2 Δ θ ) { [ cos ( Δ φ ) K ] [ sin ( Δ φ ) K + ] [ cos ( Δ φ ) K + ] } [ sin ( Δ φ ) K ] ,
I ^ ( X ) = I ( X ) / I + ( X ) = sin [ Δ φ ( X ) ] [ ( K ( X + Δ X ) K ( X Δ X ) ) ] Δ φ ( X ) [ ( K ( X + Δ X ) K ( X Δ X ) ) ] .
Δ Φ ( f ) I ( f ) / C P ( f ) ,
C P ( f ) = 2 i sin ( 2 π f Δ X ) K ( f ) ,
Δ φ ( X ) = IFT [ Δ φ ( f ) ] IFT [ i I ( f ) 2 sin ( 2 π f Δ X ) K ( f ) ] .
Δ φ ( f ) I ( f ) C P ( f ) I ( f ) C P * ( f ) | C P ( f ) | 2 + n ( f ) ,
n ( f ) = c 1 exp ( 0.5 f 2 / c 2 2 ) ,

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