Abstract

Analysis of image formation in a differential interference contrast (DIC) microscope and retrieval of the specimen’s properties require calibration of its key parameters, viz. shear and bias. We present a method of measuring the shear and the bias of a DIC microscope from the interference fringes produced in the back focal plane of the objective. Previous approaches, which use calibrated specimens such as polysty rene or fluorescent beads, provide rather approximate measurements of shear or require a complex optical setup. The method presented is accurate, relies on simple image analysis, and does not require a specimen. We provide a succinct and accurate description of properties of Nomarski prisms to explain the rationale behind the method.

© 2010 Optical Society of America

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References

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  1. G. Nomarski, “Interference polarizing device for study of phase objects,” U.S. patent 2924142 (9 February 1960).
  2. M. Pluta, Advanced Light Microscopy. Vol. 2. Specialized Methods (PWN-Polish Scientific, 1989).
  3. C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
    [CrossRef]
  4. 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]
  5. B. Kouskousis, D. J. Kitcher, S. Collins, A. Roberts, and G. W. Baxter, “Quantitative phase and refractive index analysis of optical fibers using differential interference contrast microscopy,” Appl. Opt. 47, 5182–5189 (2008).
    [CrossRef] [PubMed]
  6. C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
    [CrossRef]
  7. M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
    [CrossRef] [PubMed]
  8. S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16, 19462–19479 (2008).
    [CrossRef] [PubMed]
  9. W. Galbraith, “The image of a point of light in differential interference contrast microscopy: computer simulation,” Microscopica acta 85, 233–254 (1982).
  10. T. J. Holmes and W. J. Levy, “Signal-processing characteristics of differential-interference-contrast microscopy,” Appl. Opt. 26, 3929–3939 (1987).
    [CrossRef] [PubMed]
  11. E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
    [CrossRef]
  12. P. Munro and P. Török, “Vectorial, high numerical aperture study of Nomarski’s differential interference contrast microscope,” Opt. Express 13, 6833–6847 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscope (Academic, 1984).
  15. C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in scanning and conventional optical microscopes,” Phil. Trans. R. Soc. London Ser. A 295, 513–536(1980).
    [CrossRef]
  16. C. Cogswell and C. Sheppard, “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging,” J. Microsc. 165, 81–101 (1992).
    [CrossRef]
  17. C. Preza, D. L. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
    [CrossRef]
  18. S. B. Mehta and C. J. R. Sheppard, “Phase-space representation of partially coherent imaging systems using the Cohen class distribution,” Opt. Lett. 35, 348–350 (2010).
    [CrossRef] [PubMed]
  19. S. B. Mehta and C. J. R. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: brightfield, phase-contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” J. Mod. Opt. (to be published).
  20. C. B. Müller , K. Weiß, W. Richtering, A. Loman, and J. Enderlein, “Calibrating differential interference contrast microscopy with dual-focus fluorescence correlation spectroscopy,” Opt. Express 16, 4322–4329 (2008).
    [CrossRef] [PubMed]
  21. R. Danz, A. Vogelgsang, and R. Kathner, “PlasDIC—a useful modification of the differential interference contrast according to Smith/Nomarski in transmitted light arrangement,” Photonik 1, 42 (2004).
  22. T. J. McIntyre, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Differential interference contrast imaging using a spatial light modulator,” Opt. Lett. 34, 2988–2990 (2009).
    [CrossRef] [PubMed]
  23. M. Pluta, “Principles and basic properties,” in Advanced Light Microscopy (PWN-Polish Scientific Publishers, 1988), Vol. 1.
  24. P. Hariharan, “The Senarmont compensator: an early application of the geometric phase,” J. Mod. Opt. 40, 2061–2064(1993).
    [CrossRef]
  25. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  26. K. J. Dana, “Three dimensional reconstruction of the tectorial membrane: an image processing method using Nomarski differential interference contrast microscopy,” M.S. thesis (Massachusetts Institute of Technology, 1992).
  27. C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference on Cybernetics and Society (IEEE, 1975), Vol. 4, pp. 163–165.
  28. P. Soille, Morphological Image Analysis: Principles and Applications (Springer-Verlag, 2003).
  29. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66(1979).
    [CrossRef]
  30. C. C. Montarou and T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 38, 6604–6616 (1999).
    [CrossRef]
  31. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
    [CrossRef] [PubMed]
  32. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793 (2006).
    [CrossRef] [PubMed]
  33. M. Françon, Optical Interferometry (Academic, 1966).
  34. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
    [PubMed]
  35. H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
    [CrossRef]
  36. M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

2010 (1)

2009 (1)

2008 (4)

2006 (3)

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[CrossRef]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

R. Danz, A. Vogelgsang, and R. Kathner, “PlasDIC—a useful modification of the differential interference contrast according to Smith/Nomarski in transmitted light arrangement,” Photonik 1, 42 (2004).

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]

1999 (2)

1997 (2)

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

1993 (1)

P. Hariharan, “The Senarmont compensator: an early application of the geometric phase,” J. Mod. Opt. 40, 2061–2064(1993).
[CrossRef]

1992 (1)

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

1987 (1)

1982 (1)

W. Galbraith, “The image of a point of light in differential interference contrast microscopy: computer simulation,” Microscopica acta 85, 233–254 (1982).

1980 (1)

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in scanning and conventional optical microscopes,” Phil. Trans. R. Soc. London Ser. A 295, 513–536(1980).
[CrossRef]

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66(1979).
[CrossRef]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[CrossRef]

1951 (1)

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
[CrossRef]

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]

Aten, J. A.

E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793 (2006).
[CrossRef] [PubMed]

Baxter, G. W.

Bernet, S.

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Biggs, D.

M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[PubMed]

Cogswell, C.

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

Cogswell, C. J.

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[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]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Collins, S.

Conchello, J.

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[CrossRef]

C. Preza, D. L. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
[CrossRef]

Dana, K. J.

K. J. Dana, “Three dimensional reconstruction of the tectorial membrane: an image processing method using Nomarski differential interference contrast microscopy,” M.S. thesis (Massachusetts Institute of Technology, 1992).

Danz, R.

R. Danz, A. Vogelgsang, and R. Kathner, “PlasDIC—a useful modification of the differential interference contrast according to Smith/Nomarski in transmitted light arrangement,” Photonik 1, 42 (2004).

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Enderlein, J.

Françon, M.

M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

M. Françon, Optical Interferometry (Academic, 1966).

Galbraith, W.

W. Galbraith, “The image of a point of light in differential interference contrast microscopy: computer simulation,” Microscopica acta 85, 233–254 (1982).

Gaylord, T. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hariharan, P.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

P. Hariharan, “The Senarmont compensator: an early application of the geometric phase,” J. Mod. Opt. 40, 2061–2064(1993).
[CrossRef]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Hines, D. C.

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference on Cybernetics and Society (IEEE, 1975), Vol. 4, pp. 163–165.

Holmes, T. J.

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[CrossRef]

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
[CrossRef]

Inoue, S.

M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

J. R., C.

Kathner, R.

R. Danz, A. Vogelgsang, and R. Kathner, “PlasDIC—a useful modification of the differential interference contrast according to Smith/Nomarski in transmitted light arrangement,” Photonik 1, 42 (2004).

King, S. V.

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[CrossRef]

Kitcher, D. J.

Kouskousis, B.

Kuglin, C. D.

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference on Cybernetics and Society (IEEE, 1975), Vol. 4, pp. 163–165.

La Fountain, J.

M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

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]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Levy, W. J.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Loman, A.

Mallick, S.

M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971).

Maurer, C.

McIntyre, T. J.

Mehta, S. B.

S. B. Mehta and C. J. R. Sheppard, “Phase-space representation of partially coherent imaging systems using the Cohen class distribution,” Opt. Lett. 35, 348–350 (2010).
[CrossRef] [PubMed]

S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16, 19462–19479 (2008).
[CrossRef] [PubMed]

S. B. Mehta and C. J. R. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: brightfield, phase-contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” J. Mod. Opt. (to be published).

Montarou, C. C.

Müller, C. B.

Munro, P.

Nomarski, G.

G. Nomarski, “Interference polarizing device for study of phase objects,” U.S. patent 2924142 (9 February 1960).

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66(1979).
[CrossRef]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Pluta, M.

M. Pluta, Advanced Light Microscopy. Vol. 2. Specialized Methods (PWN-Polish Scientific, 1989).

M. Pluta, “Principles and basic properties,” in Advanced Light Microscopy (PWN-Polish Scientific Publishers, 1988), Vol. 1.

Preza, C.

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[CrossRef]

C. Preza, D. L. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
[CrossRef]

Richtering, W.

Ritsch-Marte, M.

Roberts, A.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793 (2006).
[CrossRef] [PubMed]

Sheppard, C.

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

Sheppard, C. J. R.

S. B. Mehta and C. J. R. Sheppard, “Phase-space representation of partially coherent imaging systems using the Cohen class distribution,” Opt. Lett. 35, 348–350 (2010).
[CrossRef] [PubMed]

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 T. Wilson, “Fourier imaging of phase information in scanning and conventional optical microscopes,” Phil. Trans. R. Soc. London Ser. A 295, 513–536(1980).
[CrossRef]

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscope (Academic, 1984).

S. B. Mehta and C. J. R. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: brightfield, phase-contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” J. Mod. Opt. (to be published).

Shribak, M.

M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

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]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Snyder, D. L.

Soille, P.

P. Soille, Morphological Image Analysis: Principles and Applications (Springer-Verlag, 2003).

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645(2006).
[CrossRef] [PubMed]

Török, P.

van Munster, E. B.

E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

van Vilet, L. J.

E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Vogelgsang, A.

R. Danz, A. Vogelgsang, and R. Kathner, “PlasDIC—a useful modification of the differential interference contrast according to Smith/Nomarski in transmitted light arrangement,” Photonik 1, 42 (2004).

Weiß, K.

Wilson, T.

C. Preza, S. V. King, J. Conchello, C. J. Cogswell, and T. Wilson, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in scanning and conventional optical microscopes,” Phil. Trans. R. Soc. London Ser. A 295, 513–536(1980).
[CrossRef]

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscope (Academic, 1984).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3, 793 (2006).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Syst. Man Cybern. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66(1979).
[CrossRef]

J. Biomed. Opt. (1)

M. Shribak, J. La Fountain, D. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

J. Microsc. (3)

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]

E. B. van Munster, L. J. van Vilet, and J. A. Aten, “Reconstruction of optical path length distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

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

J. Mod. Opt. (2)

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Supplementary Material (5)

» Media 1: MOV (3749 KB)     
» Media 2: MOV (1427 KB)     
» Media 3: MOV (748 KB)     
» Media 4: MOV (1204 KB)     
» Media 5: MOV (1357 KB)     

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Figures (11)

Fig. 1
Fig. 1

Only with the OPrism does one observe blurring effect of the shear on bright-field images of beads: images of 780 nm diameter polystyrene beads from Micro-particles GmBH (courtesy Bai Jianhao from National University of Singapore), obtained with (a) only the CPrism or (b) only the OPrism in the bright-field light path. Neither polarizer was inserted in the light path. Direction of shear is along the horizontal.

Fig. 2
Fig. 2

Measurement of angular shear of our DIC prism using monochromatic illumination with a carefully aligned benchtop setup. PO is the polarizer and AN is the analyzer.

Fig. 3
Fig. 3

DIC image of a bead due to the central point of the condenser aperture: a snapshot from an image sequence (Media 1) showing computed images and their peaks at different shears. All coordinates are in the normalized units of λ / NA obj . The bead is assumed to have a diameter of 0.4, RI of 1.59, and is immersed in water (RI 1.33). For the purpose of calculating the optical path length of the bead, the wavelength is assumed to be 0.55 μm ; (a) and (b) are real and imaginary parts of the effective transmission t D ( x , y ) , (c) is the amplitude PSF of the aberration-free system (i.e., jinc function), (d) and (e) are real and imaginary parts of the amplitude image produced by convolution of the transmission and the PSF, (f) is the image intensity, and (g) is the plot of shear versus distance between peaks in the image. The markers in (f) identify the peaks of the image. The bias is assumed to be π / 2 at all shears. Note that the color maps of the different plots are adjusted to allow clear display of data. In particular, the imaginary part of the image is an order of magnitude stronger than the real part.

Fig. 4
Fig. 4

Distance between peaks in the image of a subresolution phase specimen is dependent on the size of the illumination aperture: DIC images of 170 μm diameter PS-Speck beads acquired with quasi-monochromatic light of 550 nm wavelength using a 40 × 0.6 NA objective, π / 2 bias, and (a) S = 1 as well as (b) S = 0.5 . Since the specimen had weak phase information, we averaged 100 images acquired in burst mode to obtain a good SNR. The scale bar is 1 μm .

Fig. 5
Fig. 5

Distance between peaks in the image of a subresolution phase specimen is nearly independent of the bias: (a), (b), and (c) are raw images of PS-Speck beads acquired with a 40 × 0.6 NA objective and matched illumination at bias ( 2 ϕ ) of π / 2 , π / 3 , and π / 6 , respectively. The color bar next to images shows that, while the image shape does not change much, contrast reduces at larger bias values. (d) shows normalized line profiles through the center of beads and clarifies the previous point. Pixel width is 6.45 / 40 μm The distance between peaks in all images is 0.49 μm . Since the specimen had weak phase information, we averaged 100 images acquired in burst mode to obtain good SNR.

Fig. 6
Fig. 6

Images of fluorophores under (a) 20 × 0.75 NA , (b) 40 × 0.9 NA , and (c) 40 × 0.6 NA objectives obtained with only the OPrism inserted in the light path.

Fig. 7
Fig. 7

Snapshot from an image sequence (Media 2, 1.5 MB ) shows (a) the computed image of a subresolution fluo rescent bead under the DIC microscope at shear of 2 Δ = 0.5 and (b) the relationship between the distance between peaks in the image and the shear. The markers in (a) identify the peaks of the image.

Fig. 8
Fig. 8

Steps involved in accurate estimation of the shear and bias of OPrism by processing the images acquired at the BFP: (a) | P BF | 2 is the recorded intensity of bright-field BFP, | P DIC | 2 , a snapshot from an image sequence (Media 3, 748 KB ) is the recorded intensity of the fringes produced due to OPrism at given bias. (b) Snapshot from an image sequence (Media 4, 1233 KB ) shows preprocessing steps to remove the artifacts due to debris and to register | P DIC | 2 with | P DIC | 2 . The red, green, and blue pixels in the rightmost panel show the edges of | P BF | 2 , acquired | P DIC | 2 , registered | P DIC | 2 , respectively. (c) Snapshot from a sequence (Media 5, 1389 KB ) shows (left panel) the normalized fringe obtained at zero bias and (right panel) an estimate of normalized shear ( 2 Δ n ) and bias 2 ϕ . (d) By stitching the normalized fringes obtained at different bias, a more accurate estimate of the shear is obtained. In (c) and (d), e rms is the root-mean-square error between the experimental data and the fitted data.

Fig. 9
Fig. 9

Estimation of shear introduced by OPrism when used with UplansAPO 40 × 0.9 NA objective.

Fig. 10
Fig. 10

Estimation of shear introduced by OPrism when used with UPlanFl 40 × 0.6 NA objective.

Fig. 11
Fig. 11

Schematic representation of the interference fringes produced by the Nomarski prism when illuminated by (a) normally incident plane wave and (b) oblique plane wave; (c) the relationship between the angular shear and the period of the fringe, and (d) the relationship between spatial shear ( 2 Δ ), angular shear ( 2 ε ), and focal length of the lens ( f o ). Colors shown on the left are used to indicate polarization of light and the orientations of the optical axes of the optical components. Note that the relative distance between angularly-split wavefronts in (a)–(c) represents the relative optical path difference between them. Solid and dashed lines represent two different wavelengths.

Tables (1)

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Table 1 Summary of Angular Half-Shear (ε) and Spatial Half-Shear (Δ) Measured with Various Methods Presented in this Paper a

Equations (13)

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P = λ / 2 tan ( ε ) λ 2 ε .
Δ = tan ( ε ) f o = λ f o 2 P ,
ε = arctan ( Δ M f l ) = arctan ( Δ n λ NA obj × M f l ) ,
ε = 3.056 × 10 6 Δ n M NA obj .
f ( x ) = 1 2 [ 1 + cos ( 2 π x P α ) ] .
ε r = 3.46 × 10 5 .
t D ( x , y ) = t ( x + Δ , y ) e i ϕ t ( x Δ , y ) e i ϕ .
I ( ξ , η ) = | e i 2 π ( ξ x + η y ) t D ( x , y ) h o ( x , y ) | 2 .
I DIC ( x , y ) = | P c ( ξ , η ) | 2 I ( ξ , η ) ( x , y ) d ξ d η .
P DIC ( ξ , η ) = i P BF ( ξ , η ) sin ( 2 π ξ Δ ϕ ) .
| P DIC ( ξ , η ) | 2 = | P BF ( ξ , η ) | 2 sin 2 ( 2 π ξ Δ ϕ ) ,
sin 2 ( 2 π ξ Δ ϕ ) = 1 2 [ 1 cos ( 4 π ξ Δ 2 ϕ ) ] = | P DIC ( ξ , η ) | 2 | P BF ( ξ , η ) | 2 .
ε = Δ f o = Δ f l M ,

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