Abstract

We describe a new technique for differential interference contrast (DIC) microscopy, which digitally generates phase gradient images independently of gradient orientation. To prove the principle we investigated specimens recorded at different orientations on a microscope equipped with a precision rotating stage and using regular DIC optics. The digitally generated images successfully displayed and measured phase gradients, independently of gradient orientation. One could also generate images showing distribution of optical path differences or enhanced, regular DIC images with any shear direction. Using special DIC prisms, one can switch the bias and shear directions rapidly without mechanically rotating the specimen or the prisms and orientation-independent DIC images are obtained in a fraction of a second.

© 2006 Optical Society of America

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References

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  1. S. Inoue and K. R. Spring, Videomicroscopy: The Fundamentals, 2nd ed. (Plenum, 1997).
  2. F. H. Smith, "Interference microscope," U.S. patent 2,601,175 (17 June 1952).
  3. G. Nomarski, "Interferential polarizing device for study of phase object," U.S. patent 2,924,142 (9 February 1960).
  4. R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).
  5. R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
    [CrossRef] [PubMed]
  6. S. Inoué, "Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy," J. Cell Biol. 89, 246-356 (1981).
    [CrossRef]
  7. R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
    [CrossRef] [PubMed]
  8. G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
    [CrossRef]
  9. G. Holzwarth, D. B. Hill, and E. B. McLaughlin, "Polarization-modulated differential-interference contrast microscopy with a variable retarder," Appl. Opt. 39, 6288-6294 (2000).
    [CrossRef]
  10. M.Pluta, ed., Specialized Methods, Vol. 2 of Advanced Light Microscopy (Elsevier, 1989),
  11. C. Preza, "Rotational-diversity phase estimation from differential-interference-contrast microscopy images," J. Opt. Soc. Am. A 17, 415-424 (2000).
    [CrossRef]
  12. M. Shribak "Orientation-independent differential interference contrast microscopy technique and device," U.S. patent application 2005-0152030 (14 July 2005).
  13. M. Shribak and R. Oldenbourg, "Technique for fast and sensitive measurements of two-dimensional birefringence distribution," Appl. Opt. 42, 3009-3017 (2003).
    [CrossRef] [PubMed]
  14. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).
  15. 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. (Oxford) 214, 7-12 (2004).
    [CrossRef] [PubMed]
  16. F. Kagalwala and T. Kanade, "Reconstructing specimens using DIC microscope images," IEEE Trans. Syst. Man Cybern. B 33, 728-737 (2003).
    [CrossRef]
  17. D. Biggs, AutoQuant Imaging, Inc., Troy, N.Y. 12180 (personal communication, 2005).
  18. T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.
  19. D. S. C. Biggs and M. Andrews, "Acceleration of iterative image restoration algorithms," Appl. Opt. 36, 1766-1775 (1997).
    [CrossRef] [PubMed]
  20. Descriptions of Hamamatsu C5985 chilled CCD camera and Hamamatsu C4742-95 high-resolution digital CCD camera are available at http://usa.hamamatsu.com.
  21. The ImageJ software is available at http://rsb.info.nih.gov/ij/.
  22. The Mathematica software is available athttp://www.wolfram.com.
  23. A. Resnick, "Differential interference contrast microscopy as a polarimetric instrument,," Appl. Opt. 41, 38-45 (2002).
    [PubMed]
  24. R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

2004 (1)

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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

2003 (2)

F. Kagalwala and T. Kanade, "Reconstructing specimens using DIC microscope images," IEEE Trans. Syst. Man Cybern. B 33, 728-737 (2003).
[CrossRef]

M. Shribak and R. Oldenbourg, "Technique for fast and sensitive measurements of two-dimensional birefringence distribution," Appl. Opt. 42, 3009-3017 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (2)

1998 (1)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

1997 (2)

D. S. C. Biggs and M. Andrews, "Acceleration of iterative image restoration algorithms," Appl. Opt. 36, 1766-1775 (1997).
[CrossRef] [PubMed]

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[CrossRef]

1981 (3)

R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
[CrossRef] [PubMed]

S. Inoué, "Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy," J. Cell Biol. 89, 246-356 (1981).
[CrossRef]

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

1969 (1)

R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).

Allen, N. S.

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[CrossRef]

R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
[CrossRef] [PubMed]

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

Allen, R. D.

R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
[CrossRef] [PubMed]

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).

Andrews, M.

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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

Bhattacharyya, S.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Biggs, D.

D. Biggs, AutoQuant Imaging, Inc., Troy, N.Y. 12180 (personal communication, 2005).

Biggs, D. 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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

Cooper, J. A.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

David, G. B.

R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

Hanzel, D.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Hill, D. B.

Holmes, T. J.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Holzwarth, G.

G. Holzwarth, D. B. Hill, and E. B. McLaughlin, "Polarization-modulated differential-interference contrast microscopy with a variable retarder," Appl. Opt. 39, 6288-6294 (2000).
[CrossRef]

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[CrossRef]

Imaz, H. Y.

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

Inoue, S.

S. Inoue and K. R. Spring, Videomicroscopy: The Fundamentals, 2nd ed. (Plenum, 1997).

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Inoué, S.

S. Inoué, "Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy," J. Cell Biol. 89, 246-356 (1981).
[CrossRef]

Kagalwala, F.

F. Kagalwala and T. Kanade, "Reconstructing specimens using DIC microscope images," IEEE Trans. Syst. Man Cybern. B 33, 728-737 (2003).
[CrossRef]

Kanade, T.

F. Kagalwala and T. Kanade, "Reconstructing specimens using DIC microscope images," IEEE Trans. Syst. Man Cybern. B 33, 728-737 (2003).
[CrossRef]

Krishnamurthi, V.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Kubinski, D. J.

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

Lin, W.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

McLaughlin, E. B.

Mei, G.

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Nomarski, G.

R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).

G. Nomarski, "Interferential polarizing device for study of phase object," U.S. patent 2,924,142 (9 February 1960).

Oldenbourg, R.

M. Shribak and R. Oldenbourg, "Technique for fast and sensitive measurements of two-dimensional birefringence distribution," Appl. Opt. 42, 3009-3017 (2003).
[CrossRef] [PubMed]

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Preza, C.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

Roysam, B.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

Shribak, M.

M. Shribak and R. Oldenbourg, "Technique for fast and sensitive measurements of two-dimensional birefringence distribution," Appl. Opt. 42, 3009-3017 (2003).
[CrossRef] [PubMed]

M. Shribak "Orientation-independent differential interference contrast microscopy technique and device," U.S. patent application 2005-0152030 (14 July 2005).

Skvarla, M.

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Smith, F. H.

F. H. Smith, "Interference microscope," U.S. patent 2,601,175 (17 June 1952).

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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

Spring, K. R.

S. Inoue and K. R. Spring, Videomicroscopy: The Fundamentals, 2nd ed. (Plenum, 1997).

Stemmer, A.

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Szarowski, D. H.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Tiberio, R.

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

Travis, J. L.

R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
[CrossRef] [PubMed]

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

Turner, J. N.

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Webb, S. C.

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[CrossRef]

Appl. Opt. (4)

Cell Motil. (2)

R. D. Allen, N. S. Allen, and J. L. Travis, "Video-enhanced contrast differential interference contrast (AVEC-DIC) microscopy: a new method capable of analyzing microtubule-related motility in the reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 291-302 (1981).
[CrossRef] [PubMed]

R. D. Allen, J. L. Travis, N. S. Allen, and H. Y. Imaz, "Video-enhanced contrast polarization (AVEC-POL) microscopy: a new method applied to detection of birefringence in motile reticulopodial network of Allogromia laticollaris," Cell Motil. 1, 275-289 (1981).
[CrossRef] [PubMed]

IEEE Trans. Syst. Man Cybern. B (1)

F. Kagalwala and T. Kanade, "Reconstructing specimens using DIC microscope images," IEEE Trans. Syst. Man Cybern. B 33, 728-737 (2003).
[CrossRef]

J. Cell Biol. (1)

S. Inoué, "Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy," J. Cell Biol. 89, 246-356 (1981).
[CrossRef]

J. Microsc. (2)

G. Holzwarth, S. C. Webb, D. J. Kubinski, and N. S. Allen, "Improving DIC microcopy with polarization modulation," J. Microsc. (Oxford) 188, 249-254 (1997).
[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. (Oxford) 214, 7-12 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Z. Wiss. Mickrosk. (1)

R. D. Allen, G. B. David, and G. Nomarski. "The Zeiss-Nomarski differential equipment for transmitted light microscopy," Z. Wiss. Mickrosk. 69(4), 193-221 (1969).

Other (12)

D. Biggs, AutoQuant Imaging, Inc., Troy, N.Y. 12180 (personal communication, 2005).

T. J. Holmes, S. Bhattacharyya, J. A. Cooper, D. Hanzel, V. Krishnamurthi, W. Lin, B. Roysam, D. H. Szarowski, and J. N. Turner, "Light microscopic images reconstructed by maximum likelihood deconvolution," in Handbook of Biological Confocal Microscopy, J.B.Pawley, ed. (Plenum, 1995), pp. 389-402.

Descriptions of Hamamatsu C5985 chilled CCD camera and Hamamatsu C4742-95 high-resolution digital CCD camera are available at http://usa.hamamatsu.com.

The ImageJ software is available at http://rsb.info.nih.gov/ij/.

The Mathematica software is available athttp://www.wolfram.com.

R. Oldenbourg, S. Inoue, R. Tiberio, A. Stemmer, G. Mei, and M. Skvarla, "Standard test targets for high resolution light microscopy," in Nanofabrication and Biosystems, H.C.Hoch, L.W.Jelinski, and H.G.Craighead, eds. (Cambridge U. Press, 1996), pp. 123-138.

M.Pluta, ed., Specialized Methods, Vol. 2 of Advanced Light Microscopy (Elsevier, 1989),

M. Shribak "Orientation-independent differential interference contrast microscopy technique and device," U.S. patent application 2005-0152030 (14 July 2005).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

S. Inoue and K. R. Spring, Videomicroscopy: The Fundamentals, 2nd ed. (Plenum, 1997).

F. H. Smith, "Interference microscope," U.S. patent 2,601,175 (17 June 1952).

G. Nomarski, "Interferential polarizing device for study of phase object," U.S. patent 2,924,142 (9 February 1960).

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Figures (8)

Fig. 1
Fig. 1

Conventional DIC microscope setup: Sc, monochromatic light source; P(45°), polarizer at 45° azimuth; R(Γ, 0°), retarder at 0° azimuth and phase shift Γ; WP1, Wollaston prism 1 with splitting angle ε1; C, condenser lens with focal distance fc ; Sp, object under investigation with OPD = φ between points A and B; O, objective lens with focal distance f ob; WP2, Wollaston prism 2 with splitting angle ε2; A(−45°), analyzer at −45° azimuth; Ex, Ey polarization components; δ, amount of shear.

Fig. 2
Fig. 2

Regular DIC image of 4 μm diameter glass rods immersed in Permount. The DIC shear direction is parallel to AA′ (left). Linear scans of normalized intensity in sections A-A′ and B-B′ are shown at the right.

Fig. 3
Fig. 3

Computed gradient magnitude image of the glass rods (left). Linear plots of normalized gradient magnitude in sections A-A′ and B-B′ are shown at the right. The experimental data are indicated by filled circles. The solid curves show the theoretical results calculated with simplified assumptions (see text).

Fig. 4
Fig. 4

Computed gradient image of the same group of glass rods with the azimuth in pseudocolor. The color wheel at the lower left corner depicts the gradient azimuth.

Fig. 5
Fig. 5

Computed phase of the glass rods (left). Linear scans of normalized phase in sections A-A′ and B-B′ are shown at the right. The experimental data are indicated by filled circles. The solid curves show the theoretical results.

Fig. 6
Fig. 6

Regular and computed orientation-independent DIC images of Siemens star and line scans along section AA′. The phase image of the Siemens star was calculated by D. Biggs (AutoQuant Imaging, Inc., Troy, N.Y.).

Fig. 7
Fig. 7

Regular and computed orientation-independent DIC images of bovine pulmonary artery endothelial cell. The phase image of the bovine cell was calculated by D. Biggs (AutoQuant Imaging, Inc., Troy, N.Y.).

Fig. 8
Fig. 8

DIC images of bovine pulmonary artery endothelial cell with various shear directions computed from orientation-independent DIC data.

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

OPD ( x , y ) = ϕ ( x , y ) ϕ ( x δ x , y δ y ) .
ϕ ( x δ x , y δ y ) = ϕ ( x , y ) ( ϕ ( x , y ) , δ ) ,
ϕ ( x , y ) g r a d [ ϕ ( x , y ) ] = [ ϕ ( x , y ) x , ϕ ( x , y ) y ]
φ ( x , y ) = 2 π λ ( Γ + ( ϕ ( x , y ) , δ ) ) = 2 π λ ( Γ + δ γ ( x , y ) cos ψ ( x , y ) ) ,
I ( x , y ) = 1 2 I ˜ [ 1 cos ( 2 π λ { Γ + δγ ( x , y ) cos [ θ ( x , y ) σ ] } ) ] + I min ,
σ = 0 °, I 1 = 1 2 I ˜ { 1 cos [ 2 π λ ( Γ + δ γ cos θ ) ] } + I min ;
σ = 90 °, I 2 = 1 2 I ˜ { 1 cos [ 2 π λ ( Γ + δ γ sin θ ) ] } + I min ;
σ = 180 °, I 3 = 1 2 I ˜ { 1 cos [ 2 π λ ( Γ δ γ cos θ ) ] } + I min ;
σ = 270 °, I 4 = 1 2 I ˜ { 1 cos [ 2 π λ ( Γ δ γ sin θ ) ] } + I min ;
σ = 0 °   or     σ = 180 °, I 0 = 1 2 I ˜ [ 1 cos ( 2 π λ δ γ cos θ ) ] + I min ;
σ = 90 °   or   σ = 270 °, I 0 = 1 2 I ˜ [ 1 cos ( 2 π λ δ γ sin θ ) ] + I min .
A I 1 I 3 I 1 + I 3 2 I 0 tan ( π Γ λ ) = tan ( 2 π λ δ γ cos θ ) ,
B I 2 I 4 I 2 + I 4 2 I 0 tan ( π Γ λ ) = tan ( 2 π λ δ γ sin θ ) .
γ ( x , y ) = λ 2 π δ [ ( arctan A ) 2 + ( arctan B ) 2 ] 1 / 2 ,
θ ( x , y ) = arctan ( arctan B arctan A ) .
I ( x , y ) = 1 2 I ˜ { 1 cos ( 2 π λ Γ ) + 2 π λ δ γ sin ( 2 π λ Γ ) cos [ θ ( x , y ) σ ] } + I min .
σ = 0 °, I 1 = 1 2 I ˜ [ 1 cos ( 2 π λ Γ ) + 2 π λ δ γ sin ( 2 π λ Γ ) cos θ ] + I min ;
σ = 90 °, I 2 = 1 2 I ˜ [ 1 cos ( 2 π λ Γ ) + 2 π λ δ γ sin ( 2 π λ Γ ) sin θ ] + I min ;
σ = 180 °, I 3 = 1 2 I ˜ [ 1 cos ( 2 π λ Γ ) 2 π λ δ γ sin ( 2 π λ Γ ) cos θ ] + I min ;
σ = 270 °, I 4 = 1 2 I ˜ [ 1 cos ( 2 π λ Γ ) 2 π λ δ γ sin ( 2 π λ Γ ) sin θ ] + I min ;
γ ( x , y ) = λ 2 π δ tan ( π Γ λ ) [ ( I 1 I 3 I 1 + I 3 ) 2 + ( I 2 I 4 I 2 + I 4 ) 2 ] 1 / 2 ,
θ ( x , y ) = arctan ( I 2 I 4 I 1 I 3 ) .
σ = 0 °, I 1 = I ˜ sin ( π λ Γ ) [ sin ( π λ Γ ) + 2 π λ δ γ cos ( π λ Γ ) cos θ ] + I min ;
σ = 90 °, I 2 = I ˜ sin ( π λ Γ ) [ sin ( π λ Γ ) + 2 π λ δ γ cos ( π λ Γ ) sin θ ] + I min ;
σ = 0 °, I bg 1 = I ˜     sin 2 ( π λ Γ ) + I min ,
σ = 90 °, I bg 2 = I ˜    sin 2 ( π λ Γ ) + I min ;
K I 1 I b g 1 I b g 1 I b g 0 tan ( π λ Γ ) = I ˜ 2 π λ δ γ sin [ ( π / λ ) Γ ] cos [ ( π / λ ) Γ ] cos θ I ˜ sin 2 [ ( π / λ ) Γ ] tan [ ( π / λ ) Γ ] = 2 π λ δ γ cos θ ,
L I 2 I b g 2 I b g 2 I b g 0 tan ( π λ Γ ) = I ˜ 2 π λ δ γ sin [ ( π / λ ) Γ ] cos [ ( π / λ ) Γ ] sin θ I ˜ sin 2 [ ( π / λ ) Γ ] tan [ ( π / λ ) Γ ] = 2 π λ δ γ sin θ .
γ ( x , y ) = λ 2 π δ A 2 + B 2 ,
θ ( x , y ) = arctan ( B A ) .
I e n h ( x , y ) = 1 cos ( 2 π λ { Γ + δ γ ( x , y ) cos [ θ ( x , y ) σ ] } ) .
Φ ( x , y ) = 2 π λ C [ γ ( x , y ) cos θ ( x , y ) d x + γ ( x , y ) sin θ ( x , y ) d y ] .
Φ ( x , y ) = 2 π λ [ 0 x γ ( x , 0 ) cos θ ( x , 0 ) d x + 0 y γ ( x , y ) sin θ ( x , y ) d y ] .
Φ m n = 2 π λ ( k = 1 n γ 0 k cos θ 0 k + p = 1 m γ p n sin θ p n ) ,
Φ ( x ) = 4 π λ ( n r n m ) r 2 x 2 = Φ max 1 ( x r ) 2 ,
γ ( x ) = Φ ( x + δ ) Φ ( x ) δ = 2 δ ( n r n m ) { 0 x < r   or   x r + δ r 2 x 2 r x < r + δ | r 2 x 2 r 2 ( x δ ) 2 | r + δ x < r r 2 ( x δ ) 2 r x < r + δ .
γ max = 2 2 ( n r n m ) r δ .
γ ( x ) / γ max = 1 2 r δ { 0 x < r   or   x r + δ r 2 x 2 r x < r + δ | r 2 x 2 r 2 ( x δ ) 2 | r + δ x < r r 2 ( x δ ) 2 r x < r + δ .

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