Abstract

The complete polarization state generator (PSG), which consists of one rotatable polarizer and one variable retarder with a quarter-wave plate, is introduced. The orientation angle of its output polarization ellipse equals half of the retardance of the variable retarder, and the ellipticity angle corresponds to the polarizer azimuth. The PSG is employed in the quantitative orientation-independent differential polarization microscope, which uses polarized light states with the same ellipticity and different orientation angles. Image processing algorithms using three or four frames are described.

© 2011 Optical Society of America

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References

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  1. P. S. Hauge, “Recent development in instrumentation in ellipsometry,” Surface Sci. 96, 108–140 (1980).
    [CrossRef]
  2. D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).
  3. R. A. Chipman, “Polarimetry,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), pp. 15.1–15.46.
  4. E. Collett, Polarized Light in Fiber Optics (PolaWave, 2003).
  5. M. Shribak, “Polarization,” in Handbook of Optical Metrology: Principles and Applications, T.Yoshizawa, ed. (CRC, 2009), pp. 339–350.
  6. N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope, 4th ed. (Edward Arnold, 1970).
  7. M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
    [CrossRef]
  8. Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
    [CrossRef]
  9. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  10. M. Shribak, “Device for measuring birefringence of reflecting optical data carrier,” USSR patent 1414097 (17 March 1986).
  11. M. Shribak, “Compensation method of measuring birefringence,” Sov. J. Opt. Technol. 60, 546–549 (1993).
  12. M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
    [CrossRef]
  13. T. Yamaguchi and H. Hasunuma, “A quick response recording ellipsometer,” Sci. Light 16, 64–71 (1967).
  14. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, 1987).
  15. R. Oldenbourg and G. Mei, “Polarized light microscopy,” U.S. patent 5,521,705 (12 May 1994).
  16. G. Mei and R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” Proc. SPIE 2265, 29–39 (1994).
    [CrossRef]
  17. M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,202,950 (8 July 2003).
  18. M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,239,388 (8 July 2003).
  19. M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,372,567 (8 July 2003).
  20. M. Shribak and R. Oldenbourg, “Techniques for fast and sensitive measurements of two-dimensional birefringence distributions,” Appl. Opt. 42, 3009–3017 (2003).
    [CrossRef]
  21. S. R. Davis, R. J. Uberna, and R. A. Herke, “Retardance sweep polarimeter and method,” U.S. patent 6,744,509 (20 August 2002).
  22. D. Lara and C. Dainty, “Double-pass axially resolved confocal Mueller matrix imaging polarimetry,” Opt. Lett. 30, 2879–2881(2005).
    [CrossRef]
  23. B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
    [CrossRef]
  24. M. Mujat and A. Dogariu, “Real-time measurement of the polarization transfer function,” Appl. Opt. 40, 34–44 (2001).
    [CrossRef]
  25. M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.
  26. A. De Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett. 28, 616–618 (2003).
    [CrossRef]
  27. E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
    [CrossRef]
  28. A. Jaulin and L. Bigue, “High speed partial Stokes imaging using a ferroelectric liquid crystal modulator,” J. Eur. Opt. Soc. Rapid Publ. 3, 080191 (2008).
    [CrossRef]
  29. D. A. Holmes, “Wave optics theory of rotary compensators,” J. Opt. Soc. Am. 54, 1340–1347 (1964).
    [CrossRef]
  30. F. Rinne and M. Berek, Anleitung zu Optischen Untersuclhungen mit dem Polarizationsmikroskop (Schweizerbart’sche Verlagsbuchhandlung, 1953).
  31. M. Shribak, “Use of gyrotropic birefringent plate as quarter-wave plate,” Sov. J. Opt. Technol. 53, 443–446 (1986).
  32. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).
  33. T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).
  34. M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
    [CrossRef]
  35. R. Oldenbourg and M. Shribak, “Microscopes,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V.N.Mahajan, eds. (McGraw-Hill, 2009), pp. 28.1–28.62.
  36. E. D. Salmon and P. Tran, “High resolution video-enhanced differential-interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
    [CrossRef]

2008 (1)

A. Jaulin and L. Bigue, “High speed partial Stokes imaging using a ferroelectric liquid crystal modulator,” J. Eur. Opt. Soc. Rapid Publ. 3, 080191 (2008).
[CrossRef]

2005 (1)

2004 (2)

B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

2003 (2)

2002 (1)

M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
[CrossRef]

1998 (1)

E. D. Salmon and P. Tran, “High resolution video-enhanced differential-interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

1995 (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

1994 (2)

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

G. Mei and R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” Proc. SPIE 2265, 29–39 (1994).
[CrossRef]

1993 (1)

M. Shribak, “Compensation method of measuring birefringence,” Sov. J. Opt. Technol. 60, 546–549 (1993).

1992 (1)

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

1986 (1)

M. Shribak, “Use of gyrotropic birefringent plate as quarter-wave plate,” Sov. J. Opt. Technol. 53, 443–446 (1986).

1980 (1)

P. S. Hauge, “Recent development in instrumentation in ellipsometry,” Surface Sci. 96, 108–140 (1980).
[CrossRef]

1967 (1)

T. Yamaguchi and H. Hasunuma, “A quick response recording ellipsometer,” Sci. Light 16, 64–71 (1967).

1964 (1)

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, 1987).

Berek, M.

F. Rinne and M. Berek, Anleitung zu Optischen Untersuclhungen mit dem Polarizationsmikroskop (Schweizerbart’sche Verlagsbuchhandlung, 1953).

Bigue, L.

A. Jaulin and L. Bigue, “High speed partial Stokes imaging using a ferroelectric liquid crystal modulator,” J. Eur. Opt. Soc. Rapid Publ. 3, 080191 (2008).
[CrossRef]

Chipman, R. A.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

R. A. Chipman, “Polarimetry,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), pp. 15.1–15.46.

Collett, E.

E. Collett, Polarized Light in Fiber Optics (PolaWave, 2003).

Dainty, C.

Davis, S. R.

S. R. Davis, R. J. Uberna, and R. A. Herke, “Retardance sweep polarimeter and method,” U.S. patent 6,744,509 (20 August 2002).

De Martino, A.

Dogariu, A.

Drevillon, B.

B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

Drévillon, B.

Ferguson, R. D.

M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.

Garcia-Caurel, E.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

A. De Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett. 28, 616–618 (2003).
[CrossRef]

Goldstein, D.

D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).

Hammer, D. X.

M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.

Hartshorne, N. H.

N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope, 4th ed. (Edward Arnold, 1970).

Hasunuma, H.

T. Yamaguchi and H. Hasunuma, “A quick response recording ellipsometer,” Sci. Light 16, 64–71 (1967).

Hauge, P. S.

P. S. Hauge, “Recent development in instrumentation in ellipsometry,” Surface Sci. 96, 108–140 (1980).
[CrossRef]

Herke, R. A.

S. R. Davis, R. J. Uberna, and R. A. Herke, “Retardance sweep polarimeter and method,” U.S. patent 6,744,509 (20 August 2002).

Holmes, D. A.

Iftimia, N.

M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.

Inoué, S.

M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
[CrossRef]

Ishikawa, T.

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

Jaulin, A.

A. Jaulin and L. Bigue, “High speed partial Stokes imaging using a ferroelectric liquid crystal modulator,” J. Eur. Opt. Soc. Rapid Publ. 3, 080191 (2008).
[CrossRef]

Kim, Y.-K.

Lara, D.

Laude, B.

Laude-Boulesteix, B.

Mahajan, V. N.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), pp. 15.1–15.46.

Mei, G.

G. Mei and R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” Proc. SPIE 2265, 29–39 (1994).
[CrossRef]

R. Oldenbourg and G. Mei, “Polarized light microscopy,” U.S. patent 5,521,705 (12 May 1994).

Mujat, M.

M. Mujat and A. Dogariu, “Real-time measurement of the polarization transfer function,” Appl. Opt. 40, 34–44 (2001).
[CrossRef]

M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.

Noguchi, M.

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

Ohno, M.

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

Oldenbourg, R.

M. Shribak and R. Oldenbourg, “Techniques for fast and sensitive measurements of two-dimensional birefringence distributions,” Appl. Opt. 42, 3009–3017 (2003).
[CrossRef]

M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
[CrossRef]

G. Mei and R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” Proc. SPIE 2265, 29–39 (1994).
[CrossRef]

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,202,950 (8 July 2003).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,239,388 (8 July 2003).

R. Oldenbourg and G. Mei, “Polarized light microscopy,” U.S. patent 5,521,705 (12 May 1994).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,372,567 (8 July 2003).

R. Oldenbourg and M. Shribak, “Microscopes,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V.N.Mahajan, eds. (McGraw-Hill, 2009), pp. 28.1–28.62.

Otani, Y.

M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Rinne, F.

F. Rinne and M. Berek, Anleitung zu Optischen Untersuclhungen mit dem Polarizationsmikroskop (Schweizerbart’sche Verlagsbuchhandlung, 1953).

Salmon, E. D.

E. D. Salmon and P. Tran, “High resolution video-enhanced differential-interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

Scharf, T.

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

Schwartz, L.

Shimada, T.

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Shribak, M.

M. Shribak and R. Oldenbourg, “Techniques for fast and sensitive measurements of two-dimensional birefringence distributions,” Appl. Opt. 42, 3009–3017 (2003).
[CrossRef]

M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
[CrossRef]

M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
[CrossRef]

M. Shribak, “Compensation method of measuring birefringence,” Sov. J. Opt. Technol. 60, 546–549 (1993).

M. Shribak, “Use of gyrotropic birefringent plate as quarter-wave plate,” Sov. J. Opt. Technol. 53, 443–446 (1986).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,372,567 (8 July 2003).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,239,388 (8 July 2003).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,202,950 (8 July 2003).

M. Shribak, “Device for measuring birefringence of reflecting optical data carrier,” USSR patent 1414097 (17 March 1986).

M. Shribak, “Polarization,” in Handbook of Optical Metrology: Principles and Applications, T.Yoshizawa, ed. (CRC, 2009), pp. 339–350.

R. Oldenbourg and M. Shribak, “Microscopes,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V.N.Mahajan, eds. (McGraw-Hill, 2009), pp. 28.1–28.62.

Stuart, A.

N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope, 4th ed. (Edward Arnold, 1970).

Tachihara, S.

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

Tran, P.

E. D. Salmon and P. Tran, “High resolution video-enhanced differential-interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

Uberna, R. J.

S. R. Davis, R. J. Uberna, and R. A. Herke, “Retardance sweep polarimeter and method,” U.S. patent 6,744,509 (20 August 2002).

Umeda, N.

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Yamaguchi, T.

T. Yamaguchi and H. Hasunuma, “A quick response recording ellipsometer,” Sci. Light 16, 64–71 (1967).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Yoshizawa, T.

M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Appl. Opt. (3)

J. Eur. Opt. Soc. Rapid Publ. (1)

A. Jaulin and L. Bigue, “High speed partial Stokes imaging using a ferroelectric liquid crystal modulator,” J. Eur. Opt. Soc. Rapid Publ. 3, 080191 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

Meth. Cell Biol. (1)

E. D. Salmon and P. Tran, “High resolution video-enhanced differential-interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

Opt. Eng. (3)

M. Shribak, S. Inoué, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high NA lenses: theory, measurement and rectification,” Opt. Eng. 41, 943–954 (2002).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, and N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimeter,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Opt. Lett. (2)

Opt. Spectrosc. (1)

M. Shribak, Y. Otani, and T. Yoshizawa, “Autocollimation polarimeter for measuring two-dimensional distribution of birefringence,” Opt. Spectrosc. 89, 155–159 (2000).
[CrossRef]

Proc. SPIE (2)

G. Mei and R. Oldenbourg, “Fast imaging polarimetry with precision universal compensator,” Proc. SPIE 2265, 29–39 (1994).
[CrossRef]

M. Noguchi, T. Ishikawa, M. Ohno, and S. Tachihara, “Measurement of 2D birefringence distribution,” Proc. SPIE 1720, 367–378 (1992).
[CrossRef]

Sci. Light (1)

T. Yamaguchi and H. Hasunuma, “A quick response recording ellipsometer,” Sci. Light 16, 64–71 (1967).

Sov. J. Opt. Technol. (2)

M. Shribak, “Compensation method of measuring birefringence,” Sov. J. Opt. Technol. 60, 546–549 (1993).

M. Shribak, “Use of gyrotropic birefringent plate as quarter-wave plate,” Sov. J. Opt. Technol. 53, 443–446 (1986).

Surface Sci. (1)

P. S. Hauge, “Recent development in instrumentation in ellipsometry,” Surface Sci. 96, 108–140 (1980).
[CrossRef]

Thin Solid Films (1)

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455–456, 120–123 (2004).
[CrossRef]

Other (17)

F. Rinne and M. Berek, Anleitung zu Optischen Untersuclhungen mit dem Polarizationsmikroskop (Schweizerbart’sche Verlagsbuchhandlung, 1953).

M. Mujat, N. Iftimia, R. D. Ferguson, and D. X. Hammer, “Mueller matrix microscopy,” in Biomedical Optics (BIOMED)/Digital Holography and Three-Dimensional Imaging (DH), CD-ROM (Optical Society of America, 2010), paper BSuD60.

S. R. Davis, R. J. Uberna, and R. A. Herke, “Retardance sweep polarimeter and method,” U.S. patent 6,744,509 (20 August 2002).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

R. Oldenbourg and M. Shribak, “Microscopes,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V.N.Mahajan, eds. (McGraw-Hill, 2009), pp. 28.1–28.62.

D. Goldstein, Polarized Light, 2nd ed. (Marcel Dekker, 2003).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, Third Edition, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, M.Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), pp. 15.1–15.46.

E. Collett, Polarized Light in Fiber Optics (PolaWave, 2003).

M. Shribak, “Polarization,” in Handbook of Optical Metrology: Principles and Applications, T.Yoshizawa, ed. (CRC, 2009), pp. 339–350.

N. H. Hartshorne and A. Stuart, Crystals and the Polarizing Microscope, 4th ed. (Edward Arnold, 1970).

M. Shribak, “Device for measuring birefringence of reflecting optical data carrier,” USSR patent 1414097 (17 March 1986).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier Science, 1987).

R. Oldenbourg and G. Mei, “Polarized light microscopy,” U.S. patent 5,521,705 (12 May 1994).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,202,950 (8 July 2003).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,239,388 (8 July 2003).

M. Shribak and R. Oldenbourg, “Retardance measurement system and method,” U.S. patent 7,372,567 (8 July 2003).

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Figures (5)

Fig. 1
Fig. 1

Schematic of a complete PSG with rotatable polarizer and one variable retarder: Sc, monochromatic light source; P, linear polarizer; VR, variable retarder; and QWP, quarter-wave plate. The X axis of the Cartesian coordinates corresponds to the slow axis of the variable retarder. Angle β is the orientation of the transmission axis of the polarizer. The variable retarder introduces a phase shift α.

Fig. 2
Fig. 2

Schematic of the complete PSG with fixed polarizer and two LC variable retarders: Sc, monochromatic light source; P, fixed linear polarizer; LC1 and LC2, LC variable retarders; and QWFs, achromatic quarter-wave retardation films. The X axis of the Cartesian coordinates corresponds to the slow axis of the second LC variable retarder. Angle θ is the orientation of the slow axis of the first LC variable retarder. The variable retarders LC1 and LC2 introduce the phase shifts γ and α, respectively.

Fig. 3
Fig. 3

Example of the quantitative orientation-independent differential polarization microscope (SLC-polscope) with proposed complete PSG: Sc, monochromatic light source; PSG, PSG consisting of rotatable linear polarizer (P1) and LC cell (LC) covered with achromatic quarter-wave retardation film QWF; S, specimen under investigation; QWP, achromatic quarter-wave plate and P2, second linear polarizer, which together construct a left-handed circular analyzer; and CCD, imaging detector (CCD camera). Δ ( x , y ) and ϕ ( x , y ) are two- dimensional distributions of the specimen’s retardance and slow axis orientation.

Fig. 4
Fig. 4

Polarization states of the illumination beam on the Poincaré sphere. The left column in the left group depicts four elliptical polarization states Σ 1 , Σ 2 , Σ 3 , and Σ 4 used with the four-frame algorithm for imaging a specimen with low retardance. They are shown in triangles on the Poincaré sphere. The right column in this group illustrates four linear polarization states Σ 1 , Σ 2 , Σ 3 , and Σ 4 used for imaging a specimen with high retardance. They are shown in diamonds on the sphere. The left column in the right group represents three elliptical polarization states Σ ˜ 1 , Σ ˜ 2 , and Σ ˜ 3 used with the three-frame algorithm for imaging a specimen with low retardance. They are shown in shaded square boxes on the Poincaré sphere. The right column in this group illustrates three linear polarization states Σ ˜ 1 , Σ ˜ 2 , and Σ ˜ 3 used for imaging a specimen with high retardance. They are shown in shaded circles on the sphere.

Fig. 5
Fig. 5

Images of the diatom test plate obtained with the SLC-polscope: three raw specimen and three background intensity images captured in a time sequence by the monochromatic camera (left and right, respectively) computed with the symmetrical three-frame algorithm retardance image after background correction (center). Image brightness is linearly proportional to retardance, where white corresponds to the maximal retardance Δ max = 5 nm and black corresponds to zero retardance.

Equations (37)

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E = 1 2 ( 1 i i 1 ) ( exp ( i α / 2 ) 0 0 exp ( i α / 2 ) ) ( cos β sin β ) .
E = 1 2 ( cos ( β + α 2 ) + i sin ( β α 2 ) sin ( β + α 2 ) + i cos ( β α 2 ) ) = 1 2 exp ( i arctan ( cos ( β α / 2 ) sin ( β + α / 2 ) ) ) ( ( 1 sin 2 β sin α ) 1 / 2 exp ( i arctan ( cos 2 β sin 2 β cos α ) ) ( 1 + sin 2 β sin α ) 1 / 2 ) .
{ E 0 x E 0 y = ( 1 sin 2 β sin α 1 + sin 2 β sin α ) 1 / 2 δ = arctan ( cos 2 β sin 2 β cos α ) .
{ tan 2 ψ = 2 E 0 x E 0 y E 0 x 2 E 0 y 2 cos δ sin 2 ε = 2 E 0 x E 0 y E 0 x 2 + E 0 y 2 sin δ .
{ ε = 45 ° β ψ = 45 ° α / 2 , if     β 0 ° or 90 ° .
{ 45 ° ε 45 ° , if     0 ° β 90 ° 0 ° ψ 180 ° , if     0 ° α 180 ° .
{ β = 45 ° ε α = 90 ° 2 ψ , if     ε ± 45 ° .
E = ( cos ε sin ψ i sin ε cos ψ cos ε cos ψ + i sin ε sin ψ ) exp ( i π / 4 ) .
{ ε = 0 ° ψ = 45 ° + θ γ / 2 .
{ ε = θ γ / 2 ψ = 45 ° α / 2 , if     θ γ / 2 ± 45 ° .
{ ε = 45 ° γ / 2 ψ = α / 2 if     γ 0 ° or 180 ° .
E ( x , y ) = τ ( x , y ) 2 ( 1 0 0 0 ) ( 1 i i 1 ) × ( cos [ Δ ( x , y ) / 2 ] i cos [ 2 ϕ ( x , y ) ] sin [ Δ ( x , y ) / 2 ] i sin [ 2 ϕ ( x , y ) ] sin [ Δ ( x , y ) / 2 ] i sin [ 2 ϕ ( x , y ) ] sin [ Δ ( x , y ) / 2 ] cos [ Δ ( x , y ) / 2 ] + i cos [ 2 ϕ ( x , y ) ] sin [ Δ ( x , y ) / 2 ] ) × ( cos ε sin ψ i sin ε cos ψ cos ε sin ψ + i sin ε cos ψ ) exp ( i π / 4 ) ,
E ( x , y ) = τ ( x , y ) exp ( i 3 π / 4 ) ( cos [ Δ ( x , y ) / 2 ] cos ( ε + 45 ° ) exp ( i ψ ) + i sin [ Δ ( x , y ) / 2 ] sin ( ε + 45 ° ) exp { i [ 2 ϕ ( x , y ) + ψ ] } 0 ) .
I ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) sin 2 ε sin Δ ( x , y ) sin 2 ( ϕ ( x , y ) + ψ ) cos 2 ε ] + I ( x , y ) ξ ( x , y ) .
ψ ( t ) = 45 ° α ( t ) / 2 .
I sur ( x , y ) = I ( x , y ) sin 2 ( 45 ° ε ) + I ( x , y ) ξ ( x , y ) .
I max ( x , y ) = 1 2 I ( x , y ) [ 1 cos Δ ( x , y ) sin 2 ε + sin Δ ( x , y ) cos 2 ε ] + I ( x , y ) ξ ( x , y ) .
I min ( x , y ) = 1 2 I ( x , y ) [ 1 cos Δ ( x , y ) sin 2 ε sin Δ ( x , y ) cos 2 ε ] + I ( x , y ) ξ ( x , y ) .
k ( x , y ) = I max ( x , y ) I min ( x , y ) I max ( x , y ) + I min ( x , y ) = sin Δ ( x , y ) cos 2 ε 1 cos Δ ( x , y ) sin 2 ε + 1 ξ ( x , y ) .
sin 2 ε max = 1 1 + 1 / ξ cos Δ .
sin 2 ε max = ( 1 1 / ξ ) cos Δ .
ε max = 45 ° Δ / 2 , β max = Δ / 2 , k max = sin 2 Δ sin 2 Δ + 1 / ξ .
ε max = 45 ° [ ( Δ 2 ) 2 + ( 90 ° π ) 2 2 ξ ] 1 / 2 , β max = [ ( Δ 2 ) 2 + ( 90 ° π ) 2 2 ξ ] 1 / 2 , k max = Δ [ Δ 2 + ( 180 ° π ) 2 2 ξ ] 1 / 2 .
I 1 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β sin Δ ( x , y ) sin 2 ϕ ( x , y ) sin 2 β ] + I ( x , y ) ξ ( x , y ) , I 2 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β sin Δ ( x , y ) cos 2 ϕ ( x , y ) sin 2 β ] + I ( x , y ) ξ ( x , y ) , I 3 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β + sin Δ ( x , y ) sin 2 ϕ ( x , y ) sin 2 β ] + I ( x , y ) ξ ( x , y ) , I 4 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β + sin Δ ( x , y ) cos 2 ϕ ( x , y ) sin 2 β ] + I ( x , y ) ξ ( x , y ) .
A ( x , y ) = I 3 ( x , y ) I 1 ( x , y ) I 1 ( x , y ) + I 3 ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β + 2 ξ ( x , y ) sin 2 ϕ ( x , y ) , B ( x , y ) = I 4 ( x , y ) I 2 ( x , y ) I 4 ( x , y ) + I 2 ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β + 2 ξ ( x , y ) cos 2 ϕ ( x , y ) .
A ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β sin 2 ϕ ( x , y ) , B ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β cos 2 ϕ ( x , y ) .
Δ ( x , y ) = 2 arctan ( { [ A ( x , y ) ] 2 + [ B ( x , y ) ] 2 } 1 / 2 tan β 1 + { 1 [ A ( x , y ) ] 2 [ B ( x , y ) ] 2 } 1 / 2 ) , ϕ ( x , y ) = 1 2 arctan [ A ( x , y ) B ( x , y ) ] .
Δ ( x , y ) = 2 arctan ( { [ A ( x , y ) ] 2 + [ B ( x , y ) ] 2 } 1 / 2 1 + { 1 [ A ( x , y ) ] 2 [ B ( x , y ) ] 2 } 1 / 2 ) .
ϕ cor = 45 ° α 1 / 2 + 180 ° m ,
I 1 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β sin Δ ( x , y ) sin 2 ϕ ( x , y ) sin 2 β ] , I 2 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β + sin Δ ( x , y ) sin ( 2 ϕ ( x , y ) 60 ° ) sin 2 β ] , I 3 ( x , y ) = 1 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β + sin Δ ( x , y ) sin ( 2 ϕ ( x , y ) + 60 ° ) sin 2 β ] .
[ I 2 ( x , y ) + I 3 ( x , y ) ] 2 I 1 ( x , y ) = 3 2 I ( x , y ) τ ( x , y ) sin Δ ( x , y ) sin 2 ϕ ( x , y ) sin 2 β , I 3 ( x , y ) I 2 ( x , y ) = 3 2 I ( x , y ) τ ( x , y ) × sin Δ ( x , y ) cos 2 ϕ ( x , y ) sin 2 β , I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) = 3 2 I ( x , y ) τ ( x , y ) [ 1 cos Δ ( x , y ) cos 2 β ] .
A ( x , y ) = [ I 2 ( x , y ) + I 3 ( x , y ) ] 2 I 1 ( x , y ) I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β sin 2 ϕ ( x , y ) , B ( x , y ) = 3 [ I 3 ( x , y ) I 2 ( x , y ) ] I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) = sin Δ ( x , y ) sin 2 β 1 cos Δ ( x , y ) cos 2 β cos 2 ϕ ( x , y ) .
Δ ( x , y ) = 2 arctan ( { [ A ( x , y ) ] 2 + [ B ( x , y ) ] 2 } 1 / 2 tan β 1 + { 1 [ A ( x , y ) ] 2 [ B ( x , y ) ] 2 } 1 / 2 ) , ϕ ( x , y ) = 1 2 arctan [ A ( x , y ) B ( x , y ) ] .
Δ ( x , y ) = 2 arctan ( { [ A ( x , y ) A b g ( x , y ) ] 2 + [ B ( x , y ) B b g ( x , y ) ] 2 } 1 / 2 tan β 1 + { 1 [ A ( x , y ) A b g ( x , y ) ] 2 [ B ( x , y ) B b g ( x , y ) ] 2 } 1 / 2 ) , ϕ ( x , y ) = 1 2 arctan ( A ( x , y ) A b g ( x , y ) B ( x , y ) B b g ( x , y ) ) .
A cor = sin Δ cor sin 2 β 1 cos Δ cor cos 2 β sin 2 ϕ cor , B cor = sin Δ cor sin 2 β 1 cos Δ cor cos 2 β cos 2 ϕ cor .
Δ ( x , y ) = 2 arctan ( { [ A ( x , y ) A bg ( x , y ) A cor ] 2 + [ B ( x , y ) B bg ( x , y ) B cor ] 2 } 1 / 2 tan β 1 + { 1 [ A ( x , y ) A bg ( x , y ) A cor ] 2 [ B ( x , y ) B bg ( x , y ) B cor ] 2 } 1 / 2 ) , ϕ ( x , y ) = 1 2 arctan [ A ( x , y ) A bg ( x , y ) A cor B ( x , y ) B bg ( x , y ) B cor ] .
ξ = 1 sin 2 β I β I 0 I 0 I dark ,

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