Abstract

We describe a new imaging polarimeter that is based on a modified Sagnac interferometer and allows full polarimetric description of complex random electromagnetic beams from only two images as compared with the four images needed in conventional polarimetry. The procedure is analyzed in terms of the interference laws of Fresnel and Arago, and very good agreement with standard Stokes polarimetry is demonstrated. In certain cases the new technique provides the degree of polarization and the retardance from only one image.

© 2004 Optical Society of America

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  1. A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
    [CrossRef]
  2. S. L. Jacques, “Video imaging of superficial biological tissue layers using polarized light,” U.S. Patent6,177,984, January23, 2001.
  3. M. H. Smith, A. Lompado, P. Burke, “Mueller matrix imaging polarimetry in dermatology,” in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, eds., Proc. SPIE3911, 210–216 (2000).
    [CrossRef]
  4. R. Walraven, “Polarization imagery,” Opt. Eng. (Bellingham) 20, 14–18 (1981).
    [CrossRef]
  5. G. W. Katawar, “Virtues of Mueller matrix detection of objects embedded in random media,” in Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, J. O. Hollinger, S. L. Jacques, eds., Proc. SPIE3914, 478–488 (2000).
    [CrossRef]
  6. M. H. Smith, “Interpreting Mueller matrix images of tissues,” in Laser–Tissue Interaction XII, D. Duncan, S. Jacques, P. Johnson, eds., Proc. SPIE4257, 82–89 (2001).
    [CrossRef]
  7. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
    [CrossRef] [PubMed]
  8. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. (Bellingham) 34, 1558–1568 (1995).
    [CrossRef]
  9. B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, G. L. Cote, “Measurement and calculation of the two–dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
    [CrossRef]
  10. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Express 1, 441–453 (1997).
    [CrossRef] [PubMed]
  11. J. L. Pezzaniti, J. M. Lindberg, “Apparatus and process for the noninvasive measurement of optically active compounds,” U.S. Patent5,788,632, August4, 1998.
  12. J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
    [CrossRef]
  13. J. D. Barter, “Visible Stokes polarimetric imager,” U.S. Patent6,122,404, September19, 2000.
  14. G. P. Nordin, J. T. Meier, P. C. Deguzman, M. W. Jones, “Micropolarizer array for infrared imaging polarimetry,” J. Opt. Soc. Am. A 16, 1168–1174 (1999).
    [CrossRef]
  15. T. Hamamoto, H. Toyota, H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H. P. Herzig, eds., Proc. SPIE4440, 293–300 (2001).
    [CrossRef]
  16. K. Oka, T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510–1519 (2003).
    [CrossRef] [PubMed]
  17. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Sect. 5.3.
  18. D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
    [CrossRef]
  19. M. Mujat, A. Dogariu, “Real-time Mueller matrix measurement for particulate systems,” in Laser Radar Technology and Applications, V. G. W. Kamerman, U. N. Singh, C. Werner, V. V. Molebny, eds., Proc. SPIE4035, 390–400 (2000).
    [CrossRef]
  20. D. F. J. Arago, A. J. Fresnel, “On the action of rays of polarized light upon each other,” Annales de Chimie et de Physique, p. 288 (1819), republished in The Wave Theory of Light. Memoires by Huygens, Young, and Fresnel, H. Crew, ed. (American Book, New York, 1900).
  21. R. Hanau, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 31, 303–304 (1963).
    [CrossRef]
  22. E. Collett, “Mathematical formulation of the interference laws of Fresnel and Arago,” Am. J. Phys. 39, 1483–1495 (1971).
    [CrossRef]
  23. C. Brosseau, Fundamentals of Polarized Light, A Statistical Optics Approach (Wiley, New York, 1998).
  24. M. Mujat, A. Dogariu, E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel–Arago interference laws,” J. Opt. Soc. Am. A (to be published).
  25. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  26. E. Wolf, “Optics in terms of observable quantities,” Nuovo Cimento 12, 884–888 (1954).
    [CrossRef]
  27. G. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960).
    [CrossRef]
  28. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
    [CrossRef]

2003

K. Oka, T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510–1519 (2003).
[CrossRef] [PubMed]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

1999

1998

1997

1995

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

1994

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1981

R. Walraven, “Polarization imagery,” Opt. Eng. (Bellingham) 20, 14–18 (1981).
[CrossRef]

1978

1971

E. Collett, “Mathematical formulation of the interference laws of Fresnel and Arago,” Am. J. Phys. 39, 1483–1495 (1971).
[CrossRef]

1963

R. Hanau, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 31, 303–304 (1963).
[CrossRef]

1960

G. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960).
[CrossRef]

1959

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

1954

E. Wolf, “Optics in terms of observable quantities,” Nuovo Cimento 12, 884–888 (1954).
[CrossRef]

1819

D. F. J. Arago, A. J. Fresnel, “On the action of rays of polarized light upon each other,” Annales de Chimie et de Physique, p. 288 (1819), republished in The Wave Theory of Light. Memoires by Huygens, Young, and Fresnel, H. Crew, ed. (American Book, New York, 1900).

Arago, D. F. J.

D. F. J. Arago, A. J. Fresnel, “On the action of rays of polarized light upon each other,” Annales de Chimie et de Physique, p. 288 (1819), republished in The Wave Theory of Light. Memoires by Huygens, Young, and Fresnel, H. Crew, ed. (American Book, New York, 1900).

Azzam, R. M. A.

Baba, J. S.

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

Barter, J. D.

J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
[CrossRef]

J. D. Barter, “Visible Stokes polarimetric imager,” U.S. Patent6,122,404, September19, 2000.

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Bigio, I. J.

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

C. Brosseau, Fundamentals of Polarized Light, A Statistical Optics Approach (Wiley, New York, 1998).

Burke, P.

M. H. Smith, A. Lompado, P. Burke, “Mueller matrix imaging polarimetry in dermatology,” in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, eds., Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Cameron, B. D.

B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, G. L. Cote, “Measurement and calculation of the two–dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
[CrossRef]

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

Chipman, R. A.

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

Chung, J. R.

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

Collett, E.

E. Collett, “Mathematical formulation of the interference laws of Fresnel and Arago,” Am. J. Phys. 39, 1483–1495 (1971).
[CrossRef]

Cote, G. L.

B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, G. L. Cote, “Measurement and calculation of the two–dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
[CrossRef]

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

Deguzman, P. C.

Dogariu, A.

M. Mujat, A. Dogariu, “Real-time Mueller matrix measurement for particulate systems,” in Laser Radar Technology and Applications, V. G. W. Kamerman, U. N. Singh, C. Werner, V. V. Molebny, eds., Proc. SPIE4035, 390–400 (2000).
[CrossRef]

M. Mujat, A. Dogariu, E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel–Arago interference laws,” J. Opt. Soc. Am. A (to be published).

Eick, A. A.

Fresnel, A. J.

D. F. J. Arago, A. J. Fresnel, “On the action of rays of polarized light upon each other,” Annales de Chimie et de Physique, p. 288 (1819), republished in The Wave Theory of Light. Memoires by Huygens, Young, and Fresnel, H. Crew, ed. (American Book, New York, 1900).

Freyer, J. P.

Hamamoto, T.

T. Hamamoto, H. Toyota, H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H. P. Herzig, eds., Proc. SPIE4440, 293–300 (2001).
[CrossRef]

Hanau, R.

R. Hanau, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 31, 303–304 (1963).
[CrossRef]

Hielscher, A. H.

Hill, A. R.

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

Jacques, S. L.

S. L. Jacques, “Video imaging of superficial biological tissue layers using polarized light,” U.S. Patent6,177,984, January23, 2001.

Jones, M. W.

Kaneko, T.

Katawar, G. W.

G. W. Katawar, “Virtues of Mueller matrix detection of objects embedded in random media,” in Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, J. O. Hollinger, S. L. Jacques, eds., Proc. SPIE3914, 478–488 (2000).
[CrossRef]

Kattawar, G. W.

Kikuta, H.

T. Hamamoto, H. Toyota, H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H. P. Herzig, eds., Proc. SPIE4440, 293–300 (2001).
[CrossRef]

Lee, P. H.

J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
[CrossRef]

Lindberg, J. M.

J. L. Pezzaniti, J. M. Lindberg, “Apparatus and process for the noninvasive measurement of optically active compounds,” U.S. Patent5,788,632, August4, 1998.

Lompado, A.

M. H. Smith, A. Lompado, P. Burke, “Mueller matrix imaging polarimetry in dermatology,” in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, eds., Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Mehrubeoglu, M.

Meier, J. T.

Mourant, J. R.

Mujat, M.

M. Mujat, A. Dogariu, “Real-time Mueller matrix measurement for particulate systems,” in Laser Radar Technology and Applications, V. G. W. Kamerman, U. N. Singh, C. Werner, V. V. Molebny, eds., Proc. SPIE4035, 390–400 (2000).
[CrossRef]

M. Mujat, A. Dogariu, E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel–Arago interference laws,” J. Opt. Soc. Am. A (to be published).

Nordin, G. P.

Oka, K.

Parrent, G.

G. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960).
[CrossRef]

Pezzaniti, J. L.

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

J. L. Pezzaniti, J. M. Lindberg, “Apparatus and process for the noninvasive measurement of optically active compounds,” U.S. Patent5,788,632, August4, 1998.

Rakovic, M. J.

Rastegar, S.

Roman, P.

G. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960).
[CrossRef]

Schneider, T. G.

J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
[CrossRef]

Shen, D.

Shmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Smith, M. H.

M. H. Smith, “Interpreting Mueller matrix images of tissues,” in Laser–Tissue Interaction XII, D. Duncan, S. Jacques, P. Johnson, eds., Proc. SPIE4257, 82–89 (2001).
[CrossRef]

M. H. Smith, A. Lompado, P. Burke, “Mueller matrix imaging polarimetry in dermatology,” in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, eds., Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Thompson, H. R.

J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
[CrossRef]

Toyota, H.

T. Hamamoto, H. Toyota, H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H. P. Herzig, eds., Proc. SPIE4440, 293–300 (2001).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Sect. 5.3.

Walraven, R.

R. Walraven, “Polarization imagery,” Opt. Eng. (Bellingham) 20, 14–18 (1981).
[CrossRef]

Wang, L. V.

Wolf, E.

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

E. Wolf, “Optics in terms of observable quantities,” Nuovo Cimento 12, 884–888 (1954).
[CrossRef]

M. Mujat, A. Dogariu, E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel–Arago interference laws,” J. Opt. Soc. Am. A (to be published).

Am. J. Phys.

R. Hanau, “Interference of linearly polarized light with perpendicular polarizations,” Am. J. Phys. 31, 303–304 (1963).
[CrossRef]

E. Collett, “Mathematical formulation of the interference laws of Fresnel and Arago,” Am. J. Phys. 39, 1483–1495 (1971).
[CrossRef]

Annales de Chimie et de Physique

D. F. J. Arago, A. J. Fresnel, “On the action of rays of polarized light upon each other,” Annales de Chimie et de Physique, p. 288 (1819), republished in The Wave Theory of Light. Memoires by Huygens, Young, and Fresnel, H. Crew, ed. (American Book, New York, 1900).

J. Opt. Soc. Am. A

Nuovo Cimento

E. Wolf, “Optics in terms of observable quantities,” Nuovo Cimento 12, 884–888 (1954).
[CrossRef]

G. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960).
[CrossRef]

E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959).
[CrossRef]

Opt. Eng. (Bellingham)

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

R. Walraven, “Polarization imagery,” Opt. Eng. (Bellingham) 20, 14–18 (1981).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. E

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Shmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Other

M. Mujat, A. Dogariu, “Real-time Mueller matrix measurement for particulate systems,” in Laser Radar Technology and Applications, V. G. W. Kamerman, U. N. Singh, C. Werner, V. V. Molebny, eds., Proc. SPIE4035, 390–400 (2000).
[CrossRef]

A. R. Hill, B. D. Cameron, J. R. Chung, J. S. Baba, G. L. Cote, “Development and calibration of an automated Mueller matrix polarimeter system for skin lesion differentiation,” in Optical Tomography and Spectroscopy of Tissues IV, B. Chamce, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 449–454 (2001).
[CrossRef]

S. L. Jacques, “Video imaging of superficial biological tissue layers using polarized light,” U.S. Patent6,177,984, January23, 2001.

M. H. Smith, A. Lompado, P. Burke, “Mueller matrix imaging polarimetry in dermatology,” in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, eds., Proc. SPIE3911, 210–216 (2000).
[CrossRef]

G. W. Katawar, “Virtues of Mueller matrix detection of objects embedded in random media,” in Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, J. O. Hollinger, S. L. Jacques, eds., Proc. SPIE3914, 478–488 (2000).
[CrossRef]

M. H. Smith, “Interpreting Mueller matrix images of tissues,” in Laser–Tissue Interaction XII, D. Duncan, S. Jacques, P. Johnson, eds., Proc. SPIE4257, 82–89 (2001).
[CrossRef]

J. L. Pezzaniti, J. M. Lindberg, “Apparatus and process for the noninvasive measurement of optically active compounds,” U.S. Patent5,788,632, August4, 1998.

J. D. Barter, P. H. Lee, H. R. Thompson, T. G. Schneider, “Stokes parameter imaging of scattering surfaces,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 314–320 (1997).
[CrossRef]

J. D. Barter, “Visible Stokes polarimetric imager,” U.S. Patent6,122,404, September19, 2000.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Sect. 5.3.

T. Hamamoto, H. Toyota, H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region,” in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B. Kley, H. P. Herzig, eds., Proc. SPIE4440, 293–300 (2001).
[CrossRef]

C. Brosseau, Fundamentals of Polarized Light, A Statistical Optics Approach (Wiley, New York, 1998).

M. Mujat, A. Dogariu, E. Wolf, “A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel–Arago interference laws,” J. Opt. Soc. Am. A (to be published).

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Figures (5)

Fig. 1
Fig. 1

Modified Sagnac interferometer: PBS, polarizing beam splitter; M, mirrors; P(θ), polarizer oriented at θ; L, image forming optics for the CCD camera.

Fig. 2
Fig. 2

Mach–Zehnder interferometer: BS, nonpolarizing beam splitters; M, mirrors; Px, Py, horizontal and vertical polarizers; F, neutral density filters; R, retarder.

Fig. 3
Fig. 3

Images obtained with the Sagnac interferometer: first row, experimental images Ix and Iπ/4 and the normalized interference pattern; second row, calculated normalized Stokes vector components q, u, and v and the degree of polarization P.

Fig. 4
Fig. 4

Images obtained with standard Stokes polarimetry: first row, experimental images Ix, Iy, Iπ/4, and Ir; second row, calculated normalized Stokes vector components q, u, and v and the degree of polarization P.

Fig. 5
Fig. 5

Comparison between the results of standard Stokes polarimetry (solid curve) and of our technique (dotted curve). Plots of the total intensity Int; normalized Stokes vector components q, u, and v; the degree of polarization P; and the retardance δ corresponding to the line indicated by the arrow in Fig. 3.  

Equations (11)

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

Wmn(r1, r2, ω)=Em*(r1, ω)En(r2, ω),
E1(θ, ϕ1)=P(θ)P(0)P(0)ExEyexp(iϕ1)=Excos θ exp(iϕ1)cos θsin θ,
E2(θ, ϕ2)=P(θ)P(π/2)P(π/2)ExEyexp(iϕ2)=Eysin θ exp(iϕ2)cos θsin θ,
I(Q, θ)=Ic(Q, θ)+Iint(Q, θ),
Ic(Q, θ)=Ixcos2 θ+Iysin2 θ,
Iint(Q, θ)=2 sin θ cos θ Re[Jxyexp(iΔ)],
μxy=Jxy(JxxJyy)1/2=|μxy|exp(iδ),
Iint(Q, θ)=2 sin θ cos θ(IxIy)1/2|μxy|cos(Δ+δ),
P=1-4 det(J)[tr(J)]21/2=1-4IxIy(1-|μxy|2)(Ix+Iy)21/2.
I(π/4)=(Ix+Iy)/2+(IxIy)1/2|μxy|cos(Δ+δ).
I(π/4)=I/2[1+P cos(Δ+δ)].

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