Abstract

We have developed a Monte Carlo algorithm that computes all two-dimensional elements of the diffuse backscattering Mueller matrix for highly scattering media. Using the Stokes–Mueller formalism and scattering amplitudes calculated with Mie theory, we are able to consider polarization-dependent photon propagation in highly scattering media, including linearly and circularly polarized light. The numerically determined matrix elements are compared with experimental data for different particle sizes and show good agreement in both azimuthal and radial direction.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Schmitt, A. H. Gandjbakhche, R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31, 6535–6546 (1992).
    [CrossRef] [PubMed]
  2. O. Emile, F. Bretenaker, A. Le Floch, “Rotating polarization imaging in turbid media,” Opt. Lett. 21, 1706–1708 (1996).
    [CrossRef] [PubMed]
  3. S. G. Demos, R. R. Alfano, “Temporal gating in highly scattering media by the degree of optical polarization,” Opt. Lett. 21, 161–163 (1996).
    [CrossRef] [PubMed]
  4. R. R. Anderson, “Polarized-light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
    [CrossRef] [PubMed]
  5. S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.
  6. S. G. Demos, R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
    [CrossRef] [PubMed]
  7. S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).
  8. A. H. Hielscher, J. R. Mourant, I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. 36, 125–135 (1997).
    [CrossRef] [PubMed]
  9. G. M. Kattawar, M. J. Rakovic, B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiment,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 105–110.
  10. C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
  11. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).
  12. R. M. A. Azzam, “Mueller-matrix ellipsometry: a review,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 396–399 (1997).
  13. W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
    [CrossRef]
  14. A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices for highly scattering media,” Opt. Exp.1, 441–454 (1997); http://epubs.osa.org/oearchive/pdf/2826.pdf .
  15. N. V. Voshchinnikov, V. V. Karjukin, “Multiple scattering of polarized radiation in circumstellar dust shells,” Astron. Astrophys. 288, 883–896 (1994).
  16. H. T. Chuah, H. S. Tan, “A Monte Carlo backscatter model for radar backscatter from a half-space random medium,” IEEE Trans. Geosci. Remote Sens. 27, 86–93 (1998).
    [CrossRef]
  17. M. Dogariu, T. Asakaru, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
    [CrossRef]
  18. M. J. Rakovic, G. W. Kattawar, M. Mehrübeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiments,” Appl. Opt. 38, 3399–3408 (1999).
    [CrossRef]
  19. L. H. Wang, S. L. Jacques, “Optimized radial and angular positions in Monte Carlo modeling,” Med. Phy. 21, 1081–1083 (1994).
    [CrossRef]
  20. L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef] [PubMed]
  21. L. H. Wang, S. L. Jacques, “Monte Carlo modeling of light transport,” in Optical-Thermal Responses of Laser Irradiated Tissue, A. J. Welch, M. van Gemert (Plenum, New York, 1995), pp. 73–100; (source code available at http://omlc.ogi.edu/software/mc/index.html ).
  22. A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
    [CrossRef] [PubMed]
  23. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier North-Holland, New York, 1977).
  24. D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
    [CrossRef]
  25. C. F. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
    [CrossRef]
  26. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  27. I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

1999 (1)

1998 (1)

H. T. Chuah, H. S. Tan, “A Monte Carlo backscatter model for radar backscatter from a half-space random medium,” IEEE Trans. Geosci. Remote Sens. 27, 86–93 (1998).
[CrossRef]

1997 (2)

1996 (2)

1995 (2)

L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

1994 (3)

D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
[CrossRef]

N. V. Voshchinnikov, V. V. Karjukin, “Multiple scattering of polarized radiation in circumstellar dust shells,” Astron. Astrophys. 288, 883–896 (1994).

L. H. Wang, S. L. Jacques, “Optimized radial and angular positions in Monte Carlo modeling,” Med. Phy. 21, 1081–1083 (1994).
[CrossRef]

1993 (1)

M. Dogariu, T. Asakaru, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

1992 (1)

1991 (1)

R. R. Anderson, “Polarized-light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
[CrossRef] [PubMed]

1985 (1)

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Alfano, R. R.

Anderson, D. G. M.

Anderson, R. R.

R. R. Anderson, “Polarized-light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
[CrossRef] [PubMed]

Asakaru, T.

M. Dogariu, T. Asakaru, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Mueller-matrix ellipsometry: a review,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 396–399 (1997).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier North-Holland, New York, 1977).

Bailey, W. M.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Barakat, R.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier North-Holland, New York, 1977).

Bickel, W. S.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bigio, I. J.

Bohren, C. F.

C. F. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

Bonner, R. F.

Bretenaker, F.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

Cameron, B. D.

M. J. Rakovic, G. W. Kattawar, M. Mehrübeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiments,” Appl. Opt. 38, 3399–3408 (1999).
[CrossRef]

G. M. Kattawar, M. J. Rakovic, B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiment,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 105–110.

Chuah, H. T.

H. T. Chuah, H. S. Tan, “A Monte Carlo backscatter model for radar backscatter from a half-space random medium,” IEEE Trans. Geosci. Remote Sens. 27, 86–93 (1998).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).

Cote, G. L.

Demos, S. G.

Dogariu, M.

M. Dogariu, T. Asakaru, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Emile, O.

Gandjbakhche, A. H.

Gutsche, A.

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

Hielscher, A. H.

A. H. Hielscher, J. R. Mourant, I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. 36, 125–135 (1997).
[CrossRef] [PubMed]

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Huffman, D.

C. F. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

Jacques, S. L.

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques, “Optimized radial and angular positions in Monte Carlo modeling,” Med. Phy. 21, 1081–1083 (1994).
[CrossRef]

L. H. Wang, S. L. Jacques, “Monte Carlo modeling of light transport,” in Optical-Thermal Responses of Laser Irradiated Tissue, A. J. Welch, M. van Gemert (Plenum, New York, 1995), pp. 73–100; (source code available at http://omlc.ogi.edu/software/mc/index.html ).

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Karjukin, V. V.

N. V. Voshchinnikov, V. V. Karjukin, “Multiple scattering of polarized radiation in circumstellar dust shells,” Astron. Astrophys. 288, 883–896 (1994).

Kattawar, G. M.

G. M. Kattawar, M. J. Rakovic, B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiment,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 105–110.

Kattawar, G. W.

Koblinger, L.

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

Le Floch, A.

Lux, I.

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

Mehrübeoglu, M.

Mourant, J. R.

Ostermeyer, M.

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Rakovic, M. J.

M. J. Rakovic, G. W. Kattawar, M. Mehrübeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Cote, “Light backscattering polarization patterns from turbid media: theory and experiments,” Appl. Opt. 38, 3399–3408 (1999).
[CrossRef]

G. M. Kattawar, M. J. Rakovic, B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiment,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 105–110.

Rastegar, S.

Schmitt, J. M.

Schwartz, J.

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

Stephens, D. V.

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Tan, H. S.

H. T. Chuah, H. S. Tan, “A Monte Carlo backscatter model for radar backscatter from a half-space random medium,” IEEE Trans. Geosci. Remote Sens. 27, 86–93 (1998).
[CrossRef]

Tittel, F. K.

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

van de Hulst, H. C.

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

Voshchinnikov, N. V.

N. V. Voshchinnikov, V. V. Karjukin, “Multiple scattering of polarized radiation in circumstellar dust shells,” Astron. Astrophys. 288, 883–896 (1994).

Wang, L.

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

Wang, L. H.

L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques, “Optimized radial and angular positions in Monte Carlo modeling,” Med. Phy. 21, 1081–1083 (1994).
[CrossRef]

L. H. Wang, S. L. Jacques, “Monte Carlo modeling of light transport,” in Optical-Thermal Responses of Laser Irradiated Tissue, A. J. Welch, M. van Gemert (Plenum, New York, 1995), pp. 73–100; (source code available at http://omlc.ogi.edu/software/mc/index.html ).

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

Wang, L. V.

Zheng, L.

L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Am. J. Phys. (1)

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt. (4)

Arch. Dermatol. (1)

R. R. Anderson, “Polarized-light examination and photography of the skin,” Arch. Dermatol. 127, 1000–1005 (1991).
[CrossRef] [PubMed]

Astron. Astrophys. (1)

N. V. Voshchinnikov, V. V. Karjukin, “Multiple scattering of polarized radiation in circumstellar dust shells,” Astron. Astrophys. 288, 883–896 (1994).

Comput. Methods Programs Biomed. (1)

L. H. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (1)

H. T. Chuah, H. S. Tan, “A Monte Carlo backscatter model for radar backscatter from a half-space random medium,” IEEE Trans. Geosci. Remote Sens. 27, 86–93 (1998).
[CrossRef]

J. Opt. (Paris) (1)

M. Dogariu, T. Asakaru, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

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

Med. Phy. (1)

L. H. Wang, S. L. Jacques, “Optimized radial and angular positions in Monte Carlo modeling,” Med. Phy. 21, 1081–1083 (1994).
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (1)

A. H. Hielscher, L. Wang, F. K. Tittel, S. L. Jacques, “Influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Other (12)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier North-Holland, New York, 1977).

S. L. Jacques, L. H. Wang, D. V. Stephens, M. Ostermeyer, “Polarized light transmission through skin using video reflectometry: toward optical tomography of superficial tissue layers,” in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VI, R. R. Anderson, ed., Proc. SPIE2671, 199–220 (1996).

C. F. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
[CrossRef]

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

I. Lux, L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

L. H. Wang, S. L. Jacques, “Monte Carlo modeling of light transport,” in Optical-Thermal Responses of Laser Irradiated Tissue, A. J. Welch, M. van Gemert (Plenum, New York, 1995), pp. 73–100; (source code available at http://omlc.ogi.edu/software/mc/index.html ).

S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in-vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. ISII of SPIE Institute Series (SPIE, Bellingham, Wash., 1992), pp. 211–226.

A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, I. J. Bigio, “Diffuse backscattering Mueller matrices for highly scattering media,” Opt. Exp.1, 441–454 (1997); http://epubs.osa.org/oearchive/pdf/2826.pdf .

G. M. Kattawar, M. J. Rakovic, B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiment,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 105–110.

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).

R. M. A. Azzam, “Mueller-matrix ellipsometry: a review,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 396–399 (1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Transformation of incident Stokes vector S into scattering plane by R(ϕ) and subsequent scattering by the single-scattering Mueller matrix M s (θ). Shown are the electric field components, E 1 and E r , from which the four-Stokes parameters are derived [Eq. (1)].

Fig. 2
Fig. 2

Local coordinate systems of the photon prior to and after scattering. The photon is incident from below; the scattering plane is denoted Σn+1.

Fig. 3
Fig. 3

(a) Simulated backscattering Mueller matrix for the suspension of 204-nm particles. (b) Experimental backscattering Mueller matrix for suspension of 204-nm particles. Each image displays a 4 cm × 4 cm area of the surface.

Fig. 4
Fig. 4

(a) Simulated backscattering Mueller matrix for suspension of 2040-nm particles. Each image displays a 4 × 4 cm area of the surface. (b) Experimental backscattering Mueller matrix for suspension of 2040-nm particles. Each image displays a 4 cm × 4 cm area of the surface.

Fig. 5
Fig. 5

Comparison of Monte Carlo simulations and experimental results. Shown are values of the m 12 element on a ring with a 2-cm diameter centered on a light-incident point.

Fig. 6
Fig. 6

Comparison of Monte Carlo simulations and experimental results. Shown are values of the m 22 element on a ring with a 2-cm diameter centered on a light-incident point.

Fig. 7
Fig. 7

Nonzero elements of the single-scattering Mueller matrix M204 for a 204-nm-diameter polystyrene sphere at a wavelength of λ = 543 nm. The log of each matrix element is given as a function of the scattering angle θ.

Fig. 8
Fig. 8

Nonzero elements of the single-scattering Mueller matrix M2040 for a 2040-nm-diameter polystyrene sphere at a wavelength of λ = 543 nm.

Equations (24)

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

S=S0S1S2S3=|El|2+|Er|2|El|2-|Er|2El*Er+ElEr*iEl*Er-ElEr*,
S02S12+S22+S32.
Φ=S12+S22+S32/S0.
S=MnM2·M1·S1.
Srl=Rϕ·Srl,
Rϕ=10000cos2ϕsin2ϕ00-sin2ϕcos2ϕ00001.
Srl=Msθ·Srl=MsθRϕ·Srl.
er=er=D3ϕer,
er=cosϕ-sinϕ0sinϕcosϕ0001100=cosϕsinϕ0;
el=-cosθsinϕcosθcosϕsinθ,
e3=sinθsinϕ-sinθcosϕcosθ,
ax,y,z=er·ar+el·al+e3·a3.
Msθ=m11m1200m12m110000m33m3400-m34m33.
wwρθ, ϕ,
ρθ, ϕ  Iθ, ϕ=S0θ, ϕ=m11θS0+m12θS1 cos2ϕ+S2 sin2ϕ+m12θS1 cos2ϕ+S2 sin2ϕ+m13θS2 cos2ϕ-S1 sin2ϕ+m14θS3,
S=M·S,
S11, 0, 0, 0T, S21, 1, 0, 0T, S31, 0, 1, 0T, S41, 0, 0, 1T,
mˆi2=Si2
mˆ11, mˆ21, mˆ31, mˆ41T=S1=M·S1m11, m21, m31, m41T,
mˆ12, mˆ22, mˆ32, mˆ42T=S2=M·S2m11+m12, m21+m22, m31+m32, m41+m42T,
mˆ13, mˆ23, mˆ33, mˆ43T=S3=M·S3m11+m13, m21+m23, m31+m33, m41+m43T,
mˆ14, mˆ24, mˆ34, mˆ44T=S4=M·S4m11+m14, m21+m24, m31+m34, m41+m44T.
Sn=MθnRϕn Mθ2Rϕ2·Mθ1Rϕ1·S0,
Smeann=iSin=iMθn,iRϕn,i Mθ2,iRϕ2,i·Mθ1,iRϕ1,i·S0,

Metrics