Abstract

A Monte Carlo method based on tracing the multiply scattered electric field is presented to simulate the propagation of polarized light in turbid media. Multiple scattering of light comprises a series of updates of the parallel and perpendicular components of the complex electric field with respect to the scattering plane by the amplitude scattering matrix and rotations of the local coordinate system spanned by the unit vectors in the directions of the parallel and perpendicular electric field components and the propagation direction of light. The backscattering speckle pattern and the backscattering Mueller matrix of an aqueous suspension of polystyrene spheres in a slab geometry are computed using this Electric Field Monte Carlo (EMC) method. An efficient algorithm computing the Mueller matrix in the pure backscattering direction is detailed in the paper.

© 2004 Optical Society of America

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  1. A. Ishimaru, Wave propagation and scattering in random media, I and II (Academic, New York, 1978).
  2. A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 38–40 (1995).
  3. S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 17–22 (1996).
  4. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–R93 (1999).
    [Crossref]
  5. S. Chandrasekhar, Radiative transfer (Dover, New York, 1960).
  6. K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
    [Crossref]
  7. A. D. Kim and M. Moscoso, “Chebyshev Spectral methods for radiative transfer,” SIAM J. Sci. Comput. 23, 2074–2094 (2002).
    [Crossref]
  8. A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
    [Crossref]
  9. G. W. Kattawar and G. N. Plass, “Radiance and polarization of multiple scattered light from haze and clouds,” Appl. Opt. 7, 1519–1527 (1968).
    [Crossref] [PubMed]
  10. I. Lux and L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).
  11. J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31(30), 6535- (1992).
    [Crossref]
  12. P. Bruscaglioni, G. Zaccanti, and Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32(30), 6142–6150 (1993).
    [Crossref]
  13. M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
    [Crossref]
  14. S. Bartel and A. H. Hielscher, “Monte Carlo Simulations of the Diffuse Backscattering Mueller Matrix for Highly Scattering Media,” Appl. Opt. 39(10), 1580–1588 (2000).
    [Crossref]
  15. M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
    [Crossref]
  16. H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
    [Crossref]
  17. B. Kaplan, G. Ledanois, and B. villon, “Mueller Matrix of Dense Polystyrene Latex Sphere Suspensions: Measurements and Monte Carlo Simulation,” Appl. Opt. 40(16), 2769–2777 (2001).
    [Crossref]
  18. X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
    [Crossref] [PubMed]
  19. G. W. Kattawar, M. J. Raković, and B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiments,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto and M. S. Patterson, eds.,  vol. 21 of OSA TOPS, pp. 105–110 (1998).
  20. J. C. Ramella-Roman, “Imaging skin pathologies with polarized light: empirical and theoretical studies,” Ph.D. thesis, OGI School of Science & Engineering at Oregon Health & Science University (2004).
  21. H. C. van de Hulst, Light scattering by small particles (Dover, New York, 1981).
  22. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1983).
  23. R. Y. Rubinstein, Simulation and the Monte Carlo method (John Wiley & Sons, 1981).
    [Crossref]
  24. J. von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand. 5, 36–38 (1951).
  25. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge university press, 1996).
  26. P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
    [Crossref]
  27. M. P. V. Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
    [Crossref]
  28. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56(14), 1471–1474 (1986).
    [Crossref]
  29. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser speckle and related phenomena ,J. C. Dainty, ed., pp. 9–75 (Springer-Verlag, Berlin, 1975).
    [Crossref]
  30. D. S. Saxon, “Tensor Scattering Matrix for the Electromagnetic Field,” Phys. Rev. 100(6), 1771–1775 (1955).
    [Crossref]
  31. B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
    [Crossref]
  32. I. Berezhnyy and A. Dogariu, “Time-resolved Mueller matrix imaging polarimetry,” Opt. Exp. 12(19), 4635–4649 (2004).
    [Crossref]
  33. EMC is available at http://www.sci.ccny.cuny.edu/minxu.

2004 (1)

I. Berezhnyy and A. Dogariu, “Time-resolved Mueller matrix imaging polarimetry,” Opt. Exp. 12(19), 4635–4649 (2004).
[Crossref]

2003 (1)

2002 (2)

A. D. Kim and M. Moscoso, “Chebyshev Spectral methods for radiative transfer,” SIAM J. Sci. Comput. 23, 2074–2094 (2002).
[Crossref]

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[Crossref] [PubMed]

2001 (3)

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
[Crossref]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

B. Kaplan, G. Ledanois, and B. villon, “Mueller Matrix of Dense Polystyrene Latex Sphere Suspensions: Measurements and Monte Carlo Simulation,” Appl. Opt. 40(16), 2769–2777 (2001).
[Crossref]

2000 (1)

S. Bartel and A. H. Hielscher, “Monte Carlo Simulations of the Diffuse Backscattering Mueller Matrix for Highly Scattering Media,” Appl. Opt. 39(10), 1580–1588 (2000).
[Crossref]

1999 (2)

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–R93 (1999).
[Crossref]

1998 (2)

G. W. Kattawar, M. J. Raković, and B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiments,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto and M. S. Patterson, eds.,  vol. 21 of OSA TOPS, pp. 105–110 (1998).

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

1996 (1)

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 17–22 (1996).

1995 (1)

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 38–40 (1995).

1993 (1)

P. Bruscaglioni, G. Zaccanti, and Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32(30), 6142–6150 (1993).
[Crossref]

1992 (1)

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31(30), 6535- (1992).
[Crossref]

1991 (1)

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
[Crossref]

1986 (1)

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56(14), 1471–1474 (1986).
[Crossref]

1985 (2)

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

M. P. V. Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

1968 (1)

1955 (1)

D. S. Saxon, “Tensor Scattering Matrix for the Electromagnetic Field,” Phys. Rev. 100(6), 1771–1775 (1955).
[Crossref]

1951 (1)

J. von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand. 5, 36–38 (1951).

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56(14), 1471–1474 (1986).
[Crossref]

Albada, M. P. V.

M. P. V. Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

Alfano, R. R.

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 17–22 (1996).

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–R93 (1999).
[Crossref]

Bartel, S.

S. Bartel and A. H. Hielscher, “Monte Carlo Simulations of the Diffuse Backscattering Mueller Matrix for Highly Scattering Media,” Appl. Opt. 39(10), 1580–1588 (2000).
[Crossref]

Berezhnyy, I.

I. Berezhnyy and A. Dogariu, “Time-resolved Mueller matrix imaging polarimetry,” Opt. Exp. 12(19), 4635–4649 (2004).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1983).

Bonner, R. F.

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31(30), 6535- (1992).
[Crossref]

Bruscaglioni, P.

P. Bruscaglioni, G. Zaccanti, and Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32(30), 6142–6150 (1993).
[Crossref]

Cameron, B. D.

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

G. W. Kattawar, M. J. Raković, and B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiments,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto and M. S. Patterson, eds.,  vol. 21 of OSA TOPS, pp. 105–110 (1998).

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

Chaikovskaya, L. I.

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

Chance, B.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 38–40 (1995).

Chandrasekhar, S.

S. Chandrasekhar, Radiative transfer (Dover, New York, 1960).

Cot, G. L.

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

Cote, G. L.

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

Dogariu, A.

I. Berezhnyy and A. Dogariu, “Time-resolved Mueller matrix imaging polarimetry,” Opt. Exp. 12(19), 4635–4649 (2004).
[Crossref]

Evans, K. F.

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge university press, 1996).

Gandjbakhche, A. H.

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31(30), 6535- (1992).
[Crossref]

Gayen, S. K.

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 17–22 (1996).

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser speckle and related phenomena ,J. C. Dainty, ed., pp. 9–75 (Springer-Verlag, Berlin, 1975).
[Crossref]

Hielscher, A. H.

S. Bartel and A. H. Hielscher, “Monte Carlo Simulations of the Diffuse Backscattering Mueller Matrix for Highly Scattering Media,” Appl. Opt. 39(10), 1580–1588 (2000).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1983).

Ishimaru, A.

A. Ishimaru, Wave propagation and scattering in random media, I and II (Academic, New York, 1978).

Kaplan, B.

B. Kaplan, G. Ledanois, and B. villon, “Mueller Matrix of Dense Polystyrene Latex Sphere Suspensions: Measurements and Monte Carlo Simulation,” Appl. Opt. 40(16), 2769–2777 (2001).
[Crossref]

Katsev, I. L.

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

Kattawar, G. W.

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

G. W. Kattawar, M. J. Raković, and B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiments,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto and M. S. Patterson, eds.,  vol. 21 of OSA TOPS, pp. 105–110 (1998).

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

G. W. Kattawar and G. N. Plass, “Radiance and polarization of multiple scattered light from haze and clouds,” Appl. Opt. 7, 1519–1527 (1968).
[Crossref] [PubMed]

Keller, J. B.

A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
[Crossref]

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
[Crossref]

Kim, A. D.

A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003).
[Crossref]

A. D. Kim and M. Moscoso, “Chebyshev Spectral methods for radiative transfer,” SIAM J. Sci. Comput. 23, 2074–2094 (2002).
[Crossref]

Koblinger, L.

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

Lagendijk, A.

M. P. V. Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

Ledanois, G.

B. Kaplan, G. Ledanois, and B. villon, “Mueller Matrix of Dense Polystyrene Latex Sphere Suspensions: Measurements and Monte Carlo Simulation,” Appl. Opt. 40(16), 2769–2777 (2001).
[Crossref]

Lux, I.

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

Maret, G.

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

Maynard, R.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56(14), 1471–1474 (1986).
[Crossref]

Mehrbeoglu, M.

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

Mehrbeolu, M.

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

Moscoso, M.

A. D. Kim and M. Moscoso, “Chebyshev Spectral methods for radiative transfer,” SIAM J. Sci. Comput. 23, 2074–2094 (2002).
[Crossref]

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
[Crossref]

Papanicolaou, G.

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
[Crossref]

Plass, G. N.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge university press, 1996).

Prikhach, A. S.

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

Rakovic, M. J.

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

G. W. Kattawar, M. J. Raković, and B. D. Cameron, “Laser backscattering polarization patterns from turbid media: theory and experiments,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto and M. S. Patterson, eds.,  vol. 21 of OSA TOPS, pp. 105–110 (1998).

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

Ramella-Roman, J. C.

J. C. Ramella-Roman, “Imaging skin pathologies with polarized light: empirical and theoretical studies,” Ph.D. thesis, OGI School of Science & Engineering at Oregon Health & Science University (2004).

Rastegar, S.

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
[Crossref]

Rubinstein, R. Y.

R. Y. Rubinstein, Simulation and the Monte Carlo method (John Wiley & Sons, 1981).
[Crossref]

Saxon, D. S.

D. S. Saxon, “Tensor Scattering Matrix for the Electromagnetic Field,” Phys. Rev. 100(6), 1771–1775 (1955).
[Crossref]

Schmitt, J. M.

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, “Use of polarized light to discriminate short-path photons in a multiply scattering medium,” Appl. Opt. 31(30), 6535- (1992).
[Crossref]

Stephens, G. L.

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge university press, 1996).

Tynes, H. H.

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light scattering by small particles (Dover, New York, 1981).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge university press, 1996).

villon, B.

B. Kaplan, G. Ledanois, and B. villon, “Mueller Matrix of Dense Polystyrene Latex Sphere Suspensions: Measurements and Monte Carlo Simulation,” Appl. Opt. 40(16), 2769–2777 (2001).
[Crossref]

von Neumann, J.

J. von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand. 5, 36–38 (1951).

Wang, L. V.

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[Crossref] [PubMed]

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H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations,” Appl. Opt. 40(3), 400–412 (2001).
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P. Bruscaglioni, G. Zaccanti, and Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32(30), 6142–6150 (1993).
[Crossref]

M. J. Rakovic, G. W. Kattawar, M. Mehrbeolu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cote, “Light Backscattering Polarization Patterns from Turbid Media: Theory and Experiment,” Appl. Opt. 38(15), 3399–3408 (1999).
[Crossref]

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B. D. Cameron, M. J. Rakovic, M. Mehrbeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cot, “Measurement and calculationof the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998).
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[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

A photon moving along s is scattered to s′ with a scattering angle θ and an azimuthal angle ϕ inside a local coordinate system spanned by orthonormal bases (m,n, s). e 1,2 and e′ 1,2 are the unit vectors parallel and perpendicular to the current scattering plane spanned by s and s′ prior to and after scattering. The local coordinate system (m,n, s) is rotated to (m′,n′, s′) after scattering.

Fig. 2.
Fig. 2.

(a) Speckle pattern formed by the angular-resolved backscattering light. (b) Normalized speckle Ix /〈Ix 〉 follows a negative exponential distribution.

Fig. 3.
Fig. 3.

Backscattering Mueller matrix for the slab. All 4×4 matrix element are displayed as a two-dimensional image of the surface, 20ls ×20ls in size, with the laser being incident in the center. The displayed Mueller matrix has been normalized by the maximum light intensity of the (1,1) element. The parameters of the slab is given in the text.

Fig. 4.
Fig. 4.

Reduced backscattering Mueller matrix for the slab. All 4×4 elements of the reduced Mueller matrix is displayed as a one-dimensional curve versus the distance ρ/ls from the origin. The reduced backscattering Mueller matrix is 2×2 block diagonal.

Equations (17)

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s = m sin θ cos ϕ + n sin θ sin ϕ + s cos θ
e 1 = m cos ϕ + n sin ϕ
e 2 = m sin ϕ + n cos ϕ
e 1 = μ m cos ϕ + μ n sin ϕ sin θ s ,
( m ' n ' s ' ) = A ( m n s )
A = ( cos θ cos ϕ cos θ sin ϕ sin θ sin ϕ cos ϕ 0 sin θ cos ϕ sin θ sin ϕ cos θ ) ,
( E 1 E 2 ) = B ( E 1 E 2 )
B = [ F ( θ , ϕ ) ] 1 2 ( S 2 cos ϕ S 2 sin ϕ S 1 sin ϕ S 1 cos ϕ ) .
F ( θ , ϕ ) = ( S 2 2 cos 2 ϕ + S 1 2 sin 2 ϕ ) E 1 2 + ( S 2 2 sin 2 ϕ + S 1 2 cos 2 ϕ ) E 2 2
+ 2 ( S 2 2 S 1 2 ) cos ϕ sin ϕ [ E 1 ( E 2 ) * ]
p ( θ ) = 0 2 π p ( θ , ϕ ) d ϕ = S 2 2 + S 1 2 Q sca x 2
M bs ( ρ , ϕ ) = R ( ϕ ) M bs ( ρ , ϕ = 0 ) R ( ϕ )
R ( ϕ ) = ( 1 0 0 0 0 cos 2 ϕ sin 2 ϕ 0 0 sin 2 ϕ cos 2 ϕ 0 0 0 0 1 ) .
I o = M 0 bs ( ρ ) I i
I i ( I i ) T = R ( ϕ ) I i I i T R ( ϕ ) = R ( ϕ ) ( 1 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 4 ) R ( ϕ ) .
D = [ I i ( I i ) T ] 1 = ( 1 0 0 0 0 3 cos 4 ϕ sin 4 ϕ 0 0 sin 4 ϕ 3 + cos 4 ϕ 0 0 0 0 4 ) ,
M 0 bs ( ρ ) = I ' o ( I ' i ) T D

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