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

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. Rakovi�?, 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 <a href="http://www.sci.ccny.cuny.edu/~minxu">http://www.sci.ccny.cuny.edu/~minxu</a>.

Appl. Opt.

• 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]
• 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]
• 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]
• 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]
• 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]

Inverse Problems

• S. R. Arridge, �??Optical tomography in medical imaging,�?? Inverse Problems 15, R41�??R93 (1999). [CrossRef]

J. Biomed. Opt.

• 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]

J. Opt. Soc. Am. A

• 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]
• A. D. Kim and J. B. Keller, �??Light propagation in biological tissue,�?? J. Opt. Soc. Am. A 20, 92�??98 (2003). [CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

• K. F. Evans and G. L. Stephens, �??A new polarized atmospheric radiative transfer model,�?? J. Quant. Spectrosc. Radiat. Transfer 46, 413�??423 (1991). [CrossRef]

J. Res. Natl. Bur. Stand.

• J. von Neumann, �??Various techniques used in connection with random digits,�?? J. Res. Natl. Bur. Stand. 5, 36�??38 (1951).

Laser speckle and related phenomena

• 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]

Opt. Exp.

• I. Berezhnyy and A. Dogariu, �??Time-resolved Mueller matrix imaging polarimetry,�?? Opt. Exp. 12(19), 4635�??4649 (2004). [CrossRef]

Opt. Lett.

• 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]

Opt. Photon. News

• S. K. Gayen and R. R. Alfano, �??Emerging optical biomedical imaging techniques,�?? Opt. Photon. News 7 (3), 17�??22 (1996).

Ph.D. thesis

• 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).

Phys. Rev.

• D. S. Saxon, �??Tensor Scattering Matrix for the Electromagnetic Field,�?? Phys. Rev. 100(6), 1771�??1775 (1955). [CrossRef]

Phys. Rev. Lett.

• 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]
• 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]

Phys. Today

• A. Yodh and B. Chance, �??Spectroscopy and imaging with diffusing light,�?? Phys. Today 48 3, 38�??40 (1995).

SIAM J. Sci. Comput.

• A. D. Kim and M. Moscoso, �??Chebyshev Spectral methods for radiative transfer,�?? SIAM J. Sci. Comput. 23, 2074�??2094 (2002). [CrossRef]

TOPS Adv. in Opt. Imag. and Phot. Migr.

• G. W. Kattawar, M. J. Rakovi�?, 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).

Other

• A. Ishimaru, Wave propagation and scattering in random media, I and II (Academic, New York, 1978).
• S. Chandrasekhar, Radiative transfer (Dover, New York, 1960).
• EMC is available at <a href="http://www.sci.ccny.cuny.edu/~minxu">http://www.sci.ccny.cuny.edu/~minxu</a>.
• H. C. van de Hulst, Light scattering by small particles (Dover, New York, 1981).
• C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 1983).
• R. Y. Rubinstein, Simulation and the Monte Carlo method (John Wiley & Sons, 1981). [CrossRef]
• W. H. Press, S. A. Teukolsky,W. T. Vetterling, and B. P. Flannery, Numerical recipes in C (Cambridge University press, 1996).
• I. Lux and L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, Boca Raton, Fla., 1991).

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