Abstract

Polarized radiative transfer in a multilayer system is an important problem and has wide applications in various fields. In this work, a Monte Carlo (MC) model is developed to simulate polarized radiative transfer in a semitransparent arbitrary multilayer medium with different refractive indices in each layer. Two kinds of polarization mechanisms are considered: scattering by particles and reflection and refraction at the Fresnel surfaces or interfaces. The MC method has an obvious superiority in that complex mathematical derivations can be avoided in solving the polarization by Fresnel reflection and refraction in an arbitrary multilayer system. We define the vector radiative transfer matrix (VRTM), which describes the polarization characteristics of radiative transfer, and obtain four elements of Stokes vector using the VRTM. The results for the two-layer model by MC method are compared against those for coupled atmosphere–ocean model by the discrete–ordinate method available in the literature, which validates the correctness of the MC multilayer model of polarized radiative transfer. Finally, the results for three-layer, five-layer, and ten-layer models are presented in graphical form. Results show that in the multilayer system, total reflections occurring at the surfaces/interfaces have significant effects on the polarized radiative transfer, which causes abrupt changes or fluctuations like waves in the curves of the Stokes vector.

© 2014 Optical Society of America

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  1. L. Tsang and J. A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,” Radio Sci. 13, 763–773 (1978).
    [CrossRef]
  2. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).
  3. L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).
  4. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (Taylor and Francis, 2010), Chap. 9, pp. 253–282.
  5. M. P. Mengüç and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. 36, 1569–1593 (1998).
    [CrossRef]
  6. 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]
  7. R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 41, 117–145 (1989).
    [CrossRef]
  8. K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
    [CrossRef]
  9. C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 64, 227–254 (2000).
    [CrossRef]
  10. J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
    [CrossRef]
  11. F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
    [CrossRef]
  12. H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
    [CrossRef]
  13. X. D. 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]
  14. M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express 12, 6530–6539 (2004).
    [CrossRef]
  15. R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
    [CrossRef]
  16. C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
    [CrossRef]
  17. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420–4438 (2005).
    [CrossRef]
  18. J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
    [CrossRef]
  19. C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
    [CrossRef]
  20. A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
    [CrossRef]
  21. G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
    [CrossRef]
  22. G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
  23. P. W. Zhai, Y. X. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
    [CrossRef]
  24. P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
    [CrossRef]
  25. P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
    [CrossRef]
  26. X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
    [CrossRef]
  27. X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
    [CrossRef]
  28. Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
    [CrossRef]
  29. E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
    [CrossRef]
  30. R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
    [CrossRef]
  31. P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
    [CrossRef]
  32. R. D. M. Garcia, “Response to ‘Comment on transmission matrix for a dielectric interface’,” J. Quant. Spectrosc. Radiat. Transfer 113, 2251–2254 (2012).
    [CrossRef]
  33. R. D. M. Garcia, “Radiative transfer with polarization in a multi-layer medium subject to Fresnel boundary and interface conditions,” J. Quant. Spectrosc. Radiat. Transfer 115, 28–45 (2013).
    [CrossRef]
  34. S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).
  35. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  36. M. I. Mishchenko, Scattering, Absorption, and Emission of Light by Small Particles (NASA, 2002).
  37. A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 1333 (1980).
    [CrossRef]
  38. 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, 400–412 (2001).
    [CrossRef]
  39. R. M. Green, Spherical Astronomy (Cambridge University, 1985).
  40. B. A. Whitney, “Monte Carlo radiative transfer,” arXiv:1104.4990 (2011).
  41. R. Siegel and C. M. Spuckler, “Refractive index effects on radiation in an absorbing, emitting, and scattering laminated layer,” J. Heat Transfer 115, 194–200 (1993).
    [CrossRef]
  42. K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Met. Geophys. 37, 1–13 (1986).
    [CrossRef]

2013 (3)

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
[CrossRef]

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

R. D. M. Garcia, “Radiative transfer with polarization in a multi-layer medium subject to Fresnel boundary and interface conditions,” J. Quant. Spectrosc. Radiat. Transfer 115, 28–45 (2013).
[CrossRef]

2012 (3)

R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
[CrossRef]

P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[CrossRef]

R. D. M. Garcia, “Response to ‘Comment on transmission matrix for a dielectric interface’,” J. Quant. Spectrosc. Radiat. Transfer 113, 2251–2254 (2012).
[CrossRef]

2010 (6)

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
[CrossRef]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

2009 (1)

2007 (3)

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
[CrossRef]

2005 (2)

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
[CrossRef]

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420–4438 (2005).
[CrossRef]

2004 (2)

M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express 12, 6530–6539 (2004).
[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
[CrossRef]

2002 (2)

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[CrossRef]

X. D. 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]

2001 (1)

2000 (1)

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 64, 227–254 (2000).
[CrossRef]

1998 (1)

M. P. Mengüç and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. 36, 1569–1593 (1998).
[CrossRef]

1993 (1)

R. Siegel and C. M. Spuckler, “Refractive index effects on radiation in an absorbing, emitting, and scattering laminated layer,” J. Heat Transfer 115, 194–200 (1993).
[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]

1989 (2)

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 41, 117–145 (1989).
[CrossRef]

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

1986 (1)

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Met. Geophys. 37, 1–13 (1986).
[CrossRef]

1980 (1)

1978 (1)

L. Tsang and J. A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,” Radio Sci. 13, 763–773 (1978).
[CrossRef]

1973 (1)

G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

1968 (1)

Adams, C. N.

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Bai, Y.

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Budak, V. P.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Cdhary, J.

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

Chaikovskaya, L. I.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).

Cornet, C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
[CrossRef]

Crofcheck, C.

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
[CrossRef]

Davis, A. B.

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
[CrossRef]

Davis, C.

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
[CrossRef]

Deuzé, J. L.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Duan, M. Z.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Emde, C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
[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]

Garcia, R. D. M.

R. D. M. Garcia, “Radiative transfer with polarization in a multi-layer medium subject to Fresnel boundary and interface conditions,” J. Quant. Spectrosc. Radiat. Transfer 115, 28–45 (2013).
[CrossRef]

R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
[CrossRef]

R. D. M. Garcia, “Response to ‘Comment on transmission matrix for a dielectric interface’,” J. Quant. Spectrosc. Radiat. Transfer 113, 2251–2254 (2012).
[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 41, 117–145 (1989).
[CrossRef]

Ghosh, N.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (Taylor and Francis, 2010), Chap. 9, pp. 253–282.

Gong, F.

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Green, R. M.

R. M. Green, Spherical Astronomy (Cambridge University, 1985).

Guinn, J. A.

G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

Harwood, R.

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
[CrossRef]

He, X. Q.

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Herman, M.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Higurashi, A.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

Hu, Y. X.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
[CrossRef]

Ishimoto, H.

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[CrossRef]

Jacques, S. L.

Josset, D. B.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

Katsev, I. L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[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, 400–412 (2001).
[CrossRef]

Kattawar, G. W.

P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[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, 400–412 (2001).
[CrossRef]

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[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]

Klyukov, D. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Kokhanovsky, A. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Kong, J. A.

L. Tsang and J. A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,” Radio Sci. 13, 763–773 (1978).
[CrossRef]

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Korkin, S. V.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Labonnote, L. C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
[CrossRef]

Lafrance, B.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Lenoble, J.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Lin, B.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

Lotsberg, J. K.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

Lucker, P. L.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
[CrossRef]

Manickavasagam, S.

M. P. Mengüç and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. 36, 1569–1593 (1998).
[CrossRef]

Masuda, K.

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[CrossRef]

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Met. Geophys. 37, 1–13 (1986).
[CrossRef]

Mayer, B.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Mengüç, M. P.

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
[CrossRef]

M. P. Mengüç and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. 36, 1569–1593 (1998).
[CrossRef]

Min, Q. L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, Scattering, Absorption, and Emission of Light by Small Particles (NASA, 2002).

Nakajima, T.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Ota, Y.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

Pan, D. L.

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Plass, G. N.

G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[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]

Prahl, S. A.

Prikhach, A. S.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[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, 400–412 (2001).
[CrossRef]

Ramella-Roman, J. C.

Rozanov, V. V.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Santer, R.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Siegel, R.

R. Siegel and C. M. Spuckler, “Refractive index effects on radiation in an absorbing, emitting, and scattering laminated layer,” J. Heat Transfer 115, 194–200 (1993).
[CrossRef]

Siewert, C. E.

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 64, 227–254 (2000).
[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 41, 117–145 (1989).
[CrossRef]

Sommersten, E. R.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

Spuckler, C. M.

R. Siegel and C. M. Spuckler, “Refractive index effects on radiation in an absorbing, emitting, and scattering laminated layer,” J. Heat Transfer 115, 194–200 (1993).
[CrossRef]

Stamnes, J. J.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

Stamnes, K.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[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]

Swamy, J. N.

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
[CrossRef]

Szczap, F.

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
[CrossRef]

Takashima, T.

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Met. Geophys. 37, 1–13 (1986).
[CrossRef]

Tanré, D.

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

Trepte, C. R.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
[CrossRef]

Tsang, L.

L. Tsang and J. A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,” Radio Sci. 13, 763–773 (1978).
[CrossRef]

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Tynes, H. H.

Vaillon, R.

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (Taylor and Francis, 2010), Chap. 9, pp. 253–282.

Wang, L. V.

X. D. 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]

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Wang, X. D.

X. D. 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]

West, R. A.

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
[CrossRef]

Whitney, B. A.

B. A. Whitney, “Monte Carlo radiative transfer,” arXiv:1104.4990 (2011).

Wong, B. T.

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
[CrossRef]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (Taylor and Francis, 2010), Chap. 9, pp. 253–282.

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Xu, F.

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
[CrossRef]

Xu, M.

Yokota, T.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

Young, A. T.

Zege, E. P.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[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, 400–412 (2001).
[CrossRef]

Zhai, P. W.

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[CrossRef]

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17, 2057–2079 (2009).
[CrossRef]

Zhu, Q.

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

Zhu, Q. K.

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Geosci. Remote Sens. (1)

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed Monte Carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Remote Sens. 43, 1096–1101 (2005).
[CrossRef]

Int. J. Eng. Sci. (1)

M. P. Mengüç and S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. 36, 1569–1593 (1998).
[CrossRef]

J. Biomed. Opt. (1)

X. D. 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]

J. Heat Transfer (1)

R. Siegel and C. M. Spuckler, “Refractive index effects on radiation in an absorbing, emitting, and scattering laminated layer,” J. Heat Transfer 115, 194–200 (1993).
[CrossRef]

J. Phys. Oceanogr. (1)

G. W. Kattawar, G. N. Plass, and J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (19)

P. W. Zhai, Y. X. Hu, J. Cdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1025–1040 (2010).
[CrossRef]

P. W. Zhai, Y. X. Hu, D. B. Josset, C. R. Trepte, P. L. Lucker, and B. Lin, “Advanced angular interpolation in the vector radiative transfer for coupled atmosphere and ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 115, 19–27 (2013).
[CrossRef]

X. Q. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean-atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transfer 111, 1426–1448 (2010).
[CrossRef]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 111, 878–894 (2010).
[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
[CrossRef]

P. W. Zhai, G. W. Kattawar, and Y. X. Hu, “Comment on transmission matrix for dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[CrossRef]

R. D. M. Garcia, “Response to ‘Comment on transmission matrix for a dielectric interface’,” J. Quant. Spectrosc. Radiat. Transfer 113, 2251–2254 (2012).
[CrossRef]

R. D. M. Garcia, “Radiative transfer with polarization in a multi-layer medium subject to Fresnel boundary and interface conditions,” J. Quant. Spectrosc. Radiat. Transfer 115, 28–45 (2013).
[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transfer 84, 383–394 (2004).
[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transfer 104, 277–287 (2007).
[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transfer 111, 174–186 (2010).
[CrossRef]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C. Labonnote, B. Mayer, Q. L. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 111, 1931–1946 (2010).
[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 41, 117–145 (1989).
[CrossRef]

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

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transfer 64, 227–254 (2000).
[CrossRef]

J. Lenoble, M. Herman, J. L. Deuzé, B. Lafrance, R. Santer, and D. Tanré, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transfer 107, 479–507 (2007).
[CrossRef]

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 117, 59–70 (2013).
[CrossRef]

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[CrossRef]

Limnol. Oceanogr. (1)

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Opt. Express (3)

Pap. Met. Geophys. (1)

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Met. Geophys. 37, 1–13 (1986).
[CrossRef]

Radio Sci. (1)

L. Tsang and J. A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,” Radio Sci. 13, 763–773 (1978).
[CrossRef]

Sci. China Ser. D (1)

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method,” Sci. China Ser. D 50, 442–452 (2007).
[CrossRef]

Other (8)

R. M. Green, Spherical Astronomy (Cambridge University, 1985).

B. A. Whitney, “Monte Carlo radiative transfer,” arXiv:1104.4990 (2011).

S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

M. I. Mishchenko, Scattering, Absorption, and Emission of Light by Small Particles (NASA, 2002).

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (Taylor and Francis, 2010), Chap. 9, pp. 253–282.

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Figures (13)

Fig. 1.
Fig. 1.

Geometry of the multilayer problem.

Fig. 2.
Fig. 2.

Geometry of scattering plane and meridian planes. The photon’s direction of propagation before and after scattering is (θ1,φ1) and (θ2,φ2), respectively.

Fig. 3.
Fig. 3.

Stokes vector elements just below the atmosphere–water interface for a collimated and polarized incident beam.

Fig. 4.
Fig. 4.

Stokes vector elements at the top and bottom surfaces of layer 1 for the three-layer model.

Fig. 5.
Fig. 5.

Stokes vector elements at the top and bottom surfaces of layer 2 for the three-layer model.

Fig. 6.
Fig. 6.

Stokes vector elements at the top and bottom surfaces of layer 3 for the three-layer model.

Fig. 7.
Fig. 7.

Stokes vector elements at the top and bottom surfaces of layer 1 for the three-layer model.

Fig. 8.
Fig. 8.

Stokes vector elements at the top and bottom surfaces of layer 2 for the three-layer model.

Fig. 9.
Fig. 9.

Stokes vector elements at the top and bottom surfaces of layer 3 for the three-layer model.

Fig. 10.
Fig. 10.

Stokes vector elements at the bottom interface for the five-layer model.

Fig. 11.
Fig. 11.

Stokes vector elements at the top interface for the five-layer model.

Fig. 12.
Fig. 12.

Stokes vector elements at the bottom interface for the ten-layer model.

Fig. 13.
Fig. 13.

Stokes vector elements at the top interface for the ten-layer model.

Equations (29)

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S=(IQUV)=1η(ElEl*+ErEr*ElEl*ErEr*ElEr*+ErEl*i(ElEr*ErEl*)),
L=ln(1RL)κ,
Ss=L(πi2)M(Θ)L(i1)Si,
M(Θ)=(M1M200M2M10000M3M400M4M3),
M(Θ)=3Δ4(cos2Θ+1cos2Θ100cos2Θ1cos2Θ+100002cosΘ00002ΔcosΘ)+(1Δ)(1000000000000000),
M(Θ)=(M1M200M2M30000M40000M5).
L(ϕ)=(10000cos2ϕsin2ϕ00sin2ϕcos2ϕ00001).
Ss=M(Θ)L(i1)Si.
Is=IiM1(Θ)+QiM2(Θ)cos2i1UiM2(Θ)sin2i1,
Is=IiM1(Θ)+Qi2+Ui2M2(Θ)cos(2i1+ϕ),
Is,Θ,max=IiM1(Θ)+Qi2+Ui2|M2(Θ)|,
Is,max=max{IiM1(Θ)+Qi2+Ui2|M2(Θ)|},
Θ[0,π],i1[0,2π).
Sref=RSi,
Srefr=TSi,
R=(ρ000000000000000),T=(1ρ000000000000000),
ρ(n)F(n)=(3n+1)(n1)6(n+1)2+n2(n21)2(n2+1)3ln(n1n+1)2n3(n2+2n1)(n2+1)(n41)+8n4(n4+1)(n2+1)(n41)2ln(n)+0.5,
ρ(n)=11n2[1F(n)].
θr=arccos(1Rθ),φr=2πRφ,
R(θi)=12(rl2+rr2rl2rr200rl2rr2rl2+rr200002Re{rrrl*}2Im{rlrr*}002Im{rrrl*}2Re{rrrl*}),
rr=nicos(θi)nt2ni2sin2(θi)nicos(θi)+nt2ni2sin2(θi),rl=nt2cos(θi)nint2ni2sin2(θi)nt2cos(θi)+nint2ni2sin2(θi),
T(θi)=cos(θt)2cos(θi)(ntni)3(tl2+tr2tl2tr200tl2tr2tl2+tr200002Re{trtl*}2Im{tltr*}002Im{trtl*}2Re{trtl*}),
tr=2nicos(θi)nicos(θi)+nt2ni2sin2(θi),tl=2nintcos(θi)nt2cos(θi)+nint2ni2sin2(θi).
θr=θi,ntsinθt=nisinθi,φr=φt=φi.
ρ=rl2+rr22.
Di,θ,φ=p=1NtSpN,
Si,θ,φ=I0|cosθ0||cosθ|ΔΩ·Di,θ,φ,
Sdir=S0δ(cosθcosθ0*)δ(φφ0*)exp(τ/cosθ),
Sdif=SSdir.

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