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Applied Optics

Applied Optics


  • Vol. 41, Iss. 33 — Nov. 20, 2002
  • pp: 7114–7134

Vector Radiative Transfer Equation for Arbitrarily Shaped and Arbitrarily Oriented Particles: a Microphysical Derivation from Statistical Electromagnetics

Michael I. Mishchenko  »View Author Affiliations

Applied Optics, Vol. 41, Issue 33, pp. 7114-7134 (2002)

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The concepts of statistical electromagnetics are used to derive the general radiative transfer equation (RTE) that describes multiple scattering of polarized light by sparse discrete random media consisting of arbitrarily shaped and arbitrarily oriented particles. The derivation starts with the volume integral and Lippmann-Schwinger equations for the electric field scattered by a fixed N-particle system and proceeds to the vector form of the Foldy-Lax equations and their approximate far-field version. I then assume that particle positions are completely random and derive the vector RTE by applying the Twersky approximation to the coherent electric field and the Twersky and ladder approximations to the coherency dyad of the diffuse field in the limit N → ∞. The concluding section discusses the physical meaning of the quantities that enter the general vector RTE and the assumptions made in its derivation.

© 2002 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(260.2110) Physical optics : Electromagnetic optics
(260.5430) Physical optics : Polarization
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

Michael I. Mishchenko, "Vector Radiative Transfer Equation for Arbitrarily Shaped and Arbitrarily Oriented Particles: a Microphysical Derivation from Statistical Electromagnetics," Appl. Opt. 41, 7114-7134 (2002)

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  1. A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).
  2. V. Kourganoff, Basic Methods in Transfer Problems (Clarendon, Oxford, 1952).
  3. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  4. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, London, 1974).
  5. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974).
  6. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  7. J. W. Hovenier and C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).
  8. J. Lenoble, ed., Radiative Transfer in Scattering and Absorbing Atmospheres (Deepak, Hampton, Va., 1985).
  9. A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, Norwood, Mass., 1994).
  10. A. Z. Dolginov, Yu. N. Gnedin, and N. A. Silant’ev, Propagation and Polarization of Radiation in Cosmic Media (Gordon & Breach, Basel, Switzerland, 1995).
  11. E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer-Verlag, Berlin, 1997).
  12. G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University, New York, 1999).
  13. K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 2002).
  14. J. W. Hovenier, C. V. M. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres (Kluwer Academic, Dordrecht, The Netherlands, to be published).
  15. A. G. Borovoy, “Method of iterations in multiple scattering: the transfer equation,” Izv. Vyssh. Uchebn. Zaved. Fiz., No. 6, 50–54 (1966).
  16. Yu. N. Barabanenkov and V. M. Finkel’berg, “Radiation transport equation for correlated scatterers,” Sov. Phys. JETP 26, 587–591 (1968).
  17. A. Z. Dolginov, Yu. N. Gnedin, and N. A. Silant’ev, “Photon polarization and frequency change in multiple scattering,” J. Quant. Spectrosc. Radiat. Transfer 10, 707–754 (1970).
  18. L. A. Apresyan and Yu. A. Kravtsov, Radiation Transfer (Gordon & Breach, Basel, Switzerland, 1996).
  19. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
  20. A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).
  21. L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley, New York, 2001).
  22. V. P. Tishkovets, “Multiple scattering of light by a layer of discrete random medium: backscattering,” J. Quant. Spectrosc. Radiat. Transfer 72, 123–137 (2002).
  23. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, New York, 2002).
  24. A. P. Prishivalko, V. A. Babenko, and V. N. Kuzmin, Scattering and Absorption of Light by Inhomogeneous and Anisotropic Spherical Particles (Nauka i Tekhnika, Minsk, USSR, 1984), in Russian.
  25. L. L. Foldy, “The multiple scattering of waves,” Phys. Rev. 67, 107–119 (1945).
  26. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
  27. V. Twersky, “On propagation in random media of discrete scatterers,” Proc. Symp. Appl. Math. 16, 84–116 (1964).
  28. D. S. Saxon, “Lectures on the scattering of light,” Science Report No. 9 (Department of Meteorology, University of California, Los Angeles, Los Angeles, Calif., 1955).
  29. G. V. Rozenberg, “Stokes vector-parameter,” Usp. Fiz. Nauk. 56(1), 77–110 (1955).
  30. M. I. Mishchenko, “Multiple scattering of light in anisotropic plane-parallel media,” Transp. Theory Stat. Phys. 19, 293–316 (1990).

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