Mishchenko 2003

Mishchenko, M.I., 2003: Radiative transfer theory: From Maxwell's equations to practical applications. In Wave Scattering in Complex Media: From Theory to Applications. B.A. van Tiggelen and S.E. Skipetrov, Eds. Kluwer Academic, pp. 367-414.

Since the pioneering papers by Khvolson and Schuster, the radiative transfer theory (RTT) has been a basic working tool in astrophysics, atmospheric physics, and remote sensing, while the radiative transfer equation (RTE) has become a classical equation of mathematical physics. However, the RTT has been often criticized for its phenomenological character, lack of solid physical background, and unknown range of applicability. The past three decades have demonstrated substantial progress in studies of the statistical wave content of the RTT. This research has resulted in a much better understanding of the physical foundation of the RTT and has ultimately made the RTE a corollary of the statistical electromagnetics.

The aim of this chapter is to demonstrate how the RTE follows from the Maxwell equations when the latter are applied to the problem of multiple electromagnetic scattering in discrete random media and to discuss how this equation can be solved in practice. The following section contains a brief summary of those principles of classical electromagnetics that form the basis of the theory of single light scattering by a small particle. Section 3 outlines the derivation of the general RTE starting from the vector form of the Foldy-Lax equations for a fixed N-particle system and their far-field version. Based on the assumption that particle positions are completely random, the RTE is derived 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. We then discuss in detail the assumptions leading to the RTE and the physical meaning of the quantities entering this equation. The final section describes a general technique for solving the RTE that allows efficient software implementation and leads to physically based practical applications.

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Mishchenko, M.I.: Radiative transfer theory: From Maxwell's equations to practical applications, in: Wave Scattering in Complex Media: From Theory to Applications, edited by van Tiggelen, B.A., and Skipetrov, S.E., 367-414, Kluwer Academic, Dordrecht, the Netherlands, 2003.

Mishchenko, M.I. (2003), Radiative transfer theory: From Maxwell's equations to practical applications, in Wave Scattering in Complex Media: From Theory to Applications, edited by B.A. van Tiggelen and S.E. Skipetrov, pp. 367-414, Kluwer Academic, Dordrecht, the Netherlands.

Mishchenko, M.I., 2003: Radiative transfer theory: From Maxwell's equations to practical applications. In Wave Scattering in Complex Media: From Theory to Applications. B.A. van Tiggelen and S.E. Skipetrov, Eds. Kluwer Academic, pp. 367-414.

Mishchenko, M.I. 2003, in Wave Scattering in Complex Media: From Theory to Applications, ed. van Tiggelen, B.A., & Skipetrov, S.E., 367 (Dordrecht, the Netherlands: Kluwer Academic).

Mishchenko MI. Radiative transfer theory: From Maxwell's equations to practical applications. In: van Tiggelen BA, Skipetrov SE, editors. Wave Scattering in Complex Media: From Theory to Applications, pp. 367-414. Dordrecht, the Netherlands: Kluwer Academic; 2003.

M.I. Mishchenko, In Wave Scattering in Complex Media: From Theory to Applications, B.A. van Tiggelen, S.E. Skipetrov, Eds. (Kluwer Academic, Dordrecht, the Netherlands, 2003), pp. 367-414.