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

Abstract

We use the concepts of statistical electromagnetics to derive the general radiative transfer equation (RTE) describing multiple scattering of polarized light by sparse discrete random media consisting of arbitrarily shaped and arbitrarily oriented particles. The derivation starts from 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. We 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 -> infinity. The concluding section discusses the physical meaning of the quantities entering the general vector RTE and the assumptions made in its derivation.