Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: a microphysical derivation from statistical electromagnetics

Abstract

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 --> infinity. The concluding section discusses the physical meaning of the quantities that enter the general vector RTE and the assumptions made in its derivation.

Fast computation of two-level circulant preconditioners

“…5.7.4], but it was considerably clarified in recent years, in particular by M.I. Mishchenko (2002Mishchenko ( , 2003 and Mishchenko et al (2004), who used methods of statistical electromagnetics to give a self-consistent microphysical derivation of the radiative transfer equation including polarization.…”

“…In other cases the theory for single scattering is much more complicated, let alone multiple scattering theory [cf., Van de Hulst, 1980]. Comprehensive treatments of single scattering by particles have been presented by Van de Hulst (1957), Kerker (1969), Bohren and Huffman (1983), Mishchenko et al (2000), and Mishchenko et al (2002). Recently two books dealing with several aspects of single and multiple scattering have been published by Kokhanovsky (2001aKokhanovsky ( , 2003.…”

“…For a microphysical derivation from statistical electromagnetics we refer to Mishchenko (2002Mishchenko ( , 2003.…”

Application of the spatial averaging theorem to radiative heat transfer in two-phase media

“…Examples of previous pertinent studies include the determination of radiative properties of porous two-phase media consisting of an optically-thin phase and an opaque phase [7][8][9] and of an optically-thin and a semi-transparent phase [10][11][12][13][14]. Equations of radiative transfer (RTEs) were derived from an RTE applied at the discrete scale in a multi-phase porous medium having an optically-thin phase and an opaque phase consisting of large opaque particles [15], formulated for a medium having an optically-thin phase and a semi-transparent phase [10], derived for heterogeneous two-phase media with irregular phase boundaries [16], and derived directly from statistical electromagnetics for a medium containing arbitrarily shaped and oriented particles in an opticallythin host medium [17]. In [8,10,14] the radiative characteristics were determined based on the exact morphology of the porous media, obtained from computer tomography.…”

Continuum Radiative Heat Transfer Modeling in Media Consisting of Optically Distinct Components in the Limit of Geometrical Optics

“…The derivations presented are aimed at providing an analytical basis for development of 'ray optics' based numerical techniques such as the Monte Carlo ray tracing that can be used to radiatively characterize media using their structure and composition. More general derivations of the RTE for media containing arbitrarily shaped and sized components, and accounting for polarization effects, can be found in [20][21][22].…”