Multiresolution Analysis of Radiative Transfer through Inhomogeneous Media. Part I: Theoretical Development

Abstract

This paper derives a multiresolution formulation of the radiative transfer equation for inhomogeneous media. The multiresolution equation is separated into two sets of equations that help in its physical interpretation. The first set represents radiative transfer at some approximation scale, the second at smaller scales. These equations describe explicitly how the local-scale couplings, which occur between the fluctuations of optical properties and radiation fields at different scales, contribute to the radiation field at a prescribed scale and at a given location by introducing additional internal sourcelike functions. These functions are expressed by terms involving connection coefficients of the chosen multiresolution system and also scaling and wavelet coefficients of the inhomogeneous optical properties. This new formulation can provide new insights into the local-scale coupling governing radiative transfer in inhomogeneous media.