Diffusion approximation for a dissipative random medium and the applications

Abstract

In almost all of the literature, the diffusion coefficient derived from a conventional transport equation changes with the absorption coefficient when there is a dissipation in the medium. The situation is also the same for the time-independent diffusion equation. In recent numerical simulations made for a biological-mechanical purpose, it happened that the absorption coefficient was increased up to one tenth of the total scattering cross section per unit volume; thereby it was strongly suggested that the diffusion coefficient should preferably be independent of the absorption coefficient. The purpose of this paper is to show theoretically that this is definitely the case. Moreover, several basic equations for applications to optical tomography and photon migration are given.