The eigenfunctions method in relation to diffuse reflection problems of the radiative energy transfer theory

Abstract

Using the new method proposed earlier by the author, a solution of diffuse reflection problem is given in this report. A case of diffuse reflection of radiation from a semi-infinite absorbing and isotropically reflecting medium is presented, when in the elementary act of scattering there is a general law of redistribution of radiation by frequencies. In the approach presented here, conventionally called the method of ”decomposition of the resulting field” - DRF, in contrast to the previously widely used traditional method of ”decomposition of a single act” of scattering - DSA, the problem of diffuse reflection is solved without the use of any decomposition or special representation of the characteristic of the elementary act of scattering, i.e., the redistribution function of radiation by frequencies. The resulting radiation field, formed in the medium by means of multiple scatterings, is sought and constructed directly in the form of a bilinear series through a specially derived system of its own eigenfunctions. The physical basis of this approach lies in the fact that after each successive act of scattering, the field formed in the medium becomes more and more smoothed, so its direct representation in a decomposed form is more expedient than the traditionally used decomposition of a pre-known ”unsmoothed” characteristic of the elementary act of scattering.