Radiation field in media with spherical symmetry

Abstract

A study is made of the structure of the Green's functions of problems in the theory of radiative transfer in media with spherical symmetry. Linear integral equations are obtained for the coefficients of reflection of light from a sphere and from an infinite medium with a spherical, absolutely black cavity. The kernels and free terms of these equations are expressed in terms of the Green's function for infinite space. The angle of incidence of the radiation and the optical radius of the sphere occur in these equations as parameters. Half-range biorthogonality relations are obtained for the eigenfunctions of the homogeneous equation of radiative transfer. The adjoint functions used in these relations are expressed in terms of the coefficients of reflection. i. Introduction To solve problems in the theory of radiative transfer in plane media, Case's method is often used [i]. It is based on expansion of the radiation intensity (or the corresponding Green's function) with respect to a complete system of eigenfunctions of the homogeneous transfer equation. The coefficients in the expansions are determined by means of orthogonality conditions. In the case of infinite media, the orthogonality of the eigenfunctions in the complete range of the angular variable ~ (--i ~ ~ ~ I) with weight is used. But in the case of semi-infinite media and plane layers of finite optical thickness one uses the biorthogonality established in [2] of the system of eigenfunctions in the half-ranges (0 < ~ < 1 or --i < ~ < O) with respect to the system of adjoint functions with weight ~H(~), where H(~) is the H function introduced into the theory by Chandrasekhar [3]. The half-range biorthogonality condition was formulated in a dif