Radiative transfer in a semi-infinite absorbing/scattering medium with reflective boundary

Abstract

A variation of Ambarzumian's method is used to formulate the equations for the source function, flux and intensity at the reflective boundary of a one-dimensional semi-infinite medium. Emission is neglected, while the medium is allowed to absorb energy and to scatter isotropically. The boundary conditions studied are collimated incident intensity and diffuse incident intensity. As in the case of unit refractive index, the solutions for the diffuse boundary condition are found to be integrals of the solutions for the collimated boundary condition. Equations are written for the desired functions just inside and outside the medium. Example numerical results are presented for an albedo of 0.7 and refractive indices of 1.1, 1.33, 1.5, and 2.0. It is also shown that the solutions for the isotropic scattering problem can be extended to the special case of anisotropic scattering, for which the phase function is made up of a forward spike superimposed upon an otherwise isotropic phase function.