Calculation of the radiance distribution at the boundary of an isotropically scattering slab

The radiance arising from an anisotropically scattering illuminated stack of n slabs is calulated using the equation of radiative transfer. It appears to be unnecessary to calculate the radiance inside the material; including only the radiance at the boundary surfaces is sufficient to obtain the desired result. The novel method used for the solution of this problem leads immediately in a straightforward and systematic way to the known appropriate basic equations valid for the problem at hand, otherwise derived by ad hoc methods. A new simple set of linear equations for the radiance at the boundary surfaces is derived. This method applies equally well to similar problems with other geometries.

Apart from this analytical derivation, this paper presents the results of the numerical solution of the set of equations that we obtained from the equation of radiative transfer, for n = 1. The results of the numerical calculations are compared with what is found in the literature and are found to give very good agreement.