Source Functions for an Isotropically Scattering Atmosphere Bounded by a Specular Reflector.

A method for reducing the calculation of the source function for a specular reflector to the solution of a set of ordinary differential equations with known initial conditions. The basic Fredholm integral equation that these source functions satisfy is transformed into a Cauchy system with known initial conditions. To deal numerically with the differential-integral equations, the integrals appearing are approximated by finite sums. Some typical computational results are displayed for the case of a perfect specular reflector at the bottom. These are contrasted with earlier results for an atmosphere having a perfect absorber at the bottom. The accuracy of the numerical results has been considered in detail. The method presented here generalizes easily to cover the systems of integral equations encountered when polarization is included. A FORTRAN program suitable for an inhomogeneous medium and a general reflecting surface is available from the authors. 30 pp. Ref. (MT)