On Cauchy system of searchlight problem in turbid slab

With the aid of invariant embedding, the authors consider a mathematical model of a searchlight on a target of turbid slab, bounded below by a diffuse reflector. In the real physical situation, the faint background light illuminating the top may be allowed for. However, for the sake of simplicity, the angular distribution of radiation emergent from the top of the turbid slab with a point source is discussed, by embedding the problem within a family of parameters. The invariant embedding is used to obtain the Cauchy system of the scattering function in the searchlight problem. The initial-value solution coincides with that obtained via the integral operator method