Invariant imbedding and Cauchy system of scattering function in searchlight problem in rugged terrain

In the present paper, allowing for such a horizontal inhomogeneous dependence due to the diffuse reflection of radiation in rugged terrain, we compute the Riccati type of the three-dimensional nonlinear integrodifferential equation for the scattering function via invariant imbedding. An allowance for the diffuse reflection of radiation at the base in mountainous terrain results in introduction of the rendering equation as a boundary condition. Then, in comparison with the case of the flat terrain, the asymptotic and numerical solutions of this problem seem to be computationally preferable.