Transmitted radiation of searchlight in turbid atmosphere

It is shown how to get an analytically Cauchy system of the scattering and transmission functions in the searchlight problem in a turbid atmosphere bounded by a diffuse reflector. An invariant imbedding leads to an initial-value solution of the scattering and transmission functions for the searchlight. The Riccati-type of nonlinear integro-differential equations are used. The authors discuss the convergence of the solutions. An approximate solution is found in terms of the standard scattering and transmission functions in a turbid slab of the same optical thickness. Finally, it is shown how to compute numerically such three-dimensional, nonlinear integro-differential equations with the aid of an asymptotic operator method and the Monte Carlo method