RECONSTRUCTION OF THE LAMBERTIAN SURFACE IN A WEAKLY SCATTERING MEDIUM

摘要

The problem of determining the sea bottom surface using a model that describes the process of radiation transfer in a randomly inhomogeneous medium was investigated. In the case of single scattering approximation, a pulsed source and the reflective properties of the reconstructable boundary obey Lambert's cosine law. As a result, a solution of the inverse problem is obtained in the form of a nonlinear differential equation for a curve function describing the bottom profile. An algorithm for solving the inverse problem based on explicit and implicit numerical schemes is developed. Using synthetic data, computational experiments were conducted comparing two approaches to solving the problem. An analysis of the effect of volume scattering on the restoration of the sea bottom surface was carried out using different methods for solving the nonlinear differential equation.