Two-step method for solving the scalar reverse three-dimensional diffraction problem on a volume heterogeneous body

Background. The aim of this work is theoretical justification and implementation of the two-step method for solving the three-dimensional inverse scalar problem of diffraction by a heterogeneous obstacle characterized by a piecewise continuous refractive index. Material and methods. The boundary value problem is reduced to a system of integral equations; the properties of this system are studied using potential theory and Fourier transform. Results. The integral formulation of the inverse problem of diffraction is given; uniqueness of a solution to the Fredholm integral equation of the first type is established in special function classes; non-iterative two-step method for solving the inverse problem is proposed and implemented; several procedures for solutions' refinement are described. Conclusions. The proposed two-step method is an efficient tool for solving three-dimensional scalar problems of near-field tomography.