The two-dimensional inverse scalar problem of diffraction by an inhomogeneous obstacle with a piecewise continuous refractive index

Background. The aim of this work is theoretical study of the two-dimensional inverse scalar problem of diffraction by an inhomogeneous obstacle characterized with a piecewise continuous refractive index. Material and methods. The original boundary value problem in the quasiclassical formulation is reduced to a system of integral equations; the properties of the latter system are studied using potential theory and Fourier transform. Results. The integral formulation of the inverse diffraction problem is proposed; uniqueness of a piecewise constant solution to the Fredholm integral equation of the first type is established; novel two-step method for solving the inverse problem is proposed. Conclusions. the proposed method and obtained results can be applied for solving two-dimensional problems of near-field tomography.