Abstract:Background. The aim of this work is to theoretical and numerical study the inverse scalar problem of diffraction by a volume obstacle characterized by a piecewise Hoelder-continuous function. Material and methods. The original boundary value problem is considered in the quasiclassical formulation and then reduced to a system of weakly singular integral equations; the properties of the latter system are studied using the potential theory and Fourier transform. Results. The inverse problem of diffraction is given the integral formulation; the theorem on uniqueness of a piecewise constant solution to the integral equation of the first type is proved; a new two-step algorythm for numerical solving the inverse problem is proposed and implemented; several numerical tests have been carried out. Conclusions. The obtained theoretical and numerical results confirm high efficiency of the proposed method, which can be applied for solving problems of near-field tomography.
Keywords:inverse diffraction problem, reconstruction of refractive index, integral equatons, uniqueness of solutions, integral equations, collocation method.