Inverse vector problem of diffraction by inhomogeneous body with a piecewise smooth permittivity

Abstract

Abstract The vector problem of reconstruction of an unknown permittivity of an inhomogeneous body is considered. The original problem for Maxwell’s equations with an unknown permittivity and a given permeability is reduced to the system of integro-differential equations. The solution to the inverse problem is obtained in two steps. First, a solution to the vector integro-differential equation of the first kind is obtained from the given near-field data. The uniqueness of the solution to the integro-differential equation of the first kind is proved in the classes of piecewise constant functions. Second, the sought-for permittivity is straightforwardly calculated from the found solution and the total electric field. A series of test problems was solved using the two-step method. Procedures of approximate solutions’ refining were implemented. Comparison between the given permittivities and the found approximate solutions shows efficiency of the proposed method.