Three-dimensional time harmonic electromagnetic inverse scattering: The reconstruction of the shape and the impedance of an obstacle

A numerical method for the reconstruction of the shape and the impedance of an obstacle from time harmonic electromagnetic scattering data is presented. Let D be a bounded, simply connected domain contained in the three-dimensional Euclidean space R3, with smooth boundary ∂D. The three-dimensional Euclidean space is filled with an isotropic homogeneous medium. We assume that D contains the origin, and D is regarded as an obstacle whose electric properties are given by a boundary impedance χ(x), x ∂D. From the knowledge of the electric far fields generated by the obstacle D when hit by known time harmonic electromagnetic waves, the shape ∂D, and the boundary impedance χ(x) of the obstacle are reconstructed. The reconstruction algorithm is based on the “Herglotz function method” introduced by Colton and Monk [1] in acoustic scattering.