Inverse scattering for a locally perturbed half-plane

We consider the inverse problem to determine the shape of a local perturbation of a perfectly conducting plate from a knowledge of the far-field pattern of the scattering of TM polarized time-harmonic electromagnetic waves by reformulating it as an inverse scattering problem for a planar domain with corners. For its approximate solution we propose a regularized Newton iteration scheme. For a foundation of Newton type methods we establish the Fréchet differentiability of the solution to the scattering problem with respect to the boundary and investigate the injectivity of the linearized mapping. Some numerical examples of the feasibility of the method are presented. For the sake of completeness, the first part of the paper outlines the solution of the direct scattering problem via an integral equation of the first kind including the numerical solution.