On inverse scattering by screens

Abstract

A generalization of Isakov's theorem ([13]) to admissible shapes that include screens with a Robin boundary condition (in which the impedance is also an unknown) is presented. We also establish a characterization that enables us to distinguish the far-field of plane screens from others. Numerical results using a quasi-Newton method are presented. 1 Introduction Identifying the object shape by means of the far field pattern of some acoustic wave, scattered by the object, is a mathematical and numerical problem with large applications in industry. For an overview on the subject we cite, for instances, the book of Colton and Kress ([7]). The first uniqueness result known on the subject, was presented by Schiffer in 1967 (cf. [18]) for the case of the Dirichlet problem, based on the eigenvalues of the interior problem. The same technique was not possible neither for screens shapes nor for the Neumann case. And it was only in 1990 that Isakov ([13]) gave a new proof that enabled Kirsch and...