Uniqueness theorems in inverse scattering theory for periodic structures

In this paper the authors prove that the scattering object which consists of a periodic surface is uniquely determined by the knowledge of the scattered fields corresponding to all quasiperiodic incident waves. They assume the TE-mode and a perfectly conducting grating. A second uniqueness result treats the case where only a finite number of amplitudes of the scattered fields are known. They show for small perturbations of the plane that one can only identify the slow variations of the scattering curve.