Schiffer's theorem in inverse scattering theory for periodic structures

This paper is devoted to the inverse scattering problem to recover a periodic structure by scattered waves measured above the structure. It is shown that a finite number of incident plane waves is sufficient to identify the structure. Additionally by a monotonicity principle for the eigenvalues of the Laplacian some upper bounds of the required number of wavenumbers are presented if a priori information on the height of the structure is available.