The factorization method in inverse scattering from periodic structures

Abstract

The application of the factorization method, the refined version ofthe linear sampling method, to scattering by a periodic surfaceis considered. Central to this method is the near field operatorN, mappingincident fields to the corresponding scattered fields on a horizontal line. A factorizationof Nforms the basis for the method. It is shown that the middle operator inthis factorization, the adjoint of the single-layer operator, is coercive ifthe wavenumber is small enough. Thus this operator can, for generalwavenumber, always be written as the sum of a coercive and a compactoperator. We use this property to define an auxiliary positive operatorN# which can beconstructed directly from Nand which makes it possible to reconstruct the scattering surface directly using asimple numerical algorithm.