A stable sampling method for inverse scattering from periodic media

Abstract

This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a new imaging functional for solving this inverse problem. This imaging functional is very simple to implement, robust against noise in the data, and does not require regularization. The resolution and stability analysis of the imaging functional is analyzed. Our numerical study shows that the proposed sampling method is more stable than the factorization method and more efficient than the orthogonality sampling method in reconstructing periodic scattering media.