Reconstruction of periodic gratings from one scattered wave

Abstract

Iterative regularization schemes are considered based on derivatives with respect to variations of the boundary to reconstruct periodic scattering object from known data of a scattered field. Representations of the required derivatives are presented which help in understanding the ill-posed nature of the problem and which are used numerically by the implementation and investigation of regularized Newton-type iteration schemes. Some numerical examples illustrate the performance of the regularization schemes.