Reconstruction of periodic gratings from one scattered wave (Q1877737)

The author considers some iterative regularization schemes based on derivatives with respect to variations of the boundary in order 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. In addition, the author presents elegant numerical examples to demonstrate that such an iterative regularization approach can be effectively used for such a severely ill-posed problem.