Newton-kantorovich method applied to the reconstruction of surface profiles under Tikhonov's regularization with domain constraint

In this work we propose an efficient algorithm for reconstructing a one dimensional perfectly conducting rough surface. The data are the complex amplitude of the diffracted far field in several directions. They are generated with a rigorous diffraction model when the surface is illuminated successively under several angles of incidence in TE polarization (electric component parallel to the invariance axis). Reconstructing the surface profile from these data is known as a nonlinear and ill-posed inverse problem. It is resolved iteratively by the Newton-Kantorovich method where its ill-posed aspect is treated under different regularisation schemes. In particular, we show that by adding a domain constraint to the standard Tikhonov regularisation, it is possible to improve the quality of the reconstructions. In this case, the role of this additional term is to force the reconstruction of the profile only on certain parts of the surface.