Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem

Abstract
An efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections. This choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions. The mathematical analysis is performed in terms of operator and functions, and the fundamental instability of the problem is demonstrated. Then the stability is restored by means of a Tikhonov-Miller regularization. The efficiency of the method is outlined by numerical examples. References are given which show that the same algorithm applies to other electromagnetic inverse problems, especially to gratings.