Application of the second domain derivative in inverse electromagnetic scattering

We consider the inverse scattering problem of reconstructing a perfect conductor from the far field pattern of a scattered time harmonic electromagnetic wave generated by one incident plane wave. In view of iterative regularization schemes for the severely ill-posed problem the first and the second domain derivative of the far field pattern with respect to variations of the domain are established. Charaterizations of the derivatives by boundary value problems allow for an application of second degree regularization methods to the inverse problem. A numerical implementation based on integral equations is presented and its performance is illustrated by a selection of examples.