An inverse problem for the Helmholtz equation

We consider the problem of determining the shape of a bounded aperture in an infinite from knowledge of the diffracted field on a plane located within the domain where the propagates. This is an ill-posed problem. We restore a logarithmic stability in the class apertures with a priori bounded perimeter. We are also concerned with the numerical of the aperture. An approximated reconstruction is obtained as a suitable level set of the minimizing function of a penalized least-square functional. Some examples are given.