Stability of the Recovery of Surface Impedances in Inverse Scattering

The inverse problem we consider is to determine the surface impedance on the boundary of a known obstacle from a knowledge of the far field pattern for the scattering of incident time-harmonic plane waves. It is well known that this problem has a unique solution w2x, but is ill-posed w3x. We show in this paper that this inverse problem becomes well-posed provided that we have an a priori upper bound of the C1 norm of the surface impedance.