Inverse scattering for surface impedance from phase-less far field data

We present a numerical comparison of a regularized Newton-type method and a direct method for reconstructing the surface impedance function of a three dimensional acoustic scatterer with known shape from the full far field pattern for scattering of one incident time-harmonic plane wave. Furthermore, we propose a modification of the Newton-type algorithm to recover a real-valued surface impedance from phase-less far field data. Numerical reconstructions illustrate the feasibility of the methods.