Reconstructing the contour of metallic planar objects from only intensity scattered field data over a single plane

The inverse scattering problem of recovering the contour of planar metallic scattering objects from only the amplitude of the scattered field is considered. A two step reconstruction procedure is proposed: first the phase of the scattered field is retrieved by solving a phase retrieval problem; then the objects' supports are reconstructed from the retrieved scattered field. Differently form previous approaches, here the amplitude of the scattered field is assumed known over a single plane in near zone but at two different frequencies. In this way, while the frequency diversity increases the number of independent data, relevant for ensuring the reliability of the phase retrieval stage, to perform measurements on a single plane allows some practical advantages. Numerical results show the performances achievable by the proposed reconstruction scheme with respect to the local minima problem and the stability against the noise on data.