Shape reconstruction from {radar cross section, phase} data

The wave scattered by the unknown obstacle is approximated by two different representations, one in the far zone, the other on the obstacle boundary. Each of these representations contains expansion coefficients which can be related by an approximate back propagator (ABP). The latter depends non-linearly on the parameters which describe the obstacle shape, and yields the boundary scattered wave from knowledge of the far field data. Reconstruction is carried out by minimising the L^2 norm of the boundary defect with respect to the shape parameters and other auxiliary unknowns. A numerical reconstruction from the Ipswich data is presented. A convergence propert of the approximate forward propagator is stated.