Invisible Bodies and Uniqueness of the Inverse Scattering Problem

Abstract It is shown that within the accuracy of the first-order Born approximation there are no bodies that are invisible for all directions of incidence, i.e. that there are neither deterministic nor random non-scattering scatterers. An alternating orthogonal projections approach is also discussed for reconstructing the structure of deterministic scatterers from the knowledge of the scattered field in the far zone.