On reconstruction of objects from measurements of the diffracted field (*)

The aim of this paper is the shape restoration of a plane object from measurements of its diffracted field at a discrete and finite set of points. The plane sampling lattice is supposed: i) rectangular; ii)periodic.

The problem is approached as an interpolation one. A numerical algorithm for practical reconstructions is presented. A-priori limitations on the perimeter of the object and conditions on the samples lead to a-priori bounds able to estimate the precision of the reconstruction.