RECONSTRUCTION OF SCATTERING POTENTIALS FROM INCOMPLETE DATA

In many situations encountered in physics and in other fields, one can frequently experimentally determine some but not all the Fourier components of a scattering potential. In this paper we present an integral equation which makes it possible to reconstruct any square-integrable function f(r) of finite support from the knowledge of its Fourier transform f(K) over any finite three-dimensional domain of K space. We illustrate the use of this integral equation by application to potential scattering at fixed energy and we show how it can be used to reconstruct details of the scattering potential beyond the usual resolution limit from measurements of the scattered field in the far zone of the scatterer.