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Determining the spatial scattering function, i.e. solving the inverse scattering problem, with the Helmholtz wave equation model is known to be an ill posed problem for a single incident radiation field. We show that the problem becomes well posed if formulated as seeking the common scattering function which produces a best prediction of the given scattering data for sufficiently many sources and receivers. The scattering function is found by solution of a system of non-linear algebraic equations which are derived by the method of moments. Our method avoids perturbation theory approximations.