Low frequency inverse scattering

Derived is an acoustic and electromagnetic low frequency direct scattering approximation in terms of the characteristic function of a scatterer. An inverse scattering solution for the complete moments tensor of this characteristic function is obtained. It is shown that this inverse scattering solution is a generalization of Rayleigh´s law, yielding the Rayleigh law volume of the scatterer for the moments tensor of rank zero. The moments tensors of rank one and two are the spatial position centroid and the principal dimensions (and their spatial orientation) of the scatterer respectively.