Hierarchical Interpolation Algorithm for Fast Born Approximation Analysis of Scattering by Electrically Large Objects

An algorithm for the fast computation of Born approximation scattered field integral for electrically large low-contrast inhomogeneous targets is presented. The algorithm takes advantage of the integrand’s phase in order to efficiently sample partial the contributions to the scattered field, in both the source and observer coordinates. These contributions are gradually interpolated and aggregated, with appropriate phase factors, in a multilevel fashion, in order to obtain the total field integral, sampled at a desired density. This reduces the cost of field integrations by three orders of the scatterer’s electrical length. For the far-field and incident plane wave scenario, the computations are further simplified and reduced to that of a single scalar component.