Multi-frequency orthogonality sampling for inverse obstacle scattering problems

We discuss a simple non-iterative method to reconstruct the support of a collection of obstacles from the measurements of far-field patterns of acoustic or electromagnetic waves corresponding to plane-wave incident fields with one or few incident directions at several frequencies. The method is a variant of the orthogonality sampling algorithm recently studied by Potthast ( 2010 Inverse Problems 26 074015 ). Our theoretical analysis of the algorithm relies on an asymptotic expansion of the far-field pattern of the scattered field as the size of the scatterers tends to zero with respect to the wavelength of the incident field that holds not only at a single frequency, but also across appropriate frequency bands. This expansion suggests some modifications to the original orthogonality sampling algorithm and yields a theoretical motivation for its multi-frequency version. We illustrate the performance of the reconstruction method by numerical examples.