A scattering support for broadband sparse far field measurements

The scattering support is an estimate of the support of a source or scatterer, based on a limited set of far field measurements. In this paper, we suppose that the far field is measured at all wavenumbers, but only at a few, say N, angles θi ∈ . From these measurements, we produce a -convex polygon (a convex polygon with normals in the θi directions). We show that this polygon must be contained in the smallest -convex polygon which contains the source. We also show by explicit construction that, if (and only if) that polygon has almost 2N faces, there really is a source, supported in the -convex scattering support, which exactly produces these measurements.