Beyond physical optics SVD shape reconstruction of metallic cylinders

We consider the problem of reconstructing the shape of perfectly conducting cylinders under the physical optics approximation. For direct scattering, physical optics provides small model errors when the scatterers are convex, smooth, have large radii of curvature as compared to the impinging wavelength, and are noninteracting. In this paper, we investigate whether these hypotheses can be relaxed for the inverse problem. In particular, we consider three classes of scatterers (circular cylinder with radius smaller than the wavelength, multiple cylinders, and a concave cylinder) and we show that for them the model error is provided by a multiplicative almost frequency-independent factor. Since this factor can be incorporated within the unknown distribution representing the scatterers' illuminated boundaries, then we are able to show that successful reconstructions also beyond the physical optics limits can be obtained.