Linear and quadratic inverse scattering for angularly varying circular cylinders

We discuss the problem of determining the class of dielectric profile functions that can be reconstructed from scattered electrical field data depending on the model to be inverted. We focus our attention on a cylindrical object with a circular cross section whose permittivity varies only along the angular coordinate. First we examine the linear Born approximation of the relationship between the permittivity function and the field scattered by the cylinder. We provide an analytical answer to this problem by singular-value decomposition of the relevant operator. We find that only slowly varying profiles can be recovered, both in the single-view and in the multiview case. Next we examine a quadratic approximation of the same relationship, which consists in adding a second-order term to the linear term. The effect of changing the model on the class of unknown functions that can be reconstructed is shown by means of both analytical arguments and numerical simulations. The result is that now the model includes more rapidly varying profiles.