Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems

Within the framework of inverse scattering problems, the quantifying of the degree of nonlinearity of the problem at hand provides an interesting possibility for evaluating the validity range of the Born series and for quantifying the difficulty of both forward and inverse problems. With reference to the two-dimensional scalar problem, new tools are proposed that allow the determination of the degree of nonlinearity in scattering problems when the maximum value, dimensions, and spatial-frequency content of the unknown permittivity are changed at the same time. As such, the proposed tools make it possible to identify useful guidelines for the solution of both forward and inverse problems and suggest an effective solution procedure for the latter. Numerical examples are reported to confirm the usefulness of the tools introduced and of the procedure proposed.