Quadratic distorted approximation for the inverse scattering of dielectriccylinders

The nonlinear (quadratic) distorted approximation of the inverse scattering of dielectric cylinders is investigated, with the aim of pointing out the influence of the background medium. We refer to a canonical geometry consis ting of a radially symmetric dielectric cylinder illuminated at a single fr equency. We discuss how the spatial variations of those unknown dielectric profile functions that can be reconstructed by a stable inversion procedure are related to the permittivity of the background cylinder. First, results for the linear distorted approximation, obtained by means of the singular- value decomposition, are recoiled and compared with the Born approximation. It turns out that the distorted model provides a smoother behavior of the singular values, and thus the inversion is more sensitive to the presence o f uncertainties in the data. Furthermore, a stable inversion procedure can reconstruct only a very limited class of unknowns in correspondence with fa st spatial variations related to the background permittivity and the excita tion frequency. On the other hand, the quadratic model improves the approxi mation in the distorted case. This can be traced not only to the higher all owable level of permittivity but mainly to the fact that the model makes it possible to reconstruct different spatial features as the solution space c hanges. Numerical results show that the quadratic inversion performs better than the linear one for the same amount of uncertainty in the data. (C) 20 01 Optical Society of America.