Two-step inverse scattering method for one-dimensional permittivity profiles

A numerical method to invert the dielectric permittivity profile from the Riccati equation using the Newton-Kantorovich iterative scheme is described. Instead of handling the equations in terms of usual geometrical depth, we determine the profile as a function of the electromagnetic path length since the convergence and the stability of the solution are found to be significantly better in this case. The initial profile used as a starting point for the inversion is obtained by another method employing successive reconstruction of dielectric interfaces and homogeneous layers in a step-like form. This method, though not always accurate, is fast and well suited for the approximate reconstruction of the profile, thus creating ideal starting conditions for the previous approach. As a result, the computation time is considerably reduced, without using any a priori information. The approach is applicable to both continuous and discontinuous profiles of high contrast and exhibits a good stability of the solution with respect to noisy input data. A lossy medium profile can also be inverted provided the overall thickness of the inhomogeneous slab and the background permittivity are known.