Profile Inversion of Stratified Dielectric Media using the Two-Step Reconstruct1On

A novel two-step reconstruction approach for one-dimensional permittivity profiles in the frequency domain is presented. At the first step, the profile is reconstructed as a stack of homogeneous layers using minimax criterion for the modulus of the reflection coefficient. This method yields accurate reconstruction of simple layered profiles. In other cases, it provides good starting conditions for another method, based on application of the Newton-Kantorovich iterative procedure to the Riccati equation describing the reflection of electromagnetic wave from an inhomogeneous half-space. Thus, a computation time is considerably reduced without using a priori information. The convergence and the stability of solution are improved due to handling the problem in terms of an optical path length rather than in spatial coordinate. This is explained by a better accuracy of the integral equation derived to obtain the next iterates to the profile. The approach is valid for the inversion of discontinuous and highly contrasted profiles and retains a good stability with respect to the noise in the simulated data.