Iterative Step-Like Reconstruction of Stratified Dielectric Media from Multifrequency Reflected-Field Data

Abstract

We describe in this paper a frequency domain microwave method to reconstruct the permittivity profile of layered dielectric half-space. The inversion algorithm is based on the iterative Newton–Kantorovitch procedure applied to the Riccati nonlinear differential equation. To obtain a correction term to the initial profile, the integral equation relating to a small change of the profile function and corresponding change of the reflection coefficient is solved twice, with different systems of expanding functions for the unknown profile. The first set of functions is utilized to determine positions of the reflecting interfaces between layers. The second set represented by the Heaviside step functions provides the profile correction term completing the iteration. The proposed approach is valid for the essentially band-limited input data, that is, when both low- and high-frequency information is not available. This alleviates practical implementation especially from the viewpoint of antenna design, dielectric rods fed by TEM horns are used as transmitting/receiving antennas. Some numerical and experimental examples are presented for the input data in the frequency range of 1–4GHz, which demonstrate validity and robustness of the method for the complicated highly contrasted dielectric profiles.