Polynomial characterization of inhomogeneous media and their inversion using non-plane wave sources

The problem of inverting inhomogeneous continuously varying dielectric profiles using open-ended waveguide radiators is studied. The ´measured´ data are numerically simulated and consist of the self-admittance of a flanged open-ended waveguide put in contact with the unknown profile. The basic method is to seek a numerical solution for the direct problem based on a layered dielectric model and to approach the inverse problem by characterizing the unknown profile as a polynomial with unknown coefficients to be determined in an optimization process. The self-admittance of the waveguide is first formulated for various frequencies. Then, using the Levenberg-Marquardt optimization algorithm, a search for unknown coefficients of the polynomial is carried out until the response of the trial medium agrees within a certain tolerance, in a least square sense, with the response of the actual medium.<>