Estimation of the Effective Electrical Parameters in Two-Dimensional Transverse Electric Case

In this article, a method is presented to estimate the effective electrical parameters of the scatterers for multi-view multi-static two dimensional transverse electric (2D-TE) scattering configurations. The derived method needs the shape and position information of scatterers a-priorly to model the targets as circular cylinders (i.e., an effective radius and center is determined for each target) with constant electrical parameters. Next, the method employs the virtual experiments to focus the incident magnetic field as a $J_{0}$ on a specific target. After focusing the excitation and neglecting the multiple scattering between targets, the scattered field is in $H_{1}<^>{(1)}$ form. Next, the error between the simulated and the virtual fields is calculated. Then, the effective electrical parameter is estimated as the minimizer of the error. Lastly, for the cases where the shape and/or position information are noisy, the introduced method links the deviation of the electrical parameters to deviations of the effective radius and center. From this relation, the method presents a way to estimate the maximum deviations in the electrical parameters, given the maximum deviations in effective radius and center. The efficiency and accuracy of the proposed formulations are tested with both numerical and experimental examples.