This dissertation is concerned with an inverse scattering problem in two dimensional electromagnetics. While inversion algorithms for transversal magnetic (TM) waves (electric field polarized along the axis of the cylindrical scatterer) are abundant, there are few inversion algorithms for transversal electric (TE) waves. This dissertation describes an iterative algorithm for the recovery of basic features of an object (shape, location and index of refraction) from measurements of the field scattered by the object when illuminated by electromagnetic waves with the magnetic field vector polarized along the cylinder axis.

The first part of this thesis concerns the formulation of the direct scattering problem. The basis of this formulation is a domain integral equation. Given the permittivity profile of an object and the incident TE wave, this integral equation can be solved to obtain the scattered magnetic field. This is how the synthetic data for the inversion is generated. This dissertation supplies an existence and uniqueness proof for this integral equation and proposes an iterative method to solve it numerically. The second part of this dissertation is the development of an efficient algorithm for TE inverse scattering. This algorithm is the analogue of that developed by Kleinman and van den Berg for TM inverse scattering and has proved quite effective in the TM case. This dissertation extends this algorithm to the TE case and some good results are obtained. Due to the presence of the gradient on both the field and the Green's function in the underlying integral equation, TE case is more complicated than TM case, thus TE inversion is more computationally intense. Nevertheless, in some cases where the contrast is large, numerical results indicate that TE inversion is superior to TM inversion. In most other cases, TE inversion is as good as TM inversion.

Finally, we point out some areas for future research, one of them is the development of an algorithm which combines the two polarizations. Since each polarization provides useful and maybe complementary information about the scatterer, we expect that their simultaneous use will yield better reconstruction than single polarization. This thesis supplies an algorithm which integrates TE and TM together.