Boundary shape reconstructions in a coaxial waveguide using Bessel functions

Abstract

This paper investigates boundary shape reconstructions in coaxial waveguides using microwave scattering. Electromagnetic field perturbation theory together with inverse problem theory is used to reconstruct two-dimensional small boundary deformations on the inner boundary of a coaxial waveguide. Due to the first-order perturbation theory employed, the scattering parameters of the waveguide have linear dependencies on the continuous deformation function. Thus, the corresponding inverse problem can be linearized, and direct inversion can be employed to obtain the shape parameters. Tikhonov regularization is used to regularize the resulting ill-conditioned linear system. Finally, reconstruction results are presented for a few examples of two-dimensional localized shape deformations of coaxial waveguide boundaries, being in agreement with the actual shapes.