3-D Imaging of Inhomogeneous Materials Loaded in a Rectangular Waveguide

A Newton-type method for the reconstruction of inhomogeneous 3-D complex permittivity variation of arbitrary shaped materials loaded in a rectangular waveguide is presented. The problem is first formulated as a system of integral equations consist of the well-known
data
and
object equations
, which contain the dyadic Green's function of an empty rectangular waveguide. Two unknowns of this system are solved in an iterative fashion by linearizing one of them, i.e., the data equation in the sense of the Newton method, which corresponds to a first-order Taylor expansion of the related integral operator. Since the problem is severely ill posed by nature, a regularization in the sense of Tikhonov is applied to the data equation. A detailed numerical implementation of the method, together with some numerical examples are also given to show the capabilities and validation limits of the method.