Analysis of inverse scattering in a waveguide using the method of volume singular integral equation

We develop a method of solution to the inverse problem of reconstructing the media parameters (complex permittivity) of a body in a waveguide. The analysis is based on the use of a volume singular integral equation and its reduction to an equation which can be solved, using iterations, both numerically and analytically. This enables us to determine, for a given single-mode rectangular waveguide, the complex permittivity from the transmission coefficient. The approach also yields the proof of uniqueness of reconstruction of complex permittivity in a rectangular waveguide from the transmission characteristics. The results of test computations performed for the inclusion in the form of a parallelepiped justify the proposed approach.