Complex permittivity determination of homogeneous objects loaded in circular waveguide via integral equation method

An integral equation approach is presented for the complex permittivity determination of arbitrarily shaped homogenous objects loaded in circular waveguide. In order to formulate the integral equation based inverse algorithm, first the well-known data and object equations, containing electric type dyadic Green's function of empty waveguide are obtained. It should be noted that the data and object equations can be solved with different techniques to determine the permittivity of the objects partially/fully loaded in a waveguide. In this paper, a Newton based iterative algorithm is applied where the nonlinear data equation is linearized by first order Taylor expansion using Frechet derivative of the integral operator. In this study, complex permittivity determination of non-magnetic, arbitrarily shaped and homogeneous material using the scattered electric fields in the circular waveguide is considered. The inverse algorithm for partially filled circular waveguide is applied for objects with different geometries and satisfactory results are obtained also in the presence of random noise.