An inverse algorithm for integral equation formulation of dielectric loaded cavities

In a large number of microwave remote sensing problems, accurate knowledge of the dielectric constant of natural media such as vegetation and soil is crucial in the estimation of the desired biophysical parameters from the measured data. In the conventional cavity perturbation method, a sample of the test material with dimensions much smaller than the wavelength is placed in a high-quality-factor microwave cavity, and then the resonant frequency and the quality factor of the loaded cavity are measured. Comparing the resonant characteristics of the empty (unloaded and loaded) cavity, one can estimate the real and imaginary parts of the dielectric constant from analytical expressions based on the perturbation theory. Besides practical limitations such as the cavity and sample geometry and size, a major drawback of the cavity perturbation method is its lack of accuracy in measuring the imaginary part of the dielectric constant of low-loss dielectric materials. The change in the quality factor of the cavity is proportional to the total dissipated power in the dielectric sample. When both the dielectric loss tangent and the sample volume are very small, the change in the quality factor becomes extremely small and falls within the measurement errors. To circumvent this difficulty, larger pieces of the material with sizes well beyond the limits of the perturbation theory are needed so that the resulting shift in the cavity characteristics can be measured accurately. In this paper, the authors extend the resonant cavity technique for dielectric constant measurement beyond the limitations of the perturbation method. The new approach incorporates a full-wave simulation of the loaded cavity structure into the inverse measurement problem. Thus, the size of the material sample can be taken arbitrarily large as long as it does not disturb the coupling mechanism of the resonator. For the forward measurement problem, an integral formulation of the related boundary value problem is developed and solved numerically using the method of moments (MoM). The MoM results are validated independently by comparing to the results based on the finite element method (FEM). For the inverse measurement problem, a numerically efficient inversion algorithm based on the Eigen-Analysis of the impedance matrix is employed. In this algorithm the dependence of the complex dielectric constant on the inverse of the impedance matrix is made explicit, thereby establishing simple polynomials relationships between the dielectric constant and the resonant characteristics of the cavity. Both forward and inverse problems are illustrated through simulation examples