A dielectric measurement technique for cylindrical objects with known cross section

Motivated by the need for an accurate method to measure the complex dielectric constant of pine needles at microwave frequencies both in situ and in vivo conditions, the problem of scattering from a dielectric post in a rectangular waveguide is considered. In this analysis, the dielectric post is assumed to be uniform in cross section and dielectric constant and is placed vertically in a rectangular waveguide supporting TE₁₀ mode. The dielectric constant is computed from the measured voltage reflection coefficient of a matched waveguide containing the dielectric post. The author describes an inversion algorithm for computation of dielectric constant ε from the reflection coefficient which is based on the method of moments and eigen analysis. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation and then the contribution of ε to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant is a solution to a complex polynomial function which can be obtained numerically using the conjugate gradient method. Practical aspect of dielectric measurement using this technique is discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used for both S₁₁ calibration and validation of the dielectric measurement technique