- are 0.766L179.1" and 0.743L -171.9", respectively, while the measured reflection coefficient is 0.763L -172.6' .
The inversion process with water as medium 1 and a conductor as medium 2 indicates even slower convergence with respect to that of methanol. In this case, the permittivity of water was determined as 80.65 -j7.51 via (lo), with the use of a reflection coefficient measured at 2 GHz, whereas it was only 65.01 -13.89 via (1). This value is available in the literature as 78.57 -j8.29 on the basis of a different technique [11]. This again indicates a limitation of the variational formulation. However, the method of moments is producing a result fairly close to this value. This computation was performed for a 10-mm-thick water layer on a conducting surface. The inversion process takes a longer time for thin sample layers. For example, attempts with a 5-mm-thick water layer could not produce results even after 4 hours. Forward computation of admittance (and hence, the reflection coefficient) hardly takes a few minutes as long as the thickness is more than 1 mm.
Evaluation of the complex permittivity of medium 2 or the thickness of medium 1 using Muller's procedure produced mixed results. It indicated that the convergence process was either very slow or it converged to a quite different root. In some cases, it even started diverging. These inversion processes seem to be very sensitive to initial values. Because the forward process of aperture admittance computation yields consistent results with (101, it is always possible to improve the root value (and hence d or .$, as the case may be) from its close approximation.
V. CONCLUSIONS
An accurate admittance model for the coaxial probe in a layered medium has been presented in this article using the method of moments. The results are compared with those of the variational formulation. Numerical results have been compared with corresponding experimental data, which indicate that the latter formulation cannot be used for a probe with an electrically large aperture. The former approach (the method of moments) produced fairly accurate results consistently. However, it converged slowly when the dielectric layer was thin. Further, an inversion procedure has been presented. The two models are used to evaluate the complex permittivity of dielectric layer. With a methanol-layer thickness of more than a millimeter over a conducting surface, the inversion process took about a minute or so with a 14-mm air line as a probe. However, the inversion process did not produce results even after several hours for water layers less than 10 mm. These computations were performed on a 75-MHz 486DX4 notebook.
The inversion process for determining the complex permittivity of medium 1 works satisfactorily with (10) in conjunction with Muller's method. On the other hand, the inversion procedures for determining the thickness of medium 1 or the complex Permittivity of medium 2 produced mixed results. These need further investigation.