Combined Thickness and Permittivity Measurement of Thin Layers with Open-Ended Coaxial Probes

Abstract

This paper presents a method to simultaneously determine the thickness and permittivity of thin layers from multi-frequency reflection coefficient measurements using an open-ended coaxial probe. This is achieved by exploiting that the probe becomes radiating at frequencies higher than the probe’s typical operating range. Permittivity information is extracted from measurements in the typical frequency range, whereas thickness information is obtained from high frequency measurements by exploiting resonances that occur when the radiated waves are reflected at the layer boundary. A finite element model of the measurement set-up is made in COMSOL MultiphysicsTM, and a matrix of simulations spanning the relevant layer thicknesses and permittivity range is generated. The measured permittivity spectra of unknown samples are compared to the simulation matrix to estimate layer thickness and permittivity. The method is verified by measurements of water–ethanol mixtures. An application example where the water fraction and layer thickness of a gas hydrate deposition layer is estimated from permittivity measurements in a multiphase flow loop is also presented.