An Analytical Model for the Contribution of Small Scatterers to Open-Ended Coaxial Probe Measurements

The open-ended coaxial probe (OECP) technique is one of the most commonly used methods for the characterization of homogeneous media properties, especially in the biomedical sciences. However, when considering inhomogeneous media, the effect of the heterogeneity on the probe terminal admittance is unclear, making the measured admittance difficult to interpret and relate to the properties of the medium. In this article, we present an analytical model for the contribution of an isotropic scatterer embedded in an otherwise homogeneous medium to the probe admittance. We utilize rigorous scattering theory and various approximations to obtain simplified, closed-form expressions. Using the obtained results, we present a method to accurately extract the scatterer properties from a measurement of the admittance. In addition, we define the sensing depth and show how it can be mapped as a function of the expected scatterer properties. Full-wave simulations are used to verify the proposed model, paving a path for further generalization to additional scenarios of open-coaxial probe sensing of an inhomogeneous medium.