Correction of Complex Permittivity Inversion in Free-Space Gaussian Beam Reflection Model

To determine the complex permittivity of material mounted on the metal surface, the free-space reflection method is a good candidate due to its advantages of being nondestructive and contactless. When using the method, the extraction of the complex reflection coefficient (CRC) of the metal-backed material is the key to realize accurate measurement. Traditionally, the free-space reflection method assumes that the interrogating wave is a single plane wave, and the plane-wave reflection model is used. However, a focused beam is usually used in practice for reducing the edge effect that leads to the difference between the actual test scene and the traditional test model. In this study, a focused-wave reflection model is constructed to invert the complex permittivity, where the focused wave is considered as a Gaussian beam. The CRC of the Gaussian beam is deduced by using the plane-wave spectrum technique and plane-wave scattering-matrix (PWSM) theory. Based on the difference between the CRCs of the focused-wave and plane-wave, inverted complex permittivity corresponding to two reflection models is compared. Numerical results are given to show how the errors introduced by the plane-wave assumption are related to the waist size of the incident beam and the thickness and relative complex permittivity of the material. Measurement of a Teflon slab is given to further demonstrate the capability of the proposed procedure.