Inverse Problems In The Measurement And Imaging Of Complex Permittivity

The measurement and imaging of complex permittivity have enormous applications both in scientific research and industrial engineering. Mathematically, they are both inverse problems. In this dissertation, we focus on the measurement and imaging methods at RF and microwave frequency.First we discussed about the electromagnetic wave inverse scattering imaging. High contrast scatterer imaging is a difficult problem in this area. In this dissertation, based on the subspace based optimization method (SOM), we further decompose the scatterer image into signal subspace part and noise subspace part, and found the reason of difficulty when applying SOM into high contrast scatterer problem. Moreover, we improved the imaging quality by adding total variation regularization to SOM, which is able to sharpen the edges of image, suitable for blocky scatterer.Then a broadband complex permittivity measurement method is studied, namely the short circuit coaxial line method. By considering the influence of higher order modes using mode matching method, we adopt coaxial discontinuity structure to measure complex permittivity. Compared to the traditional short circuit coaxial line method, the proposed method enables larger sample holder and the fabrication and calibration process is quite easy.At last, based on the concept of coupled magnetic resonance used in mid-range wireless power transfer, we propose a non-contact complex permittivity measurement method. In this method, high-Q resonant coils are used as sensors, through the coupling of resonant coils, impedance matching is achieved. Compared to traditional magnetic induction method, the proposed method has much higher sensitivity and is suitable for measuring small sized and low conductivity samples. By using Rayleigh approximation, a concise relation between the measured impedance and sample’s complex permittivity can be derived. Thus accurate complex permittivity can be retrieved after calibration by measuring one known material.