MODELING AND INVERSION IN NEAR-FIELD MICROWAVE MICROSCOPY AND ELECTRICAL IMPEDANCE TOMOGRAPHY

Abstract

This thesis addresses the modeling and inversion in near-field microwave microscopy (NFMM) and electrical impedance tomography (EIT) problems. Both the modeling and inversion are conducted in the framework of Laplace's equation. Firstly, the thesis presents a complete analysis of tip-sample interaction in NFMM. Secondly, based on the analysis of tip-sample interaction, the thesis proposes a novel forward solver for NFMM. Thirdly, a nonlinear image reconstruction method with total variation constraint in NFMM is presented. Numerical results show that the proposed method can accurately reconstruct the permittivity distribution in three dimensional samples for NFMM. Most importantly, it is found that the resolution has been significantly improved in the reconstructed image. Finally, inversion method is also applied to solve the electric impedance tomography (EIT) problem in a domain with arbitrary boundary shape, and two new inversion methods are presented.