Radio Frequency Tomography Based Electromagnetic Inverse Scattering For Reinforced Concrete Structures

Radio Frequency (RF) Tomography is proposed to inspect reinforced concrete structures by providing tomographic images of the internal structure. Radio Frequency Tomography has been studied for underground imaging, in particular deeply buried objects such as tunnels or underground facilities. RF Tomography utilizes multi-static measurements which are processed to obtain images of complex dielectric permittivity distribution. RF Tomography is known to have advantages on resolution by use of spatial diversity of sensors contrary to limitation of mono-static configuration which has nominal range resolution criteria and bandwidth. Also, the forward models of RF Tomography are based on volume integral equations that are derived from Maxwell's equations, which leads to the possibility to obtain unique information on material property. Ground Penetrating Radar is widely used to examine the structural health of reinforced concrete structure. This thesis aims to convince one to utilize RF Tomography as inspection and rehabilitation program for reinforced concrete structure. During the discussion, resolution analysis and tomographic examples are provided to show the advantages of RF Tomography. RF Tomography is well studied for simple choices of background medium such as freespace and half-space medium. In order to extend the idea of RF Tomography to reinforced concrete structure, effect of bounded medium must be considered. A forward model for a circular dielectric cylinder is constructed as a numerical example of the supporting pillar structure of a bridge. The forward model uses Born approximation, however the scatter field and propagation due to the dielectric cylinder are included in the forward model. In the chapter on resolution analysis, this thesis focuses on studying achievable resolutions of mono-static and multi-static configurations. In order to achieve the purpose, the level of complexity was reduced in the analysis. A scattered field is found from forward calculation of the forward model instead of actual electromagnetic scattered field. This consideration allows us to analyze only ill-conditioning and achievable resolution of a system matrix. The analysis uses L-curve to determine optimum regularization parameter for Truncated Singular Value Decomposition (TSVD) scheme, and the optimum regularization parameter is used to provide resolution analysis of point spread function (PSF) and Spectral Content. The Chapter on tomographic reconstruction demonstrates the reconstruction of images by RF Tomography. Scattered fields are provided by the Method of Moment numerically and measured experimentally in the Andrew Electromagnetics Laboratory, University of Illinois at Chicago. Tomographic reconstructions of mono-static and multi-static configurations are compared to confirm that multi-static configurations have the advantage on image quality. In addition to TSVD, iterative regularization methods such as Conjugate Gradient method (CG) and Algebraic Reconstruction Technique (ART) are used. The iterative regularization methods allow us to introduce constraints during the inversion process, which ensure the physical meaning of the permittivity.