Dyadic Contrast Function and Quadratic Forward Model for Radio Frequency Tomography

Radio Frequency Tomography is an underground imaging technology that aims to reconstruct extended, deeply buried objects such as tunnels or Underground Facilities (UGF). A network of sensors collects scattered electromagnetic field samples, which are processed to obtain 2D or 3D images of the complex dielectric permittivity profile of the volume under investigation. Unlike systems such as Synthetic Aperture Radar (SAR) or Ground Penetrating Radar (GPR) which normally employ wide-band pulses, RF Tomography uses Continuous Wave (CW) signals to illuminate the scene. The information about the target is not retrieved by relying on bandwidth but by exploiting spatial, frequency and/or polarization diversity. Interestingly, RF Tomography can be readily adapted to obtain images of targets in free space. In this context, in the Andrew Electromagnetics Laboratory of the University of Illinois at Chicago, a measurement system aimed to validate experimentally the performance of RF Tomography has been designed and built. Experimental data have been used to validate its forward model, different inversion algorithms, its performance in terms of resolution and the ability of the system to distinguish between metallic and non-metallic targets. In the specific case of imaging of metallic targets, this thesis proposes to extend the capabilities of RF Tomography by introducing a dyadic permittivity contrast. Electromagnetic scattering from a thin, wire-like object placed in free space with its main axis at an angle with respect to the incident electric field is studied. It is possible to show that for this configuration a fundamental difference exists between a metallic and a dielectric object. This phenomenon can be modeled into Maxwell’s equations by using a dyadic permittivity contrast, as it is commonly done when studying crystals. As a result a new formulation of the RF Tomography forward model is obtained, based on a dyadic contrast function. Reconstruction of this dyad allows to estimate not only the location and shape, but also the spatial orientation of the target. In addition, this dissertation proposes an alternative modification of the forward model which removes some limitations caused by the Born approximation. Traditionally, the Born approximation is used to linearize the inherently non-linear forward model. This approximation is valid if the scatterer is small and does not interact strongly with other objects. A quadratic forward model represents a more correct formulation of the scattering phenomenon, and it allows to attempt quantitative reconstruction. Numerical results are presented to highlight the advantages that such a formulation provides over the Born approximation.