Near-Field Scattering Tomography System for Object Imaging and Material Characterization

Abstract

Electromagnetic inverse scattering based permittivity profile estimation is one of the most promising techniques for object imaging and material characterization. Electromagnetic scattering tomography at the microwaves and THz frequency range can be used for medical imaging since all parts of the human body are naturally non-magnetic and dielectric, and millimeter and submillimeter waves can penetrate inside dielectrics. However, because electromagnetic inverse scattering problems are ill-conditioned and ill-posed, electromagnetic inverse scattering has not yet been successfully implemented in many potential application areas, particularly in clinical imaging. This dissertation presents a new formulation, a novel concept, and an effective implementation procedure to alleviate these problems and hopefully shorten the gap between the current state-of-the-art and real applications and to improve the electromagnetic inverse scattering technique in general.

The major contribution of this dissertation is a new formulation of the electromagnetic inverse scattering problem based on a discrete modal analysis. To do so, the scattered electric field and the volume equivalent current source (VECS) are projected into a subspace spanned by the singular vectors obtained from the spatial Green’s function of the near-field scattering tomography system representation. Differentiating between the significant singular values and the less significant one is an important step. The scattered electric field coefficients are bounded and stable, while the VECS coefficients are not stable in the new subspaces since the singular values of the Green’s function modal representation start decaying very rapidly beyond a certain threshold. Minimizing the mean square error of the estimated scattered electric field or the estimated permittivity profile is used to find the threshold. The singular vectors below the threshold are considered as the radiating singular vectors, so the VECS projected into the radiating singular vectors are called the radiating VECS, and the contrast factor calculated by the radiating VECS are called the radiating contrast factor. The expected radiating contrast factor is constructed by repeating the measurements at different angles and/or frequencies. Then, the radiating permittivity profile and radiating conductivity profile of the object under-test (OUT) are obtained. In fact, the radiating permittivity profile carries important information about the OUT. The experimental results show that the OUT boundary information is embedded into the radiating permittivity profile, and the boundary of the OUT is effectively determined by using the radiating permittivity profile of region of interest.

The second and foremost contribution of this dissertation is proposing a novel approach for solving the electromagnetic inverse scattering problem to make the solution unique by introducing the non-radiating contrast factor and the non-radiating objective function. Decomposing the permittivity into two complementary parts, the radiating permittivity profile and the non-radiating permittivity profile, improves the ill-posedness nature of the electromagnetic inverse scattering problem. Since the radiating permittivity profile is visible, and the non-radiating permittivity profile is invisible from the view point of the outside observer, in the first step, the boundary of the OUT is determined by using the aforementioned radiating permittivity profile obtained from the measurement outside the OUT. Then, the electromagnetic properties of the OUT are estimated – with sufficient accuracy – by minimizing the non-radiating objective function. The electromagnetic properties of the low-contrast and high-contrast OUTs are successfully estimated by the proposed approach, and the approach performance is also verified in a noisy environment through extensive simulations.

The third major contribution of this dissertation is the introduction of a new planar near-field scattering tomography (PNFST) system. The PNFST system calibration and operational procedures are discussed. The proposed PNFST system is the first scattering tomography system implemented at the W-band frequency range in free space. Eliminating the multipath effects in the system enable us to make the incident field measurement process fast and quite effective since the field is measured in the absence of the scatterer only once. The PNFST system reconstructs the radiating permittivity profile of the region of interest, determines the boundary of the OUT, characterizes the material, and provides the electromagnetic properties of the low-contrast and high-contrast OUT. The experimental results validate the performance of the implemented PNFST system.