Imaging and inverse problems of electromagnetic nondestructive evaluation

Electromagnetic nondestructive evaluation (NDE) is used widely in industry to assess the character of structures and materials noninvasively. A major aspect of any NDE system is solving the associated inverse problem to characterize the material under study. The solution of the inverse problem is directly related to the physics of a particular electromagnetic NDE system which can be either fully dynamic, quasistatic, or static depending on the operating frequency and material parameters. In a general electromagnetic NDE system, indirect inversion techniques which utilize large amounts of a priori knowledge and some type of calibration scheme are employed to characterize materials. However, in certain test situations the governing physics of an electromagnetic NDE system allow direct inversion techniques to be employed which can be used to image flaws in a material. There has, however, been research which attempts to utilize direct inversion methods which do not rely on the underlying physics of the electromagnetic NDE system;This dissertation first describes the importance of the underlying physics to the solution of the electromagnetic NDE inverse problem. In this context, the inverse problem of fully dynamic electromagnetic NDE and magnetoquasistatic (MQS) NDE are developed to elucidate their underlying mathematical and physical properties. It is shown that the inverse problem for MQS phenomena is generally much more difficult than that of fully dynamic electromagnetic phenomena. Experiments are conducted which utilize fully dynamic millimeter wave NDE and MQS eddy current NDE to compare and contrast the physics and inverse problem of each technique. Two methods are then examined as a possible means of inverting MQS data with direct techniques. A transformation from diffusion to waves is examined as a method of inverting MQS data as a pseudo-wave field. An analytic inversion of the transformation is developed and used to gain insight into robustness issues associated with the method. Also, an averaging scheme is developed to increase the robustness of the transformation. Next, a technique is developed which utilizes phase shifts of steady state eddy current impedance measurements to directly image subsurface flaws in electrically conducting materials. A 1-D analytic study and a 2-D finite element simulation are used to gain insight into the underlying physics associated with the method. A modification to the technique is developed which utilizes the finite element model to account for phase distortions associated with the induced eddy currents in a test sample. An experiment is then carried out to demonstrate this direct inversion technique on actual eddy current data;The results of this study show that the use of direct inversion methods for imaging electromagnetic NDE must be carried out with a clear understanding of the underlying physical phenomena. There are many instances where direct inversion schemes can be applied to fully dynamic electromagnetic fields. Due to physical limitations associated with MQS phenomena, direct inversion methods are not generally applicable to MQS data. However, a transformation technique is shown to be a potential means for utilizing direct inversion techniques on MQS. A second direct inversion technique introduced for MQS data has potential for imaging subsurface flaws in electrically conducting materials. There are, however, severe limitations to both inversion methods which reduce their usefulness

Multi-View Polarimetric Scattering Cloud Tomography and Retrieval of Droplet Size

Tomography aims to recover a three-dimensional (3D) density map of a medium or an object. In medical imaging, it is extensively used for diagnostics via X-ray computed tomography (CT). We define and derive a tomography of cloud droplet distributions via passive remote sensing. We use multi-view polarimetric images to fit a 3D polarized radiative transfer (RT) forward model. Our motivation is 3D volumetric probing of vertically-developed convectively-driven clouds that are ill-served by current methods in operational passive remote sensing. Current techniques are based on strictly 1D RT modeling and applied to a single cloudy pixel, where cloud geometry defaults to that of a plane-parallel slab. Incident unpolarized sunlight, once scattered by cloud-droplets, changes its polarization state according to droplet size. Therefore, polarimetric measurements in the rainbow and glory angular regions can be used to infer the droplet size distribution. This work defines and derives a framework for a full 3D tomography of cloud droplets for both their mass concentration in space and their distribution across a range of sizes. This 3D retrieval of key microphysical properties is made tractable by our novel approach that involves a restructuring and differentiation of an open-source polarized 3D RT code to accommodate a special two-step optimization technique. Physically-realistic synthetic clouds are used to demonstrate the methodology with rigorous uncertainty quantification

Quantitative MR Imaging of the Electric Properties and Local SAR based on Improved RF Transmit Field Mapping

This work presents three new quantitative methods for magnetic resonance imaging. A method for simultaneous mapping of B1 and T1 (MTM) is developed and validated. Electric Properties Tomography (EPT), a method for quantitative imaging of dielectric properties of tissue, is presented. Based on EPT, separate (phase-based) conductivity and (amplitude-based) permittivity measurements are introduced. Finally, a B1-based method for patient-specific local SAR measurements is presented