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

Computational Inverse Problems for Partial Differential Equations

The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges

Photonics simulation and modelling of skin for design of spectrocutometer

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Adaptive finite element methods for fluorescence enhanced optical tomography

Fluorescence enhanced optical tomography is a promising molecular imaging modality which employs a near infrared fluorescent molecule as an imaging agent and time-dependent measurements of fluorescent light propagation and generation. In this dissertation a novel fluorescence tomography algorithm is proposed to reconstruct images of targets contrasted by fluorescence within the tissues from boundary fluorescence emission measurements. An adaptive finite element based reconstruction algorithm for high resolution, fluorescence tomography was developed and validated with non-contact, planewave frequency-domain fluorescence measurements on a tissue phantom. The image reconstruction problem was posed as an optimization problem in which the fluorescence optical property map which minimized the difference between the experimentally observed boundary fluorescence and that predicted from the diffusion model was sought. A regularized Gauss-Newton algorithm was derived and dual adaptive meshes were employed for solution of coupled photon diffusion equations and for updating the fluorescence optical property map in the tissue phantom. The algorithm was developed in a continuous function space setting in a mesh independent manner. This allowed the meshes to adapt during the tomography process to yield high resolution images of fluorescent targets and to accurately simulate the light propagation in tissue phantoms from area-illumination. Frequency-domain fluorescence data collected at the illumination surface was used for reconstructing the fluorescence yield distribution in a 512 cm3, tissue phantom filled with 1% Liposyn solution. Fluorescent targets containing 1 micro-molar Indocyanine Green solution in 1% Liposyn and were suspended at the depths of up to 2cm from the illumination surface. Fluorescence measurements at the illumination surface were acquired by a gain-modulated image intensified CCD camera system outfitted with holographic band rejection and optical band pass filters. Excitation light at the phantom surface source was quantified by utilizing cross polarizers. Rayleigh resolution studies to determine the minimum detectable sepatation of two embedded fluorescent targets was attempted and in the absence of measurement noise, resolution down to the transport limit of 1mm was attained. The results of this work demonstrate the feasibility of high-resolution, molecular tomography in clinic with rapid non-contact area measurements

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

Towards Improved Understanding of Mass Transport in Polymer Electrolyte Membrane Water Electrolysers

The advent of a global societal and governmental movement to curb climate change has put low-carbon technologies at the centre stage of public interest and scientific efforts. In the wake of rising concerns around the carbon footprint of personal mobility and the energy sector, the concept of a ‘Hydrogen Economy’ has experienced yet another rapid spur of popularity. Polymer electrolyte membrane water electrolysers (PEMWEs) are a promising candidate for large-scale hydrogen production, and improvements in the technology have led to increasingly high operational current densities exceeding 2 A cm-2, which requires adequate mass transport strategies to ensure sufficient supply of reactant and removal of products. Optimization and diagnosis of mass transport processes in PEMWEs has long been neglected despite its significance, but the amount of scientific literature has recently increased sharply. This thesis uses existing diagnostic tools to gather new insights into the processes within PEMWE flow channels and liquid-gas diffusion layers, aims at providing new low-cost diagnostic tools to accelerate the investigation of mass transport processes, and consequently deduces novel approaches to the design of PEMWEs components, cells, and stacks. Neutron and X-ray imaging are used to demonstrate the effect of liquid-gas diffusion layer microstructure on the water-gas distribution in a PEMWE, revealing significant inhomogeneity across the active area. Due to cost and accessibility issues around radiation imaging, acoustic methods are explored as alternative diagnostic tools. Acoustic emission is successfully demonstrated as an operando technique to monitor two-phase flow in the flow channels, detecting the transition from bubbly to slug flow. Bubbly flow is observed at the onset of electrochemical activity and low current densities, with a high number of small bubbles, while at higher current densities these small bubbles coalesce and form larger slug bubbles. Lastly, acoustic time-of-flight imaging is used to monitor the water-gas distribution in the liquid-gas diffusion layer and the flow channels, with results being consistent with expectations and previous results obtained via neutron imaging