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

Spectrally Resolved Absorption Tomography for Reacting, Turbulent Gas Phase Systems: Theory and Application

This work proposes tomographic absorption spectroscopy as a complementary measurement method to other non-intrusive methods that are applied in the research of reactive gas-phase flows. A coherent methodological framework based on conventional Bayesian inference is presented, that contains new methods and improvements in several key procedures. The framework relies on linear hyperspectral absorption tomography, that is favored for its higher computational efficiency compared to nonlinear tomography, and separates tomographic reconstruction and spectroscopic regression. The methods target the analysis of direct absorption spectroscopic measurements like direct tunable diode laser absorption spectroscopy. The improved key procedures include a spatial resolution measure based on a modified Maximum-a-posteriori covariance matrix. This resolution measure is applicable to sparse and dense beam arrangements alike, without inconsistencies arising from unprobed mesh nodes. The compatibility with resolution measures based on point spread functions is demonstrated in simulations. Additionally, the design question of the spatial-temporal resolution trade-off is discussed on spatio-temporal correlation maps with a constraint imposed by the effective measurement data-rate. Typical data-rates of spectrally resolved tomographic absorption spectroscopy setups often do not allow for capturing turbulent structures. In consequence, the optimum trade-off for quasi-stationary systems often is the focus on spatial resolution, neglecting temporal resolution. A regularization parameter choice method, relying on residuals of the spectroscopic regressions, is introduced. The idea is to balance noise amplification through under-regularization, and incompatibility with the spectroscopic model through excessive spatial-averaging of temperature structures due to over-regularization. This method allows to partially reclaim the informative advantage of nonlinear tomography, by inferring information on temperature structures from the nonlinear temperature dependence of the spectroscopic model. The selected prior parameters are shown to result in spatial resolutions matching spatial structures in the application cases. The same model error used to judge the compatibility with the spectroscopic model for parameter selection, leads to a temperature bias if temporally averaged data of a turbulent system is fitted by a homogeneous spectroscopic model. Ideas from methods to prevent this bias in spatial averaging are transferred to temporal averaging. The resulting temperature fluctuation model reduces the bias and additionally gives a qualitative measure of temperature fluctuations. The often neglected problem of estimating absorbance spectra from intensity traces is treated with Bayesian inference. This new Bayesian absorbance estimation method is shown to be numerically efficient if large numbers of absorbance traces are to be inferred like in tomography. Unlike fitting methods it is compatible with inhomogeneous line-of-sights without modification or computational penalties. Further, the incident intensity shape is not restricted to arbitrary model functions, but modeled with all degrees of freedom. The framework of methods is applied to practically relevant scenarios in the industrial characterization of selective catalytic reduction systems, and in the research of oxy-fuel combustion. The application cases feature different levels of complexity, with turbulent and laminar flows, stationary and instationary processes, axisymmetric and two dimensional flows, as well as homogeneous and inhomogeneous temperature distributions. Also the scalability of the methods is demonstrated by experiments with beam counts from 8 to 10440, and (pseudo) temporal resolutions of up to 5 kHz. For all application cases a specific discussion of uncertainty and spatial resolution is provided

Radar Imaging in Challenging Scenarios from Smart and Flexible Platforms

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Cosmic Microwave Background and Large Scale Structure: Cross-Correlation as seen from Herschel and Planck satellites

As well as providing us with a snapshot of the Universe at the time of recombination, the cosmic microwave backround (CMB) radiation carries a wealth of information about the later evolution of the Universe through the so-called CMB secondary anisotropies that originates from the interaction between CMB photons and the Large Scale Structure (LSS). This thesis deals with two of these effects: the CMB lensing and the kinematic Sunyaev-Zel'dovich (kSZ). In particular, we present the first cross-correlation analysis between the CMB lensing maps reconstructed by Planck team and the angular position of galaxies from the Herschel H-ATLAS survey, the highest redshift sample exploited for cross-correlation analysis to date. By splitting the galaxy catalog in two redshift bins, we also attempt a tomographic analysis of the signal and reconstruct the galaxy bias evolution over cosmic time. On the other hand, the kSZ effect measures the integrated free electron momentum up to high redshift, thus being sensitive to the cosmic flows and the reionization history. Here we study its capabilities in constraining theories of modified gravity

Laboratory Studies of the Electromagnetic Properties of Saline Ice: A Multi-disciplinary Research Plan Submitted to the Office of Naval Research

This plan describes laboratory and theoretical research to be carried out under the Sea Ice Electromagnetics Accelerated Research Initiative of the Office of Naval Research. The plan is built around three broad objectives: 1) to understand the mechanisms and processes that link the orphological/physical and the electromagnetic properties of sea ice; 2) to further develop and verify predictive models for the interaction of visible, infrared and microwave radiation with sea ice; 3) to develop and verify selected techniques in the mathematical theory of inverse scattering that are applicable to problems arising in the interaction of EM radiation with sea ice. The plan will be executed by over 30 investigators from 15 institutions. Research includes measuring and quantifying the physical properties of sea ice, collecting radiometric signatures of different ice types and morphologies, developing and testing forward models of scattering and emission from sea ice, and developing and testing inverse models to extract geophysical data about sea ice from remotely sensed data. Experiments will begin in January of 1993 at the Cold Regions Research and Engineering Laboratory in Hanover, New Hampshire. Work will focus around studies on the Geophysical Research Facility which is a new, concrete lined pool filled with saline water. The facility can be shielded from local fluctuations in weather by using a movable roof and refrigerated blanket. Three measurement series are planned for the winter of 1993. These will focus on collecting data on the microwave and optical properties of an undeformed ice sheet grown from the melt. Measurements to resolve the contributions of volume and surface scattering to sea ice signatures will be performed on an artificially roughened ice sheet. A snow covered ice sheet will be created to study the effects of brine wicking and scattering from snow grains on electromagnetic signatures. Data from these measurements will be used to evaluate the performance of existing forward models. The data will also be used to begin the development of inverse models.The Office of Naval Researc