Imaging with Diffraction Tomography

The problem of cross sectional (tomographic) imaging bf objects with diffracting sources is addressed. Specifically the area of investigation is the effect of multiple scattering and attenuation phenomena in diffraction imaging. This work reviews the theory and limits of first order diffraction tomography and studies iterative techniques that can be used to improve the quality of tomographic imaging with diffracting sources. Conventional (straight-ray) tomographic algorithms are not valid when used with acoustic or microwave energy. Thus more sophisticated algorithms are needed; First order diffraction tomography uses a linearized version of the wave equation and gives an especially simple reconstruction algorithm. This work reviews first order approximations to the scattered field and studies the quality of the reconstructions when the assumptions behind these approximations are violated. It will be shown that the Born approximation is valid when the phase change across the object is less than it and the Rytov approximation is valid when the refractive index changes by less than two or three percent. Better reconstructions will be based on higher order approximations to the scattered field. This work describes two fixed point algorithms (the Born and the Rytov approximations) and an algebraic approach to more accurately calculate the scattered fields. The limits of each of these approaches is discussed and simulated results are shown. Finally a review of higher order inversion techniques is presented. Each of these techniques is reviewed and some of their limitations are discussed

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