School of Physics - Theses
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ItemStudies in phase and inversion problems for dynamical electron diffraction( 2003)This thesis examines problems in electron diffraction and related areas of theoretical optics. It begins with a study of the phase of a quantum mechanical wave function and the behaviour of phase vortices and vortex cores. Several rules for vortex core evolution are given and simulated vortex trajectories are studied. These simulations show that in electron microscopy at atomic resolution and in other similar situations, vortices occur in the wave functions very frequently. This means any image processing methods which deal with the wave function phase must permit vortices to occur. In this context a number of methods of phase retrieval are compared and evaluated. The criteria of evaluation are the accuracy of the phase retrieval, its ability to cope with vortices, its numerical stability and its required computational resources. The best method is found to be an iterative algorithm similar in approach to the Gerchberg-Saxton method, but based on a through focal series of images. Using this phase retrieval method as an essential tool, the thesis continues with a study of inverse problems in electron optics. The first problem considered is that of using a set of images taken to characterise the coherent aberrations present in a general imaging system. This problem occurs in many areas of optics and is studied here with a focus on transmission electron microscopy. A method of using software to simultaneously determine aberrations and subsequently remove them is presented and tested in simulation. This method is found to have a high level of accuracy in aberration determination. The second inverse problem studied in this thesis is the inversion problem in dynamical electron diffraction. This problem is solved for a periodic object, giving an accurate and unique solution for the projected potential in the multiple scattering case. An extension of this solution to objects which are non-periodic in the direction of the incident wave is investigated. Finally a model computation solving the general inversion problem for dynamical diffraction in an aberrated transmission electron microscope is performed, illustrating this and previous material and summing up the advances presented in this work.
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ItemSpatial coherence measurement of undulator radiation using uniformly redundant arrays( 2003)Synchrotron light source are accelerating research and development and fueling innovation in a wide range of research disciplines and industries worldwide. The third-generation synchrotron radiation facilities such as Advanced Photon Source (APS), produce ultra-brilliant x-rays using insertion devices consisting mainly of undulators, which provide exciting opportunities for advanced research into materials, earth science, life science, and medicine. Using high brightness x-ray radiation with high spatial coherence, unique coherence-based experiments are now becoming possible: coherence imaging techniques such as phase contrast imaging, holography, and tomography, are under intensive development, opening up a range of new areas of investigation. At the same time some useful optical elements used in the synchrotron radiation system have been created rapidly. Crucial to the development of all these fields is some knowledge of the spatial coherence of the light produced by these sources. In other words, the characterization of spatial coherence is a high priority. The aim of this project is to develop a theoretical and experimental program to allow the measurement of the spatial coherence of synchrotron radiation. A technique to measure the spatial coherence of x-rays from undulators is presented. The essence of the coherence measurement technique is based on the interpretation of a complex diffraction pattern. We measure the spatial coherence function of a 7.9 keV x-ray beam from an undulator at a third-generation synchrotron (APS) using a sophisticated diffracting aperture known as a Uniformly Redundant Array (URA). The URA was also used to measure the spatial coherence function for soft x-rays at the APS. When a traditional Young’s double-slit experiment is used to test the degree of coherence, the separations of the two-slit have to be changed repeatedly to full map the spatial coherence function. The URA is a complex aperture consisting of many slits, (or, for a two-dimensional array, pinholes), organized such that all possible slit separations occur, and do so with exactly the same frequency. One might regard the URA as able to simultaneously perform many Young’s experiments a precisely equal number of times across the full range of slit separations permitted by the overall size of the URA. Therefore one experiment using a one-dimensional (1D) URA can perform the equivalent of multiple double-slit experiments. The diffraction theory developed in this thesis a convenient theoretical basis for interpreting this diffraction pattern.