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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ItemExperimental phase retrieval using coherent X-ray diffraction( 2005-08)Coherent Diffractive Imaging (CDI) has become an increasingly popular frame work in which to solve the classic phase problem in imaging due to benefits in resolution and the facility of collecting data in this modality. In particular, there is considerable interest in using the short wavelength and high coherence of fourth generation x-ray sources with CDI techniques to phase non-crystalline, or nano-crystalline biomolecular samples. CDI provides an opportunity to determine the structure of proteins and other biological samples which are unable to be phased with the standard techniques of protein crystallography, typically due to lack of adequate crystalline samples. Methods of non-crystalline phase retrieval are legion, however many suffer from limitations in resolution or the inability to recover phase fields containing a pathological singularity. Wavefields containing phase singularities are common in optical fields. The creation of an x-ray wavefield containing a pathological phase singularity is demonstrated. In this thesis a form of CDI termed astigmatic diffraction is presented, that is able tophase uniquely this class of wavefield. This is achieved by illuminating the sample with beams containing known phase curvature. The theory of the method and simulations of its application to a nano-crystalline biomolecule are presented. The experimental recovery of the direction of the phase gradient of a sample illuminated with coherent x-rays produced by a synchrotron source is shown to verify this method.