Computational methods of approaching the inverse problem for electron diffraction

This thesis describes four distinct computational approaches for retrieving information from Convergent Electron Beam Diffraction (CBED) patterns. Firstly, phase retrieval techniques have been used to invert one dimensional rocking curves to obtain strain profiles. The inherent problems of multiple minima are outlined and it is demonstrated how these may be overcome in certain cases. Using this technique, experimental rocking curves from inclined ion-thinned and chemically thinned samples have been inverted and it has been shown that ion thinning does indeed induce dilation of surface layers, attributable to Ar implantation. Secondly the Zone Axis Pattern matching (ZAPMATCH) technique has been used to refine the low order x-ray structure factors of Ni, Cu and Cr. It has been demonstrated that the ZAPMATCH routine can be successfully applied to metallic samples, and the structure factors measured are in good agreement with other published values. Recent advances in the area of blind deconvolution have been rapid and we have attempted to apply a recent advance to a deconvolute a simulated CBED disc. It has been demonstrated that it is not possible to use current techniques on experimental data. Finally a new method for quantitatively assessing symmetry breaking in experimental images has been developed and its use has been demonstrated on a variety of different data sets. (author)