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A solution to the phase problem of electron diffraction is described which allows an aberration-free atomic resolution image of Si<110>, showing the expected dumbbell contrast, to be reconstructed at a resolution of 3 times the point resolution and 2.5 times the information limit of the scanning transmission electron microscope (STEM) used. The data set required consists of coherent microdiffraction patterns recorded as a function of illuminating probe position and the method of image reconstruction beyond the conventional resolution limits using this data set is described. Using the inherent redundancy in the experimental data set, the accuracy of the reconstructed image is examined and the experimental imperfections that affect it are identified. It is found that aperture charging, compounded by distortions in the detection system, are the major sources of error. As an additional application of this method of phase retrieval, the diffracted-beam phases of electrons that have lost energy by exciting a plasmon are compared with those of elastically scattered electrons in a specimen of graphite. Within the limits of this approach, it is found that there is no difference in the beam phases, supporting the view that electrons that have undergone multiple elastic and inelastic scattering dominate the plasmon-loss scattering at higher angles.
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