Three-dimensional contrast in dark-field images

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Abstract
It is shown that, under suitable conditions of N-beam interaction, distinctive contrast is obtained from crystal surface detail in the dark-field image which allows edges or steps on the upper (beam-incident) surface to be distinguished from those on the lower (beam-emergent) surface. The ability to distinguish between the orientations of apex up, and apex down, for a crystal of triangular cross-section is shown to derive from a break-down of Friedel's law which results from the imaging process. An interpretation is given in terms of an extended charge-density approximation’ using the theory developed by Moodie for interpretation of aperiodic features in the bright-field image. Illustrations are from [111] orientations of MgO cubes, although this technique is expected to be of more general application.