Improved methods for the high speed calculation of electron microscopic structure images

The interpretation of high-resolution TEM and STEM images by computer simulation is impeded by the high computer demands of the present computational techniques. In this paper, alternative faster procedures are constructed from higher order expansions of the basic expression for the dynamical electron diffraction amplitudes, by treating scattering and transmission separately in direct, respectively reciprocal space. A first “iterative” method of arbitrary order is very appropriate for thick, perfect crystals where the gain in speed can reach several orders of magnitude when accurate results are required. A second class of methods consists of “slice” methods of various orders. The slowly convergent first-order member of this class appears to be the currently used “multislice” method. However, with only a minor modification it can be transformed into a faster second-order method. Finally a third-order method can be constructed, which proves to be a compromise between order of slices.