High-Resolution Electron Microscopy is able to determine structures of crystals and interfaces with a spatial resolution of somewhat less than 2 Å. As the image is strongly dependent on instrumental parameters, notably the defocus and the spherical aberration, the interpretation of micrographs necessitates a comparison with calculated images. Whereas one has often been content with a qualitative comparison of theory with experiment in the past, one is currently striving for quantitative procedures to extract information from the images [1,2]. For the calculations one starts by assuming a static potential, thus neglecting inelastic scattering processes.We shall confine the discussion to periodic specimens. All electrons, which have only been elastically scattered, are confined to very few directions, the Bragg spots. In-elastically scattered electrons, however, can be found in any direction. Therefore the influence of inelastic processes on the elastically (= Bragg) scattered electrons can be described as an attenuation [3]. For the calculation of high-resolution images this procedure would be correct only if we had an imaging energy filter capable of removing all phonon-scattered electrons. This is not realizable in practice. We are therefore forced to include the contribution of the phonon-scattered electrons.
