Incoherent imaging using dynamically scattered coherent electrons

We use a Bloch wave approach to show that, even for coherent dynamical scattering from a stationary lattice with no absorption, annular dark-field imaging in a scanning transmission electron microscope gives a direct incoherent structure image of the atomic-column positions of a zone-axis-aligned crystal. Although many Bloch waves may be excited by the probe, the detector provides a filtering effect so that the 1s-type bound states are found to dominate the image contrast for typical experimental conditions. We also find that the column intensity is related to the transverse kinetic energy of the 1s states, which gives atomic number, Z, contrast. The additional effects of phonon scattering are discussed, in particular the reasons why phonon scattering is not a prerequisite for transverse incoherence.