A simple intuitive theory for electron diffraction

It is shown that the dynamical diffraction can simply be described in real space using the property that electrons are trapped in the electrostatic potential of the atomic columns. Due to this channelling effect, the electron diffraction can be highly dynamical inside each column, and at the same time retain a one-to-one relationship with the crystal structure. This description does not require the crystal to be periodic. Influence of adjacent columns can be treated using a perturbation theory. If the crystal is sufficiently thin, i.e. of the order of 10 nm, and the accelerating voltage is not too high (e.g. 100-300 keV), the motion of the electrons is almost perfectly periodic with depth. The theory shows how the depth periodicity is related to the mass/thickness of the column which allows the exit wavefunction to be parametrized in a simple analytical form. These results open perspectives to solve the inverse problem of how to derive the projected structure of the object from the exit wavefunction.