Direct structure inversion from exit waves. Part I: Theory and simulations

In order to interpret the amplitude and phase of the exit wave in terms of mass and position of the atoms, one has to "invert" the dynamic scattering of the electrons in the object so as to obtain a starting structure which can then be used as a "seed" for further quantitative structure refinement. This is especially challenging in case of a zone axis condition when the interaction of the electrons with the atom column is very strong. Based on the channelling theory we will show that the channelling map not only yields a circle on the Argand plot but also a circular "defocus curve" for every column. The former gives the number of atoms in each column, while the latter provides the defocus value for each column, which reveals the surface roughness at the exit plane with single atom sensitivity.