Sufficient Conditions for Direct Methods with Swift Electrons

We investigate cases where one can argue that sufficient conditions exist for Direct Methods to work with swift electrons. In addition to simple cases where kinematical scattering holds (e.g., surfaces in plan view), we identify three other configurations: (a) when 1s channeling holds and kinematical scattering is statistically correct; (b) when there is a mapping from kinematical to dynamical intensities that preserves the order of the intensities, for instance with powder or precession data, and (c) when the scattering is dominated by one type of atom. We also briefly discuss the possibility of using Direct Methods to restore the complex exit wave leaving a sample in the most general case.