Atomic structures by direct transform of diffraction patterns

We propose all the diffraction patterns can be directly transformed to provide three-dimensional atomic structures for the system studied. Depending on the scattering process, either the holography or Patterson transform scheme is used. For diffraction patterns which are generated from a localized emitter source or dominated by an inelastic-scattering feature like core-level photoelectron or low-energy Kikuchi electron, holography transform is needed. On the other hand, for diffraction patterns which were dominated by elastic-scattering, like grazing-incidence X-ray diffraction, electron correlated thermal diffuse scattering or low-energy electron diffraction curves, Patterson transform is needed. To prove our point, high-fidelity and artifact-free three-dimensional atomic structures obtained by transform of low-energy Kikuchi electron patterns and low-energy electron diffraction curves are presented. The future of these direct methods by transforming diffraction patterns will be discussed.