  Solving crystal structures from kinematical X-ray or electron diffraction
patterns of single crystals requires many more diffracted beams to be recorded
than there are atoms in the structure, since the phases of the structure
factors can only be retrieved from such data if the atoms can be resolved as
sharply peaked objects. Here a method is presented by which the fact that
multiple scattering encodes structure factor phases in the diffracted
intensities is being used for solving the crystallographic phase problem. The
retrieval of both amplitudes and phases of electron structure factors from
diffraction patterns recorded with varying angle of incidence will be
demonstrated. No assumption about the scattering potential itself is being
made. In particular, the resolution in the diffraction data does not need to be
sufficient to resolve atoms, making this method potentially interesting for
electron crystallography of 2-dimensional protein crystals and other
beam-sensitive complex structures.
