Obtaining the crystal potential by inversion from electron scattering intensities

A method to obtain the crystal potential from the intensities of the diffracted beams in high-energy electron diffraction is proposed. It is based on a series of measurements for specific well determined orientations of the incident beam, which determine the moduli of all elements of the scattering matrix. Using unitarity and the specific form of the scattering matrix (including symmetries), an overdetermined set of non-linear equations is obtained from these data. Solution of these equations yields the required phase information and allows the determination of a (projected) crystal potential by inversion that is unique up to an arbitrary shift of the origin. The reconstruction of potentials from intensities is illustrated for two realistic examples, a {111} systematic row case in ZnS and a [110] zone-axis orientation in GaAs (both noncentrosymmetric crystals).