OBTAINING THE CRYSTAL-POTENTIAL BY INVERSION FROM ELECTRON-SCATTERINGINTENSITIES

A method to obtain the crystal potential from the intensities of the d iffracted beams in high-energy electron diffraction is proposed. It is based on a series of measurements for specific well determined orient ations of the incident beam, which determine the moduli of all element s of the scattering matrix. Using unitarity and the specific form of t he scattering matrix (including symmetries), an overdetermined set of non-linear equations is obtained from these data. Solution of these eq uations yields the required phase information and allows the determina tion 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} s ystematic row case in ZnS and a [110] zone-axis orientation in GaAs (b oth noncentrosymmetric crystals).