Solving the structure completion problem in surface crystallography Original Research Article

Measured intensities of short-wavelength radiation diffracted from a crystal surface contain a contribution from the known bulk structure and the unknown surface structure. The recovery of the diffracted amplitude from the unknown surface from the experimental intensity measurements and from calculated amplitudes from the known bulk (treated as a reference wave) is closely analogous to holography, or to the structure completion problem in bulk crystallography. We show how an algorithm based on ideas of Bayesian statistics enables the direct recovery of the surface electron density from simulated surface X-ray diffraction data.