Phase retrieval methods for surface x-ray diffraction

We develop an iterative input-output feedback method for the phasing of surface x-ray diffraction (SXRD) amplitudes that relies on successive operations in real and reciprocal space. We demonstrate its use for the recovery of the real and positive electron density of a surface unit cell from simulated SXRD intensities. We have successfully recovered the entire surface electron density in a case where the two-dimensional surface unit cell is the same as that of the bulk and also in one where the surface unit cell is four times larger than chat of the bulk. We show that the exponential modelling algorithm for structure completion derived earlier from maximum entropy theory may be regarded as a special case of an input-output phasing algorithm with a particular form of object-domain operations.