General solution for three-dimensional surface structures using direct methods

A general method for solving surface structures in three dimensions using surface x-ray-diffraction data coupled with direct methods is outlined. The method exploits the existence of a support constraint normal to the surface, and couples the concepts of projections, operators, and sets used in the image reconstruction literature with statistical operators used in direct methods. The approach presumes nothing beyond the fact that the scattering comes from atoms, and is a true model-independent approach.