On least-squares refinement of the phases of crystallographic structure factors

A least-squares technique for direct refinement of the phases of structure-factors of crystals which obey the equations a_hF_h = F_kF_{h - k} is described. It is shown by tests carried out under somewhat idealized conditions that the initial phases need not be of a completeness or accuracy sufficient to resolve the atoms of the structure. The technique may be able to provide a bridge in protein crystallography and structure determination generally between preliminary phasing techniques and final refinement of atom parameters.