Dual-space phase retrieval algorithms

A class of algorithms to solve the phase problem in diffraction, which is in crystallography commonly known as the crystallographic phase problem. The phases of the structure factors are retrieved by iterative modifications of the current model in direct space (elecron density) and reciprocal space (structure factors). The disctinction between dual-space algorithms and other phase retrieval methods (direct methods, Patterson method, VLD algorithm) is not clear-cut. However, in dual-space algorithms in the strict sense neither of the two spaces plays dominant role in the phasing process, and it is the alternation between the two spaces that is crucial. The dual space algorithms most relevant to crystallography are:

∙charge flipping algorithm

∙Fienup's hybrid input-output algorithm

∙Elser's difference map

∙Gerchberg-Saxton algorithm, in crystallography known as low-density elimination