PHASE PROBLEM IN CRYSTALLOGRAPHY

Phase recovery from unphased data is the central problem in the interpretation of crystal diffraction data. There are a number of experimental methods for determining phases, and for small molecules computational methods work very well. The problem of developing robust computational methods for large molecules is not yet solved. Most of the approaches for large molecules are variants of the Grechburg-Saxton algorithm [Optik 35, 237-246 (1972)]; with sufficiently good initial phase estimates these converge, but in general they fail with phase stagnation similar to that seen in image processing [J. C. Dainty and J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987); J. R. Fienup and C. C. Wackerman, J. Opt. Soc. Am. A 3, 1897-1907 (1986)].