The SAS Maximal Principle: a New Approach to the Phase Problem

The phase problem, when single-wavelength anomalous scattering (SAS) diffraction data are available, is formulated as a problem in global optimization. Although the objective function has a myriad of local maxima, its global maxima, never more than two, are readily accessible and easily identified by virtue of their isolation. The ability to determine the global maxima of the objective function represents the latest and most successful attempt to go directly from the known probabilistic estimates of the three-phase structure invariants to the values of the individual phases. The relationship between the maxima of the objective function and the solutions of the newly formulated system of SAS tangent equations plays a key role in this development.