Derivation by statistical methods of phase information from multiple-wavelength anomalous diffraction data. Basic questions, 'best' electron-density map, implementation and tests

A probability distribution of the structure factor is established from the analysis of the effects of errors involved in the multiple-wavelength anomalous diffraction (MAD) method. This probability distribution, derived from those of the intensities, is two-dimensional for acentric reflections and uni-dimensional for centric reflections. It permits, using the centroid of the distribution, the calculation of the modulus and the phase of the `best' structure factor. The procedure for extracting the phase and its figure of merit is presented. Tests performed on simulated data show the contribution of this method with respect to other methods which use a distribution of only the phase as a function of the error of closure.