Improving triplet-phase accuracy by symmetry observations in reference-beam diffraction measurements

The reference-beam X-ray diffraction technique allows parallel measurements of many three-beam interference profiles in a modified rotating-crystal experiment. Because of the unique symmetry relations that exist in the reference-beam geometry, a complete 360° rotation leads to a fourfold redundancy of any given triplet phase δ_H involving primary reflection H, reference reflection G and coupling reflection H−G, measured in a data set. Two such redundant measurements correspond to simple duplications with the reciprocal node H going into and coming out of the Ewald sphere, while the other two correspond to the Friedel mate G−H of the coupling reflection H−G passing through the Ewald sphere in a similar fashion. It is shown that substantial differences may exist between the H and the G−H cases, with an enhanced triplet-phase interference effect in one of them. These symmetry-related observations, coupled with inverse-beam triplet measurements, would improve the phase measurement accuracy of the reference-beam diffraction technique.