Recursive direct phasing with reference-beam diffraction

The reference-beam diffraction technique provides a practical way to measure a large number of triplet phases in a standard oscillating-crystal diffraction experiment for protein crystals. The triplet-phase data set from such reference-beam measurements contains a unique phase-ocurrence pattern that leads to a new recursive phasing algorithm for the individual structure-factor phases. Application of the new algorithm is demonstrated for tetragonal lysozyme using 7360 triplet phases measured in a reference-beam experiment with a median phase discrepancy of 45°. An electron-density map obtained using this phasing algorithm and the measured triplet phases shows good agreement with the known protein structure.