The use of phase relationships between quartets of reflexions

Phase relations between quartets of reflexions can be found either directly from a generalized Hughes expression or by elimination of the phase of a reflexion common to two Σ₂ relationships. By combining the information from both types, strengthened quartet relationships (SQR) can be constructed, which are comparable to the Σ₂ relations in reliability and number. Most of the reliable SQR's involve the strong reflexions only. The phases of these reflexions are related by a highly overdetermined system of equations leading in a simple manner to a good starting set.