Application of a segment description of the unique set of reflections to data collection and data reduction

The relationships h₁ = h₀ + Δhn and n = Δh⁻¹(h₁ − h₀) [Gabe (1969). In Crystallographic Computing, edited by F. R. Ahmed. Copenhagen: Munksgaard], establishing the correspondence between the crystal indices h₁ and the segment indices n of a given reflection, can be used to generate the reflections in the unique set, decide whether a reflection belongs to the unique set, find the unique indices of a given reflection and check the correctness of the segment data Δh and h₀. These relationships have been used as the basis of the index generation scheme of the NRC diffractometer program to collect intensity data as a sequence of symmetry-related sets and as the principle of the ordering algorithm of a data reduction program which can treat all symmetries including the trigonal symmetries in rhombohedral cells without the requirement of any special logic.