Angle and index calculations for `z-axis' X-ray diffractometer

Closed formulas are given for the calculation of the orientation matrix and the angles for a given reflection in a `z-axis' diffractometer geometry. These equations are derived for the conditions where the angle of incidence of the primary beam to the surface of the crystal is specified. Comparison is made with the standard four-circle configuration and the differences between these two geometries are evaluated. Some further applications are discussed.