Angle calculations for a z-axis/(2S+2D) hybrid diffractometer

Efficient use of any diffractometer design requires easy translation between points in reciprocal space and the setting of diffractometer angles. While it is reasonably straightforward to go from angle to reciprocal space, the opposite direction presents more challenges. In this paper, angle calculations are presented for a new 'hybrid' diffractometer consisting of a base instrument that can be combined with two different detector arms. With one of the detector arms, the instrument is a standard z-axis diffractometer as commonly used in surface studies. The other detector arm is designed for a heavy two-dimensional detector. The calculations are formulated in a general framework making it easy to incorporate, e. g. a second sample rotation stage, whereby it is possible to perform reflectivity and standard surface-crystallography measurements in the same geometry.