Determination of pole figure coverage for texture measurements with neutron time-of-flight diffractometers

The coverage of a given diffraction instrument as a percentage of the area 2 pi of a pole figure hemisphere is a crucial parameter of each diffraction instrument used for texture or strain pole figure determination. On the basis of this knowledge, the number of rotations and rotation angles for a full determination of the orientation distribution function can be optimized. However, the determination of this quantity is non-trivial. This paper presents a method that projects a given detector coverage into pole figure space, i.e. outlines the detector areas in a pole figure, and then determines the fraction of the entire 2 pi pole figure hemisphere around the sample that is covered. The freely available Generic Mapping Tools (GMT) and ImageJ are utilized for this quantification. With this method, it is shown that the empirically determined rotation angles for the HIPPO neutron time-of-flight diffractometer are close to optimal for a set of three rotations.