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Figure 4
Geometry considerations in the weighted-measurement approach, based on equations (8)[link] and (14)[link]. (a) The coordinates of neutron detection events (red dots) are stored in reciprocal coordinate space of the goniometer. A grid in (H,K,L) coordinates is obtained through affine transformations by rotating/scaling/skewing the axes (blue grid in the figure – the thick lines correspond to axes along the [{\bf a}^{*}] and [{\bf c}^{*}] crystallographic axes). (b) In the reciprocal space, trajectories for each different detector or sample orientation (green and red curves correspond to some random detector positions or sample orientations) are straight lines, given by equation (14)[link]. The intersections with the reciprocal-lattice grid are obtained from equation (15)[link]. The statistical weight of the scattering from a particular detector, in each voxel, depends on the momentum (wavevector) associated with the intersection of the detector's trajectory with the voxel's boundary. Neither of the trajectories in the figure contribute to voxels with [H\,\gt\,4] and [K\,\gt\,4]. Some voxels, such as the one closest to the origin, contain partial contributions from multiple detectors.

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 55| Part 6| December 2022| Pages 1514-1527
https://doi.org/10.1107/S1600576722009645
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