Accurate cells from area-detector images

A procedure is described, for an Eulerian or Kappa goniostat, to determine the exact spindle value φ at the moment of impact of a reflection on an area detector; such information is essential for the calculation of accurate reflection vectors and, eventually, the unit-cell and lattice orientation. The method is based on a comparison of reflection impact coordinates on two related images. One image is obtained by spindle rotation over a few degrees (`φ scan') and the other by the same φ rotation, but with a superposed rotation (χ) perpendicular to the first (`φ/χ scan'). In both cases, the spindle is kept perpendicular to the primary beam, i.e. ω = 0 or 180°. Therefore, on the second image, exactly the same reflections as on the first will appear, but on a different spot on the detector. From the tangential separation between corresponding reflection impacts, the moment of impact (φ value) is calculated. The method is especially useful in small-molecule work, where rather wide scans are required for a reasonable number of reflections in one image. It is shown that for our purpose the Eulerian φ/χ scan can be simulated practically exactly by simultaneous uniform rotations of the axes ω_K, κ and φ_K of the Kappa goniostat.