Automatic indexing of oscillation images

Abstract

The first step in indexing an oscillation diffraction pattern is to determine the position of diffraction maxima and to record their coordinates on the detector relative to the camera axes. These coordinates can then be transformed into reciprocal-lattice coordinates assuming a zero rotation angle. These positions are then projected onto a vector emanating from the crystal position. If this radius vector is chosen perpendicular to a principal set of reciprocal-lattice planes for the given crystal setting, then a plot of the frequency of the projected reflections onto the vector will show a regular set of equally spaced maxima. These will correspond to the intersection of reciprocal-lattice planes with the selected radius vector. All possible directions, separated from each other by small incremental angles, are tested. One-dimensional Fourier inversion of each of the frequency plots identifies those directions that intersect widely spaced reciprocal-lattice planes, corresponding to principal reciprocal axial directions. Thus the orientation and lattice repeats of the crystal axes will have been determined relative to the camera axes. These parameters can be converted into a 3 × 3 crystal-setting matrix, [A], which relates Miller indices to reciprocal-lattice coordinates. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.