A general Lorentz correction for single-crystal diffractometers

A single-crystal Lorentz correction is derived for the case of a general scan through an out-of-plane reflection on a four-circle diffractometer with relaxed sample-to-detector collimation. When the Lorentz correction is expressed in terms of the incremental steps in the Eulerian setting angles, structure amplitudes observed by different scan trajectories, for example, some angular in real space and others linear in reciprocal space, are put on a common scale, and errors due to known missetting of the angles or rounding off of the angles are avoided.