Section 19.5.6.1. Coordinate transformation

Data must be transformed from detector space into reciprocal space (Fraser et al., 1976). Transformation of coordinates requires determination of the origin of the diffraction pattern in detector space, the fibre tilt angle β, the twist angle (often called in-plane tilt, the inclination of the projection of Z along the beam to the detector coordinate system) and the specimen-to-detector distance. It may also require determination of the detector mis-setting angles (the deviation of the normal to the detector plane from the beam). All of these parameters can be determined by comparing equivalent reflections in the diffraction pattern.

Most data-processing programs determine the transformation parameters by some form of minimization of the deviation from equivalence in the positions of well resolved equivalent reflections. The tilt was traditionally determined by comparing the apparent Z values of equivalent reflections, but the apparent value of R for near-meridional reflections is much more sensitive to tilt. The minimization set should therefore include some near-meridional reflections if the tilt value is to be determined accurately. The helical repeat distance and, for polycrystalline fibres, the unit-cell parameters must also be determined at this time, but helical repeat distance and specimen-to-detector distance are so highly correlated that it is not often practical to refine both.