Convenient off-line error quantification and characterization of concentricity of two circles of rotation for diffractometer alignment

To ensure concentricity of the θ–2θ rotation stages, but with a very limited 2θ range of rotation, an alignment technique using two dial gauges mounted at right angles to each other (X and Y axes) is described. The deflections of the orthogonal dial gauges are measured as a function of 2θ, with their probes impinging on a cylindrical pin centred on the θ axis. The X and Y corrections required to bring the two rotation stages into concentricity can then be found using a least-squares fitting via a freestanding program or via the `solver' optimization within the Microsoft Excel spreadsheet software. The same dial gauges provide guidance for applying the required positional corrections. An Excel spreadsheet for determining the X and Y corrections via least squares has been deposited.