Multi-pitch self-calibration measurement using a nano-accuracy surface profiler for X-ray mirror metrology

For high accuracy X-ray mirror measurement, the analysis and corrections of minute systematic errors of the measuring instrument are required. As an X-ray mirror metrology tool, the nano-accuracy surface profiler (NSP) consists of two autocollimators (AC) serving its reference and sample beams, in which the sample-beam AC maintains a fixed distance from the mirror. In this work, the multi-pitch self-calibration method is applied to an NSP instrument to reconstruct both the mirror slope and the instrument error of the sample-beam AC through a series of x scans and pitch angle scans. It is more technically sound to apply this multi-pitch self-calibration method to a working-distance-fixed slope scanner, such as the NSP. First of all, we introduce the principle of the multi-pitch self-calibration method, discuss its ambiguities, and provide our regularization illustrated with simulations. Second, some real measurements of a spherical mirror with 10-mrad total slope are demonstrated to verify the effectiveness of the multi-pitch self-calibration technique with an NSP. Furthermore, the experimental reconstruction of the low- and high-frequency signals of the instrument error with different settings in x and pitch steps are addressed and studied in terms of repeatability, reproducibility, self-consistency, and effectiveness in compensation for single-pitch scans.