Bootstrap calibration of an autocollimator, index table and sine bar ensemble for angle metrology

摘要

An in-situ bootstrap method used at NRC to calibrate an ensemble of instruments for angle metrology traceable to international standards for angle and length is described. No prior knowledge is assumed, beyond nominal values with arbitrary large uncertainty, for the index-table step angles, the autocollimator scale factor, and the sine-bar length. Only the sine-bar displacements are known as calibrated values with uncertainty traceable to the SI unit for length. First, the nominal-length sine-bar is used to check the autocollimator linearity, stability, and estimate a nominal scale factor, thus giving a first-iteration improvement in the uncertainty of autocollimator readings. Then, the index table (and a polygon) are measured by a full-closure method at the polygon intervals, and index steps of one interval are measured by the caliper method, with results expressed using improved autocollimator readings. This provides improved index angles. Finally, the autocollimator beam is aimed obliquely at the sine-bar mirror, and the beam deflects to the index-table mirror, where it retroreflects back to the autocollimator via the sine bar. As the index table is stepped through a sequence of angles (with improved uncertainty), the sine-bar angle is adjusted in opposite rotation to produce a zero reading by the autocollimator, and the required sine-bar displacement recorded. This provides a better estimate of the sine-bar length. The steps can be re-iterated--hence bootstrap--to further improve the calibration of each device, until a limit is reached. In recent years, we have linked the data from the three setups in a single spreadsheet analysis, allowing the calibration variables to be jointly and optimally adjusted with just one data run through the three setups. Results using a Moeller-Wedel Elcomat HR autocollimator, a Moore 1440 index table and the NRC sine-bar interferometer are presented, along with an uncertainty analysis.