Calibration of a Rotary Encoder and a Polygon Using a Two-Autocollimator Method

In this work, we propose a two-autocollimator method in which all pitch angle deviations of a polygon and angle errors of a rotary encoder can be calibrated simultaneously. A polygon with any number of faces can be calibrated. Any face of the polygon is a measurement cycle of one. Compared to a traditional method, cross-calibration calibrates a rotary encoder and a polygon. This method can simultaneously calibrate all pitch angle deviations of the polygon and angle errors of the rotary encoder. The measurement cycle depends on how many faces the polygon has. There are 24 measurement cycles for a 24-faced polygon. In the experiment, we use two autocollimators to calibrate a 24-faced polygon and the SelfA rotary encoder to conduct the proposed two-autocollimator method. According to the uncertainty evaluation, the expanded uncertainty is 0.46”. For a 95% confidence level, the coverage factor is 2.00. To verify all pitch angle deviations, the shift-angle method, based on cross-calibration, uses one autocollimator to measure the same polygon. The difference in pitch angle deviations is smaller than ±0.28”. The maximum En-value is 0.58. The SelfA rotary encoder comprises 12 read heads and calibrates using self-calibration. The difference in angle errors is smaller than ±0.27”. The maximum En-value is 0.59. The two En-values mean that the proposed two-autocollimator method is practical.