Characterized environmental influences on autocollimator measurement uncertainty using an extended Allan variance

•This paper proposes the extended Allan variance to characterize environmental influences on the AC measurement uncertainty based on a point-wise scanning measurement mode.•Based on the characteristic curve parameters, the number of averages (N) was optimized using statistical features to realize an optimization strategy for random and drift error suppression.•Suppress the time-varying error caused by the change of environmental factors of the autocollimator, so that the measurement accuracy is decreased from 15nrad rms to 2.3nrad rms. Autocollimators play an important role in the high-precision testing of the slope errors of X-ray and large flat mirrors. However, the time-varying errors caused by environmental changes exhibit different characteristics over time, such as low-frequency drift errors and high-frequency random errors. Time-varying errors can seriously affect the accuracy of the autocollimator (AC) and the read repeatability. They have become important factors limiting the continued improvement of nano-optic-measuring machines and scanning pentaprism system accuracy. Considering the difficulty in quantitatively analyzing the influence of time-varying errors on the measurement uncertainties of the AC, this paper proposes the extended Allan variance to characterize environmental influences on the AC measurement uncertainty based on a point-wise scanning measurement mode. Taking advantage of the extended Allan variance's characteristics, which allow the identification of various errors and provide stability information about the AC measurement, the characteristic curves of the AC measurement uncertainty in a specific environment were obtained. Based on the characteristic curve parameters, the ultimate accuracy of AC in the current environment was obtained by optimizing the measurement strategy. Experimental results show that the measurement uncertainty of the AC can reach 2.3 nrad RMS in the measurement time-domain window.