In view of the difficulty in measuring large flat mirrors, this paper introduces a pentaprism system that measures the angle differences between points on the mirror surface with a scanning pentaprism. Based on the angle differences, many equations were established and the mirror surface was expressed through a least squares calculation. The error analysis reveals that the system accuracy was 11.6nm root-mean-square (rms) over a 1.5m flat mirror. Then, the pentaprism measurement was compared with Ritchey-Common test. The comparison shows that the difference between the two results is 10.2nm rms over a 1.5m flat mirror, which is within the error range of the pentaprism system. Thus, the proposed pentaprism system is applicable to the measurement of large flat mirrors.
pentaprism, large flat mirror, tilt angle, angle difference, least squares calculation.
This work was supported by National Natural Science Foundation of China (Grant Nos. 61675198 and 61307114).
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