Random error analysis of profile measurement of large aspheric optical surface using scanning deflectometry with rotation stage

Scanning deflectometry method has been successfully employed for the measurements of large flat surfaces with sub-nanometer uncertainty. In this paper, we propose an alternative scanning deflectometry method for measuring large aspheric optical surfaces, wherein a rotation stage is incorporated to increase the measurement range of the high-accuracy autocollimators used to measure small angles. Further, the pitching error of the linear stage is compensated with offline measurement data. In this study, we conducted random error analysis to estimate the measurement repeatability. Our results show that for the measurements of large aspheric surfaces with large slope changes, 10-nm repeatability is achievable under the suitable conditions. To verify the random error analysis results, we also constructed an experimental setup for test the measurement repeatability. The repeatability distribution of the experimental results was in good agreement with the error analysis distribution. We have thus demonstrated the applicability of the random error analysis in the measurement of large aspheric surfaces with high accuracies.