偏折术中的几何结构标定误差是制约低阶面形测量精度的主要因素。分析几何结构标定中校直误差与平面镜低阶面形测量误差之间的关系,给出描述校直误差与面形测量误差之间关系的灵敏度方程和权重因子,并通过模拟和实验结果对其进行验证。结果表明,校直误差会在面形测量结果中引入倾斜、离焦、像散和彗差等像差项,且面形测量误差与校直误差成正比。本研究有助于选择合适的偏折术系统结构,以提高低阶面形测量精度,同时可为偏折术测量中面形误差的评估和分析提供理论指导。

The geometric calibration errors of deflectometry are the principle factors that limit the precision of low-order surface measurements. In this study, the relationship between the alignment error of geometric calibration and low-order surface measurement error of a flat mirror is analyzed. Further, the sensitivity equations and weight factors that describe the relationship between the alignment error and surface measurement error are introduced and verified using simulations and experiments. The results denote that the alignment errors will introduce tilt, defocus, astigmatism, and coma aberrations to the surface measurement results. Furthermore, the surface measurement errors are observed to be proportional to the alignment errors. This study aids in achieving a system configuration of deflectometry that can improve the accuracy of the low-order surface measurements and provides a theoretical guide for assessing and analyzing the surface measurement errors associated with the deflectometry measurements.