三坐标检测光学元件曲率半径的误差分析

对光学元件曲率半径的通用检测方法进行评估,理论分析了三坐标系统检测元件曲率半径误差的主要来源、分布以及总和,并通过与激光干涉仪测量结果的对比,明确了三坐标测量系统的检测精度,为铣磨加工阶段进一步修正光学元件曲率半径提供数据支持。首先介绍了三坐标系统检测曲率半径的基本原理,对测量误差的主要来源进行简单分析,获得三坐标系统测量曲率半径的不确定度;阐述了激光干涉仪测量曲率半径的基本原理以及误差来源,并计算了测量不确定度,证实激光干涉仪的理论测量精度优于三坐标系统。然后利用三坐标系统对简单抛光后的F数分别为2.17、1.45、0.923的光学元件进行实际测量,并与激光干涉仪的测量结果进行了比较。最后,对实验结果与理论计算结果进行对比。论文研究结果确定了三坐标系统测量光学元件曲率半径的不确定度,证实了利用三坐标测量曲率半径满足铣磨加工阶段的要求,能够为铣磨加工提供指导;同时研究发现,随着光学元件F数的增加,三坐标和激光干涉仪的测量误差都有增大的趋势。

Error analysis of optical element curvature radius measured by CMM

The paper evaluates the existing detection method for curvature radius, analyzes the origin, the distribu-tion and the summation of measurement error of optical element curvature radius in theoretic, and then demonstrates the measurement precision of Coordinate Measuring Machine（ CMM） through contrast the measurement result from CMM and laser interferometer, provides date auspice for optical element curvature radius correcting in grinding. And this paper introduces the basic principle of curvature radius measurement using CMM , analyzes the error sources.Finally, we get the measurement uncertainty of the curvature radius using PMAC Ultra CMM by error syn-thesis.Also the paper introduces the basic principle of curvature radius measurement using laser interferometer which is 12 inch VWS made by ZYGO, analyzes the error sources, and gets the measurement uncertainty of the curvature radius using laser interferometer by error synthesis.The results show that the measurement precision of the CMM is lower than that of the interferometer.Then we measure the polished optical element with different F-number（2.17, 1.45, 0.93） using CMM and laser interferometer, and compare the measurement results.The results establish the measurement uncertainty of the curvature radius using CMM , substantiate that CMM can meet the request of curvature radius measurement.Meanwhile, with the increase of F-number, the measurement errors of the two measurements have increasing trend.