多步相移中被测件径向相移不均匀引入误差比较及校正  

Comparison and Correction of Errors Caused by Radial Phase-Shifting Nonuniformity of Test Optics in Multi-Step Phase-Shifting

作　　者：高芬[1,2] 倪晋平[1] 李兵[2] 田爱玲[1] Gao Fen;Ni Jinping;Li Bing;Tian Ailing(School of Optoelectronic Engineering, Xi＇ an Technological University, Xi＇ an, Shaanxi 710032, China;State Key Laboratory for Manufacturing Systems Engineering, Xi＇an Jiaotong University, Xi＇an, Shaanxi 710049, China)

机构地区：[1]西安工业大学光电工程学院,陕西西安710032 [2]西安交通大学机械制造系统工程国家重点实验室,陕西西安710049

出　　处：《光学学报》2018年第4期207-213,共7页Acta Optica Sinica

基　　金：国家自然科学基金(51275398);陕西省科学技术研究发展计划(2014K05-4)

摘　　要：不同步数相移算法下被测件径向相移不均匀引入的误差不同,对测量的影响也将不同。基于点衍射干涉测量光路,构建了误差分析模型,以5、6、7和13步相移算法为例,对不同相移算法下被测件径向相移不均匀引入的移相误差进行了分析,并将该移相误差的影响引入到实际干涉测量模型中,进一步分析比较了该误差对最终面形检测结果的影响,进而提出了一种基于误差预估计的多项式误差校正新方法。研究结果表明,相移算法步数越多,被测件径向相移不均匀引入的面形检测误差越大,误差均呈类抛物面分布;最终面形检测结果经Zernike多项式拟合消离焦项后已等同于进行了二次多项式校正,对于数值孔径为0.3以下的被测件,经二次多项式校正后该误差对测量的影响基本可以忽略。Errors causesd by radial phase-shifting nonuniformity of test optics are different when using different steps of phase-shifting algorithms to process interference fringes.Here,a error analysis model is established based on optical principle of point diffraction interferometery.Take 5,6,7 and 13 step phase-shifting algorithms as example,phase-shifting errors which are directly caused by radial phase-shifting nonuniformity are first analyzed,and then be introduced into the interferometry model.The influence of this phase-shifting error to final optical surface testing results are analyzed later and a new polynomial error correction method based on error preestimate is proposed.The analysis results show that the more the phase-shifting steps are,the larger the figure error caused by radial phase-shifting nonuniformity is.Each of these figure error shows a paraboloid like distribution.Also,removing the defocus item from Zernike polynomial of final optical surface testing results is equal to have had a quadratic polynomial correction of this error.If the numerical aperture of test optics are no more than 0.3,the error caused by radial phase-shifting nonuniformity can be ignored after the quadratic polynomial correction.

关 键 词：测量 干涉测量 点衍射干涉仪 多步相移 径向相移不均匀 误差分析 

分 类 号：O436[机械工程—光学工程]