点衍射干涉仪系统误差标定算法研究  

Research on System Error Calibration Algorithm of Point Diffraction Interferometer

作　　者：蒋庄德[1,2] 高芬[1,2] 李兵[1,2] 

机构地区：[1]西安交通大学机械制造系统工程国家重点实验室,西安710049 [2]西安交通大学机械工程学院,西安710049

出　　处：《机械工程学报》2013年第16期48-56,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51275398);国家自然科学基金重点(90923001);国家科技重大专项(2011ZX04004-061);高等学校学科创新引智计划(B12016);教育部科学技术研究重大(311001);长江学者和创新团队发展计划(IRT1033)资助项目

摘　　要：为评估面形检测点衍射干涉仪的检测精度,提出用被检镜倾斜旋转法标定点衍射干涉仪的系统误差,研究可同时分离出被检球面镜旋转对称及旋转非对称面形误差的标定算法。将被检球面镜绕初始光轴及相对成小角度的倾斜光轴作两次平分角度旋转检测,利用单次平分旋转检测数据估计出被检镜面形的旋转非对称部分,利用两次旋转检测重叠区域各点系统误差不变性构建旋转对称部分的差值方程,运用最小二乘法求解用泽尼克多项式表述的旋转对称部分的系数,估计出的被检镜面形的旋转对称部分,两者相加估计得被检镜的真实面形。从干涉仪测试数据中减去被检镜的真实面形数据计算得系统误差。分析标定原理,推导标定算法公式,并仿真验证算法正确性。仿真研究结果表明,经算法估计的被检镜面形和系统误差与仿真输入值吻合,方均根误差的差值均小于0.03 nm,残差的方均根值均小于0.3 nm,满足亚纳米级标定精度需求。In order to evaluate absolute accuracy of point diffraction interferometer（PDI）,a system error calibration method based on tilting and rotation of test mirror is used and calibration algorithm are discussed in detail.Calibration formulas are deduced and a verified simulation is conducted.In the method,figure errors of spherical test mirror are measured in N equal position around an initial axis and a tilt axis.The rotationally asymmetric component of real figure about test mirror in each axis position can be calculated through rotation method.As system errors in same coordinate are constant in two rotate measurements,subtract one from another,an equation can be acquired without system error term.The rotationally symmetric component of real figure which expressed in Zernike rotationally items can be evaluated in solving this differential equation with least square.System error can be acquired through deprive real figure error of test mirror from measurement data.The simulation results shows that figure error of test mirror and system error which calculated through this algorithm are consistent with the simulation input values,difference of errors are less than 0.03 nm and residual errors are less than 0.3 nm,it can meet the requirement of the calibration accuracy.

关 键 词：点衍射 面形误差 衍射波面 旋转对称 旋转非对称 

分 类 号：TH774[机械工程—仪器科学与技术]