基于非零位校正和同步拼接的大口径凸非球面形状测量方法和相关理论

Theory and method of figure measurement of large convex aspheric surface based on non-null calibration and simultaneous stitching are studied. Errors in non-null testing are calibrated. Model of phase error and mapping error is established by ray tracing method on non-null condition. The influences of phase error and mapping error on sub-aperture wave-front and stitching results are analyzed. The even/odd synthesis method is proposed for the calibration of reference surface. Utilizing the property that surface error could be divided into rotationally symmetric and non-rotationally symmetric terms, odd and even parts of the reference surface can be obtained respectively, and the least square algorithm with dual-objective optimization function proposed is used to calibrate the odd aberrations of the reference wave-front. This method conquers the disadvantage of traditional method -being sensitive to misalignments. Furthermore, environment effects such as air turbulence and vibration can also be effectively suppressed. Simultaneous stitching method with global averaging error and constrained optimization is proposed. Self-compensated wave-front aberration with registration errors calibration is obtained by the relationship between ideal aspheric surface and stitching path. Considering the produce and mechanism of stitching error, constrains on the optimization and the merit function are proposed for simultaneous stitching. The method decreases the influence caused by the error of sub-aperture, inhibits the error transfer and accumulation, and conquers the demerit of traditional stitching method- ill conditioned easily.

探索一种基于非零位校正和同步拼接的大口径凸非球面形状测量方法和相关理论；开展非零位误差产生机理和校正方法研究，采用光线追迹方法，建立非零位条件下的相位误差和映射误差校正模型，揭示两者与拼接测量结果的关联关系；提出基于奇偶合成的参考波前校正方法，利用任意波前可描述为奇偶组合的特性，分别获得参考波前的奇分量和偶分量，采用基于双目标线性优化函数的最小二乘拟合算法进行奇分量校正，克服传统方法对失调误差敏感的缺点，抑制环境振动、扰动的影响；提出基于全局误差均化和约束优化的同步拼接方法，根据拼接轨迹与被测非球面理想波前的关联关系，建立基于配准误差校正的子孔径波像差自适应补偿模型；对拼接测量中各种误差的产生和作用机理进行深入研究，构建优化目标函数和误差补偿项的约束条件，实现子孔径的同步拼接合成，抑制子孔径测量误差对拼接结果的影响，避免拼接过程中的误差传递和累积，克服传统拼接方法容易出现病态的缺点。

非球面检测是空间相机、天文望远镜等现代光学系统中亟需解决的难题。本课题针对该问题开展基于非零位校正和同步拼接的大口径非球面形状测量方法研究。主要开展了非零位误差产生机理和校正方法研究，采用光线追迹方法，建立了非零位条件下的映射误差校正模型，提出了基于该模型的非零位测量回程误差校正方法，无需预知被测波前及参考波前的理论值，可有效的分离非零位测量原理误差；提出了基于双向差动旋转剪切的绝对检测方法，采用基于最小二乘的优化算法重构剪切波像差数据，从而分离系统误差和参考波前误差，克服了传统方法对失调误差敏感的缺点，抑制环境振动、扰动以及非旋转对称误差的影响；提出了基于全局误差均化和约束优化的同步拼接方法，根据拼接轨迹与被测非球面理想波前的关联关系，建立了基于配准误差校正的子孔径波像差自适应补偿模型；采用全局误差均化和约束优化的方法实现了子孔径的同步拼接合成，抑制了子孔径测量误差对拼接结果的影响，避免了拼接过程中的误差传递和累积，克服了传统拼接方法容易出现病态的缺点。