基于低相位模糊条纹反射技术的自由曲面镜表面纳米尺度形貌测量方法研究

The study of metrologies for freeform specular surface with Nano-scale accuracy has been a hot topic in the field of modern optics. The interferometry is currently the main technique for measuring the specular surface. While dealing with the freeform optics, the interferometry suffers in the problems of a) the need for compensation optics is inflexible and costly, b) integrating interferometric techniques into a harsh production environment is an extremely challenging endeavor. Based on the fringe reflection technique(FRT), this project will analysis and solve the problems in FRT induced by the profile characteristics of freeform mirror. To solve the phase ambiguous problem when measuring the freeform surface with significant height and slope variation, this project will establish the phase ambiguous modal based on the reverse ray-tracing method, and therefore reveal the quantitative relation between phase ambiguous error and system parameters. The system light path setup conditions for minimizing the phase ambiguous error will be then studied. In order to calibrate this low phase ambiguous system, a system calibration method based on the phase-slope-height analytical expression will be studied. This calibration method will also release the requirements to the calibration of system geometry structure. Meanwhile, to compensate the systematic error emerges around the geometry or reflectivity discontinuous edges of the freeform surface, a mathematical model will be identified based on the finite size of the imaging system’s point spread function and the resulting phase bias produced near to discontinuities, from which a compensation algorithm to calculate and remove the errors will be derived. This project will hopefully benefit to the high accuracy measurement of freeform surface theoretically and technically.

自由曲面镜表面形貌的纳米尺度测量技术是现代光学领域的重要研究课题，现有的主要测量方法激光干涉法在测量自由曲面镜时存在光学补偿元件昂贵且获取不便、环境要求苛刻等难题。本申请针对自由曲面镜的表面特性，分析并解决条纹反射技术测量自由曲面镜过程中所产生的关键问题，以提升测量精度。针对自由曲面镜表面梯度和高度变化复杂导致的相位模糊严重的问题，采用逆向光线追迹思路建立相位模糊误差模型，揭示系统各参量与相位模糊误差的定量关系，进而研究极小化相位模糊误差的系统参量条件和光路优化方案。此外，研究基于相位-梯度-高度解析表达式的标定方法，实现对该低相位模糊误差系统高精度标定，并简化对系统几何结构的标定需求。针对自由曲面镜表面几何/反射率不连续边界附近的相位畸变问题，建立相位畸变量与点扩散函数关系的数学模型，并进一步研究相位畸变计算与补偿方法。本项目的研究将为自由曲面镜面的高精度检测提供理论和技术基础。

本项目针对自由曲面镜的表面特性，分析并解决条纹反射技术测量自由曲面镜过程中所产生的相位模糊、不连续区域测量误差等关键问题。针对自由曲面镜表面测量时的相位模糊问题，本项目建立了相位模糊误差模型，揭示了系统各参量与相位模糊误差的关系，得到了相位模糊误差的系统参量极小值条件，并基于此提出了基于同轴远心光路的极小化相位模糊误差的系统结构，仿真和实验验证该系统对相位模糊误差的抑制能力，结果表明所提出的结构能够降低相位误差2个数量级；针对自由曲面镜表面几何/反射率不连续边界附近的相位畸变问题，提出了基于空间点扩散函数标定的条纹反射三维测量方法，建立了相位畸变量与点扩散函数关系的数学模型，结合标定的点扩散函数反求不连续区域真实相位，可大大降低不连续区域的相位畸变误差，提高不连续区域三维测量精度，实验表明不连续边界附近区域相位畸变量均方根值可降低至原来的1/4；此外，针对工业领域的对自由曲面镜面/类镜面的在线检测的迫切需求，对条纹反射动态测量中的单帧和两步相位提取算法展开了研究，对比与现有的单帧和多帧相位提取算法，在细节重建能力、条纹需求数方面有明显的优势。本项目的研究成果解决了条纹反射技术中的相位模糊、不连续区域测量误差等关键问题，提出了针对动态测量场景的相位提取算法，对抑制条纹反射技术自由曲面测量误差、条纹反射技术工业场景下在线测量应用有重要参考意义。

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