基于积分去除函数的小盘镜尺寸比光学元件确定性面形收敛理论研究

Manufacturing large aperture mirrors is one of the key technologies in the development of optical systems of large astronomical telescopes. For the correction of the surface error of large aperture optics, the ratio of the diameter of the polishing laps in MRF, which is a deterministic manufacturing technology, to the size of mirrors is so small that the data scale is very large and the accuracy and computing efficiency in the surface error convergence algorithm under strict constraints are not high enough. In view of this, a new surface error convergence theory based on the integral removal function is proposed: the integral removal function is produced from continuously removing material along a tool path by the removal function, then the tool path is optimized to decrease the data scale and improve the figuring determinacy, then the convolution operation is transformed into a matrix multiplication to obtain the dwell time map of the integral removal function, the strategy of the quantitative evaluation of the deterministic manufacturing capacity is, moreover, analyzed from the perspective of the spatial frequency. The model of the integral removal function and related surface error convergence theory will be mainly studied. Furthermore, the surface error convergence algorithm with multiple optimization objectives under strict constraints will be built and the strategy of the quantitative evaluation of the deterministic manufacturing capacity based on spatial-frequency correlation will be studied deeply as well. Finally, a surface error convergence theory for large aperture optics polished by a method with a small ratio of the diameter of the polishing laps to the size of mirrors will be established. This project will provide new ideas and new theories for the development of the deterministic optical surfacing technologies, effectively instruct the rapid and high precision manufacturing of large aperture optical components and provide a strong support for the construction of large aperture telescopes in China.

大口径反射镜制造是大型天文望远镜光学系统研制的核心技术之一。磁流变抛光等技术进行大口径反射镜加工时，由于抛光盘(去除函数)尺寸与镜面尺寸比值小，导致传统面形收敛模型中数据规模大，严格约束下面形收敛算法效率和精度不足。鉴于此，本项目创新性地提出基于积分去除函数的面形收敛思想：去除函数沿着加工轨迹对材料连续去除，形成作用区域明显扩展的积分去除函数，以此为基础优化加工轨迹，降低数据规模，提高加工确定性，再将卷积转化为矩阵乘积求解驻留时间，结合算法从空间频谱的角度对面形收敛能力进行分析。重点阐明积分去除函数及其面形收敛模型，建立严格约束的快速高精度面形收敛多目标优化算法，剖析基于频谱相关性的面形收敛能力评价机制，最终形成基于积分去除函数的小盘镜尺寸比元件确定性面形收敛理论。本项目将为光学加工技术的发展提供新思路和新理论，有效指导大口径光学元件的高精度制造，为我国大口径望远镜的顺利建设提供有力保障。

光学望远镜是人类认知宇宙的重要工具，是现代科学技术发展的基石，在精细天文、对地观测、态势感知等领域发挥着不可替代的作用。以非球面、离轴非球面及自由曲面等为主要形式的大口径复杂曲面光学元件是大型光学望远镜的核心器件，其口径和精度直接决定了光学系统的性能。现代科技对光学系统性能需要的不断提升，促使望远镜向着口径越来越大、精度越来越高的方向不断发展，这对大口径反射镜的高精度制造技术提出了前所未有的挑战。目前的复杂曲面加工方法主要是子孔径加工方法，即使用相对较小工具加工较大口径的反射镜。但是当使用磁流变抛光等技术进行大口径反射镜子孔径加工时，由于抛光盘(去除函数)尺寸与镜面尺寸比值小，导致传统面形收敛模型中数据规模大，严格约束下面形收敛算法效率和精度不足。本项目以磁流变抛光为研究载体，改进现有子孔径确定性加工技术的面形收敛模型，提出基于积分去除函数的面形收敛思想：去除函数沿着加工轨迹对材料连续去除，形成作用区域明显扩展的积分去除函数，以此为基础优化加工轨迹，降低数据规模，提高加工确定性，再将卷积转化为矩阵乘积求解驻留时间，结合算法从空间频谱的角度对面形收敛能力进行分析。重点阐明积分去除函数及其面形收敛模型，建立严格约束的快速高精度面形收敛多目标优化算法，剖析基于空间频谱的全频段面形收敛机制，最终形成基于积分去除函数的小盘镜尺寸比元件确定性面形收敛理论。本项目将为光学加工技术的发展提供新思路和新理论，有效指导大口径光学元件的高精度制造，为我国大口径望远镜的顺利建设提供有力保障。

内容获取失败，请点击重试