超精密光学元件是高精尖大科学系统工程中非常关键的一部分，在高精度测量、高速通信、医学成像、强激光等领域有着重要的应用。计算机控制表面成形技术（CCOS）目前被广泛应用于的先进光学制造领域。而在大口径、高精度光学元件的加工制造中，面形中频误差（MSFE）是一个严重影响光学元件光学性能的因素。目前，中频误差抑制策略与抛光工艺参数关系十分复杂且不明确，中频误差抑制的工艺参数定量预测相当困难，还没有能够揭示中频误差抑制与工艺参数选择之间的定量模型。本文针对大型科学系统中的大口径光学元件全频段误差收敛需求，对现有的中高频误差抑制手段进行调研分析，以小工具匀滑抛光技术作为基础，提出用于中频误差抑制的多变量PSD优化模型。主要内容如下：（1）小工具抛光移动去除轮廓函数建模与优化。通过行星运动形式下的小工具抛光去除函数，并在该函数基础上叠加抛光压力不均匀分布函数，建立压力修正后的去除函数，再根据匀滑抛光原理得到移动去除轮廓函数；（2）提出了基于匀滑模型的初始面形预处理方法，解耦了径偏比、转速比协同影响去除函数非线性形变的规律，并根据单峰去除函数创成机制及其截止频率，给出了径偏比、公自转速比、抛光盘半径等工具参数的优选范围；（3）建立关于抛光工具参数（Preston常数，抛光载荷力，抛光盘半径，公自转速比，径偏比，公转角速度）与轨迹参数（进给速度，轨迹间距）的多参数中频PSD优化求解模型，给出了基于初始面形对特定抛光轨迹进行工具参数、轨迹参数的确定性求解算法，并进行了匀滑实验验证，实验结果显示中频误差得到了有效抑制，中频能量函数平均值降低了63%。本文采用的小工具匀滑抛光技术通过建立的多变量中频PSD优化模型针对匀滑抛光工艺各类参数，如工具形状、轨迹参数、材料属性等，进行了定量分析和选择策略，进一步提高了匀滑抛光的中频误差控制过程的可控性和可预测性。
Ultra precision optical components are a crucial part of high-precision and cut-ting-edge scientific systems engineering, and have important applications in fields such as high-precision measurement, high-speed communication, medical imaging, and high-power lasers. Computer Control Optical Surfacing (CCOS) is currently wide-ly used in the field of advanced optical manufacturing. In the processing and manufac-turing of large aperture and high-precision optical components, Mid Spatial Frequency Error (MSFE) is a serious factor that affects the optical performance of optical com-ponents. At present, the relationship between MSFE suppression strategies and polish-ing process parameters is very complex and unclear, and the quantitative prediction of process parameters for MSFE suppression is quite difficult. There is no quantitative model that can reveal the relationship between MSFE suppression and the selection of process parameter.This article focuses on the demand for full frequency error convergence of large-aperture optical components in large-scale scientific systems, conducts research and analysis on existing methods for suppressing MSFE and HSFE, and proposes a multi-variate PSD optimization model for suppressing MSFE based on small tool smooth polishing technology. The main contents are as follows: (1) Modeling and optimiza-tion of the contour function for small tool polishing movement removal. By using the small tool polishing removal function under planetary motion, and adding the uneven distribution function of polishing pressure to this function, a pressure corrected re-moval function is established, and then the moving removal contour function is ob-tained based on the principle of smooth polishing; (2) A preprocessing method for ini-tial surface shape based on a smooth model was proposed, which decoupled the non-linear deformation of the removal function under the synergistic effects of the radial to offset ratio and rotational speed ratio. Based on the mechanism of creating a single peak removal function and its cutoff frequency, the optimal range of tool parameters such as radial to offset ratio, common rotational speed ratio, and polishing disc radius was given; (3) Establish a multi-parameter intermediate frequency PSD optimization solution model for polishing tool parameters (Preston constant, polishing load force, polishing disc radius, common rotation speed ratio, radial deviation ratio, common corner speed) and trajectory parameters (feed speed, trajectory spacing). Provide a de-terministic solution algorithm for tool parameters and trajectory parameters for specif-ic polishing trajectories based on initial surface shape, and conduct smooth experiment verification.The small tool smooth polishing technology used in this article quantitatively an-alyzes and selects strategies for various parameters of the smooth polishing process, such as tool shape, trajectory parameters, material properties, etc., through the estab-lishment of a multivariate intermediate frequency PSD optimization model, further improving the controllability and predictability of the intermediate frequency error control process in smooth polishing.
