光学镜面可控柔体抛光误差特性研究.pdf

国防科学技术大学博士学位论文光学镜面可控柔体抛光误差特性研究姓名：吴冬良申请学位级别：博士专业：机械工程指导教师：戴一帆20091201国防科学技术大学研究生院博士学位论文 第 i 页 摘 要 离子束和磁流变抛光的抛光模具有可控的柔性，常被称为可控柔体抛光技术，属于确定性小磨头抛光的一种和传统大面抛大面的光学加工手段不同，被加工光学表面的加工误差分布规律及其对光学性能的影响规律也不尽相同现代光学系统，如高能/高功率激光系统、高分辨率观测系统等，其性能指标要求的提高要求对光学镜面各频段误差进行严格的控制为了在满足光学性能要求的基础上降低光学零件加工难度，有效评价高精度光学零件对光学性能指标的影响必须解决的关键问题本文以离子束、磁流变等可控柔体抛光的高精度光学镜面为研究对象，分析可控柔体抛光误差的形成规律，进而研究其对强激光/高聚能和高分辨率光学系统的影响，为制造误差的特征分析和性能评价提供理论支撑 本文基于 Collins 积分公式、 概率统计理论、 Harvey-Shack 散射理论和 Goodman统计光学理论，研究抛光误差、误差梯度分布等镜面误差参数与光学性能指标之间的关系，建立相互关系的数学模型，并通过数值仿真和实验分析验证关系模型；在此基础上，基于这些模型分析抛光误差对光学性能指标的影响规律，从而为光学镜面的误差修正提供技术支撑，为有效解决高性能光学系统中高精度光学零件的加工和评价提供参考。

论文的研究工作主要包括以下几个部分： 1. 基于功率谱密度分析离子束、磁流变抛光误差的频谱分布和演变规律：对离子束、磁流变抛光误差进行功率谱密度分析，得到光栅扫描和螺旋扫描加工对抛光误差的影响规律；利用二维功率谱密度对光学镜面不同频段误差进行特征分析，得到抛光误差的二维频谱分布；最后利用功率谱密度曲线对不同口径光学镜面面形误差进行频段划分，为后续章节分析光学镜面中高频误差对环围能量比和散射损失比指标的影响奠定了基础 2. 针对离子束、磁流变抛光误差对环围能量比指标的影响进行研究，基于Collins 积分公式、差分理论以及概率统计理论，分别建立光学镜面全频段误差、中高频段误差与环围能量比指标之间的关系模型，并通过数值仿真和实验分析进行验证，从而可以方便地分析抛光误差对环围能量比指标的定量影响，为光学镜面误差修正提供技术支撑 3. 针对离子束、磁流变抛光误差对散射损失比指标的影响进行研究，基于统计光学理论和 Harvey-Shack 散射理论，分别建立光学镜面全频段误差、中高频段误差与散射损失比指标之间的关系模型，并通过数值仿真和实验分析进行验证，从而可以方便地分析抛光误差对散射损失比指标的定量影响，为光学镜面的误差修正提供技术支撑。

4. 基于抛光误差对环围能量比和散射损失比指标的影响模型，通过理论计算国防科学技术大学研究生院博士学位论文 第 ii 页 和数值仿真对比分析离子束、磁流变抛光误差对光学性能指标的影响规律，从而为判断抛光误差是否满足性能指标要求提供依据；同时针对不同工艺参数对抛光误差的影响特点，研究工艺参数对环围能量比和散射损失比指标的定量影响，并根据性能指标要求合理选择加工参数 关键词：离子束修形；磁流变抛光；抛光误差；频段误差；梯度均方根；功率谱密度；环围能量比；散射损失比 国防科学技术大学研究生院博士学位论文 第 iii 页 Abstract The polishing pad of the ion beam figuring (IBF) and the magnetorheological finishing (MRF) has the controllable flexibility, and the IBF and MRF are usually considered as the controllable deformable polishing which belongs the deterministic small tool polishing. Differently with the optical processing method of the conventional big pad polishing on the large mirrors, the distribution regularity of the fabrication errors of the optical mirrors and the influence regularity of the fabrication errors on the optical performance are also different. The performance improvement of the modern optical system such as the high-energy and high-power laser system, high-resolution surveillance system require the strict control of the various frequency errors of the optical mirrors. In order to reduce the fabrication difficulty of the optical elements, the influence of the high-precision optical elements on the optical performance is evaluated effectively is the key problem to be solved. In view of the high-precision optical mirrors machined by the IBF and MRF, the forming regularity of the polishing errors by the controllable deformable polishing is analyzed and the influence of the polishing errors on the high-energy and high-resolution optical system is studied in supporting the characteristic analysis and performance evalution of the fabrication errors. This thesis is dedicated to analyze the influence of the errors parameters such as the polishing errors and the errors gradient distribution of the optical mirrors on the optical performance and build the models among them based on the Collins diffraction formula, probability statistics, Harver-Shack scattering theory and statistical optical theroy. And the models are validated by the numerical simulation and experimental analysis. The error correction of the optical mirrors and the machining and evaluation of the high precision optical elements in the high-performance optical system are supported by the influence regularity of the polishing errors on the performance indices with the models. The major research efforts include the following points. 1. The power spectral density (PSD) distribution is analyzed to obtain the influence regularity of the grating scanning and helical scanning methods on the polishing errors produced by the IBF and MRF. And the various frequency band errors of the optical mirrors are analyzed with two dimensions PSD to obtain the frequency spectrum distribution of the polishing errors. Finally, the polishing errors of the various aperture optical mirrors are divided into the various frequency band errors based on the PSD curve, which supports the influence analysis of the mid- and high-frequency band errors of the optical mirrors on the fractional encircled energy (FEE) and the ratio of scattering loss (RSL). 2. Based on the Collins diffraction formula, difference theory and probability statistics, the influence models of the full frequency band errors and the mid-and-high 国防科学技术大学研究生院博士学位论文 第 iv 页 frequency errors of the optical mirrors on the FEE are obtained, and are validated by the numerical simulation and experimental analysis. Thus the quantitative influence of the polishing errors on the FEE can be analyzed conveniently which can support the error correction of the optical mirrors. 3. Based on the statistical optics theory and the Harvey-Shack scattering theory, the influence models of the full frequency band errors and the mid-and-high frequency errors of the optical mirrors on the RSL are obtained, and are val。