Xue Jiadai, Li Yuhao, Gao Mingyang, Gu Dongyun, Wu Yanlin, Liu Yanwen, Fan Yuxin, Zheng Peng, Chen Wentao, Chen Zhigao, Qiao Zheng, Jin Yuan, Ding Fei, Wu Yangong, Wang Bo
Center for Precision Engineering, Harbin Institute of Technology, Harbin 150001, China.
School of Mechanical and Electrical Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China.
Micromachines (Basel). 2024 Nov 25;15(12):1415. doi: 10.3390/mi15121415.
Over the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechanisms for variable-curvature X-ray mandrels, which are crucial for achieving the desired surface roughness and form accuracy, especially in reducing mid-spatial frequency (MSF) errors. It is essential to incorporate flexible control in deterministic small-tool polishing to improve the tool's adaptability to curvature variations and achieve stable, Gaussian-like tool influence functions (TIFs). In this paper, we introduce a curvature-adaptive prediction model for compliance figuring, based on the Preston hypothesis, using a compliant shaping tool with high slurry absorption and retention capabilities. This model predicts the compliance figuring process of variable-curvature symmetrical mandrels for X-ray grazing incidence mirrors by utilizing planar tool influence functions. Initially, a variable-curvature pressure model was developed to account for the parabolic and hyperbolic optical surfaces' curvature characteristics. By introducing time-varying removal functions for material removal, the model establishes a variable-curvature factor function, which correlates actual downward pressure with parameters such as contact radius and contact angle, thus linking the variable-curvature surface with a planar reference. Subsequently, through analysis of the residence time distribution across different TIF models, hierarchical filtering, and PSD distribution, real-time correction of the TIFs was achieved to enable customized variable-curvature polishing. Furthermore, by applying a time-varying deconvolution algorithm, multiple rounds of flexible polishing iterations were conducted on the mandrels of a rotationally symmetric variable-curvature optical component, and the experimental results demonstrate a significant improvement in form accuracy, surface quality, and the optical performance of the mirror.
在过去30年里，研究人员利用薄金属膜中的全反射原理开发了X射线聚焦望远镜。具有可变曲率表面的沃尔特-I聚焦镜要求高精度。然而，对于可变曲率X射线芯轴的去除机制研究有限，这些机制对于实现所需的表面粗糙度和形状精度至关重要，尤其是在减少中空间频率（MSF）误差方面。在确定性小工具抛光中纳入灵活控制，以提高工具对曲率变化的适应性并实现稳定的、类似高斯的工具影响函数（TIF）至关重要。在本文中，我们基于普雷斯顿假设，使用具有高浆料吸收和保留能力的柔性成型工具，引入了一种用于顺应性修形的曲率自适应预测模型。该模型通过利用平面工具影响函数预测X射线掠入射镜可变曲率对称芯轴的顺应性修形过程。最初，开发了一个可变曲率压力模型，以考虑抛物面和双曲面光学表面的曲率特性。通过引入用于材料去除的时变去除函数，该模型建立了一个可变曲率因子函数，该函数将实际向下压力与接触半径和接触角等参数相关联，从而将可变曲率表面与平面参考联系起来。随后，通过分析不同TIF模型的停留时间分布、分层滤波和PSD分布，实现了TIF的实时校正，以实现定制的可变曲率抛光。此外，通过应用时变反卷积算法，对旋转对称可变曲率光学元件的芯轴进行了多轮柔性抛光迭代，实验结果表明，该镜的形状精度、表面质量和光学性能有了显著提高。
