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标题: 大口径光学元件磁流变加工驻留时间求解算法 [打印本页]

作者: 风轻扬 时间: 2015-7-12 19:04
标题: 大口径光学元件磁流变加工驻留时间求解算法
大口径光学元件磁流变加工驻留时间求解算法
Dwell Time Algorithm for Large Aperture Optical Element in Magnetorheological Finishing
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作　　者：李龙[1,2] 邓伟杰[2] 张斌智[2] 白杨[1,2] 郑立功[2] 张学军[2]
Li Longxiang Deng Weijie Zhang Binzhi Bai Yang Zheng Ligong Zhang Xuejun（1.Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China 2 University of Chinese Academy of Sciences, Beijing 100049, China）
机构地区：[1]中国科学院长春光学精密机械与物理研究所,吉林长春130033 [2]中国科学院大学,北京100049
出　　处：《光学学报》 EI CSCD 2014年第5期 209-215页,共7页
Acta Optica Sinica
基　　金：国家自然科学基金（61036015）
摘　　要：为了解决大口径光学元件磁流变高精度加工问题，基于矩阵运算模型，提出了SBB（Subspace Barzilai andBorwein）最小非负二乘与自适应Tikhonov正则化相结合的驻留时间快速求解方法。同时，在一次收敛中采用双去除函数优化螺旋线轨迹下光学元件的加工，保证中心区域与全口径面形精度一致。仿真表明该算法与常用Lawson-Hanson最小非负二乘法相比，计算精度一致且求解效率大幅提高。对西600 mm以彗差为主的光学表面模拟加工，峰谷（Pv）值和均方根（RMS）值从初始的2．712a与0．461a中心区域全局一致收敛到0．306A和0．0199A（A632．8 nm）。因此，提出的算法能够在有效保证面形收敛精度的同时快速获得稳定可靠的驻留时间分布，为磁流变抛光应用于大口径光学元件提供有力支持。
In order to obtain high precise optical surface by magnetorheological finishing （MRF）, an algorithmcombined with SBB （Subspace Barzilai and Borwein） and adaptive Tikhonov regulation is proposed to get dwell timedistribution based on matrix multiplication. Moreover, double removal functions are introduced to polishing of thecircle mirror with spiral path to guarantee the convergence of center area and surface precision of full aperture.Algorithm＇s simulation shows that the accuracy of the method mentioned above is the same with traditional Lawson-Hanson method, but the computing rate is much faster than the latter. The example calculation of Ф600 mm circlemirror with main coma surface error presents that the value of peak-valley （PV） value and root mean square （RMS）from 2.712λ and 0. 461λ converges to 0. 306λ and 0. 0199λ（λ = 632. 8 rim） with the center and full apertureconsistent. Therefore, the algorithm in this paper can ensure the convergence accuracy of the surface shape whilesolving the dwell time distribution effectively and keeping the solution accurate and stable fast. The result providessupport to the application of MRF on large aperture optical element.
关键词：光学制造驻留时间矩阵运算全局收敛磁流变抛光
optical fabrication ; dwell time ; matrix multiplicatiom full aperture convergence ; magnetorheological finishing ;

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