连续位相板磁流变加工中高精度边缘延拓技术
|
摘要
为了提高磁流变加工连续位相板边缘加工质量,实现元件全口径抛光,必须对元件原始误差面形进行边缘延拓,针对现有边缘延拓算法的不足,提出了采用改进的二维Gerchberg带宽受限延拓算法实现连续位相板元件面形频域匹配的边缘延拓。该方法首先采用复调制频谱放大技术Zoom FFT对元件原始误差面形进行频谱分析,计算其高低截止频率;然后采用改进后的二维Gerchberg带宽受限延拓算法进行迭代计算,在原始面形外围延拓出与原始面形同频的高精度延拓结构面形。采用尺寸为100 mm×100 mm具有复杂频谱结构的连续位相板元件进行边缘延拓和磁流变加工实验,实验结果表明:采用改进的Gerchberg边缘延拓技术延拓的面形边缘更加规整,边缘效应影响半径由5 mm减小到2 mm,面形残余误差RMS从19.3 nm减小到了9.7 nm。这说明该边缘延拓技术可以明显提高连续位相板面形的边缘加工质量和整体收敛精度。
In order to improve the edge quality of the continuous phase plate in magnetorheological polishing and realize the full aperture polishing of the components, the edge extrapolation of the original error profile must be carried out. In view of the shortcoming of the existing edge extrapolation algorithm,a two-dimensional Gerchberg bandlimited extrapolation algorithm was proposed to realize the edge extrapolation technique that was frequency domain matching for continuous phase plate. Firstly, Zoom Fourier transform was applied to the original error profile to get its high and low cutoff frequencies.Then, the modified two-dimensional Gerchberg extrapolation algorithm was used to fill data in extrapolation region around the original region to get the same spectral structure as the original region. At last, an magnetorheological polishing experiment was performed on a 100 mm ×100 mm continuous phase plate element with complex frequency spectrum structure. The experimental results show that the edge processed by the method is more regular and the edge effect radius is reduced from 5 mm to 2 mm, and the residual error RMS is reduced from 19.3 nm to 9.7 nm. It indicates that the modified Gerchberg edge extrapolation technique can obviously improve the edge quality and the overall convergence precision of continuous phase plate.
In order to improve the edge quality of the continuous phase plate in magnetorheological polishing and realize the full aperture polishing of the components, the edge extrapolation of the original error profile must be carried out. In view of the shortcoming of the existing edge extrapolation algorithm,a two-dimensional Gerchberg bandlimited extrapolation algorithm was proposed to realize the edge extrapolation technique that was frequency domain matching for continuous phase plate. Firstly, Zoom Fourier transform was applied to the original error profile to get its high and low cutoff frequencies.Then, the modified two-dimensional Gerchberg extrapolation algorithm was used to fill data in extrapolation region around the original region to get the same spectral structure as the original region. At last, an magnetorheological polishing experiment was performed on a 100 mm ×100 mm continuous phase plate element with complex frequency spectrum structure. The experimental results show that the edge processed by the method is more regular and the edge effect radius is reduced from 5 mm to 2 mm, and the residual error RMS is reduced from 19.3 nm to 9.7 nm. It indicates that the modified Gerchberg edge extrapolation technique can obviously improve the edge quality and the overall convergence precision of continuous phase plate.
引文
[1] Xu Mingjin, Dai Yifan, Xie Xuhui, et al. Error analysis of ion beam figuring for fabrication of continuous phase plates with small feature structures[J]. Optics and Precision Engineering, 2016, 24(12):2975-2982.(in Chinese)
[2] Yan Hao, Tang Caixue, Luo Zijian, et al. Control of magnetorheological finishing on mid-spatial frequency error of flat optics[J]. Optics and Precision Engineering, 2016,24(12):3076-3082.(in Chinese)
[3] Jiao Changjun, Li Shengyi, Xie Xuhui, et al. Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors[J]. Journal of Mechanical Engineering, 2009, 45(11):253-259.(in Chinese)
[4] Li Yun, Duan Guping, Xing Tingwen. Smoothly extending algorithm for the surface error of optics[J]. Infrared and Laser Engineering, 2013, 42(2):408-412.(in Chinese)
[5] Li Yun, Xing Tingwen. Surface error of optical componets extended with non uniform rational B-spline surface[J].Acta Optica Sinica, 2012, 32(7):212-218.(in Chinese)
[6] Li Longxiang. Study on the key techniques of magnetorheological finishing for large aspheric optics[D].Changchun:Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2016.(in Chinese)
[7] Wang Wanyin, Qiu Zhiyun. The research to a stable minimum curvature gridding method in potential field data processing[J]. Progress in Geophysics, 2011, 26(6):2003-2010.(in Chinese)
[8] Jones M C. The discrete Gerchberg algorithm[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1986, 34(3):624-626.
[9] Wu Jianfen, Lu Zhenwu, Zhang Hongxin, et al. Optimized dwell time solution for optics in ion beam figuring[J]. Acta Optica Sinica, 2010, 30(1):192-197.(in Chinese)
[10] Cheng Haobo. Independent Variables for Optical Surfacing Systems[M]. New York:Springer, 2014.
[11] Robert J Marks. Gerchberg′s extrapolation algorithm in two dimensions[J]. Applied Optics, 1981, 20(10):1815-1820.
[12] Papoulis A. A new algorithm in spectral analysis and bandlimited extrapolation[J]. IEEE Trans Circ Sys, 1975, 22(9):735-742.
[13] Ding Kang, Xie Ming, Yang Zhijian. The Theory and Technology of Discrete Spectrum Correction[M]. Beijing:Science Press, 2008.(in Chinese)
[14] William Press, Saul Teukolsky, William Vetterling, et al.Numerical Recipes-The Art of Scientific Computing[M]. 3rd ed. New York:Cambridge University Press, 2007.
[15] Luo Yuan, Zhang Ke, Ji Ming. Color image fusion method for enhancing situation awareness of ICA[J]. Infrared and Laser Engineering, 2016, 45(S1):S126002.(in Chinese)
[2] Yan Hao, Tang Caixue, Luo Zijian, et al. Control of magnetorheological finishing on mid-spatial frequency error of flat optics[J]. Optics and Precision Engineering, 2016,24(12):3076-3082.(in Chinese)
[3] Jiao Changjun, Li Shengyi, Xie Xuhui, et al. Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors[J]. Journal of Mechanical Engineering, 2009, 45(11):253-259.(in Chinese)
[4] Li Yun, Duan Guping, Xing Tingwen. Smoothly extending algorithm for the surface error of optics[J]. Infrared and Laser Engineering, 2013, 42(2):408-412.(in Chinese)
[5] Li Yun, Xing Tingwen. Surface error of optical componets extended with non uniform rational B-spline surface[J].Acta Optica Sinica, 2012, 32(7):212-218.(in Chinese)
[6] Li Longxiang. Study on the key techniques of magnetorheological finishing for large aspheric optics[D].Changchun:Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2016.(in Chinese)
[7] Wang Wanyin, Qiu Zhiyun. The research to a stable minimum curvature gridding method in potential field data processing[J]. Progress in Geophysics, 2011, 26(6):2003-2010.(in Chinese)
[8] Jones M C. The discrete Gerchberg algorithm[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1986, 34(3):624-626.
[9] Wu Jianfen, Lu Zhenwu, Zhang Hongxin, et al. Optimized dwell time solution for optics in ion beam figuring[J]. Acta Optica Sinica, 2010, 30(1):192-197.(in Chinese)
[10] Cheng Haobo. Independent Variables for Optical Surfacing Systems[M]. New York:Springer, 2014.
[11] Robert J Marks. Gerchberg′s extrapolation algorithm in two dimensions[J]. Applied Optics, 1981, 20(10):1815-1820.
[12] Papoulis A. A new algorithm in spectral analysis and bandlimited extrapolation[J]. IEEE Trans Circ Sys, 1975, 22(9):735-742.
[13] Ding Kang, Xie Ming, Yang Zhijian. The Theory and Technology of Discrete Spectrum Correction[M]. Beijing:Science Press, 2008.(in Chinese)
[14] William Press, Saul Teukolsky, William Vetterling, et al.Numerical Recipes-The Art of Scientific Computing[M]. 3rd ed. New York:Cambridge University Press, 2007.
[15] Luo Yuan, Zhang Ke, Ji Ming. Color image fusion method for enhancing situation awareness of ICA[J]. Infrared and Laser Engineering, 2016, 45(S1):S126002.(in Chinese)