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变形镜高斯函数指数对迭代法自适应光学系统的影响

程生毅 陈善球 董理治 王帅 杨平 敖明武 许冰

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变形镜高斯函数指数对迭代法自适应光学系统的影响

程生毅, 陈善球, 董理治, 王帅, 杨平, 敖明武, 许冰

Influence of Gaussian function index of deformable mirror on iterative algorithm adaptive optical system

Cheng Sheng-Yi, Chen Shan-Qiu, Dong Li-Zhi, Wang Shuai, Yang Ping, Ao Ming-Wu, Xu Bing
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  • 基于613单元自适应光学系统, 描述了迭代矩阵和斜率响应矩阵的特性. 在变形镜驱动器间距和交连值不变的情况下, 研究了变形镜高斯函数指数对迭代矩阵和斜率响应矩阵稀疏度的影响, 对自适应光学系统稳定性和校正能力的影响. 研究表明, 迭代矩阵和斜率响应矩阵的稀疏度随着变形镜高斯函数指数的增大而减小. 高斯函数指数过大或者过小都会影响自适应光学系统的稳定性和校正能力. 最后, 综合迭代矩阵和斜率响应矩阵的稀疏度、自适应光学系统的稳定性和校正能力, 给出了合理的变形镜高斯函数指数的取值范围.
    Among all kinds of wavefront reconstruction algorithms in adaptive optical systems, the standard and mostly used algorithm is the direct gradient wavefront reconstruction algorithm. As the number of sub-apertures in Shack-Hartmann wavefront sensor and the actuators for deformable mirror increases, the reconstruction matrix in direct gradient wavefront reconstruction algorithm takes too much space and the number of multiplication in the algorithm increases sharply. So, the iterative algorithm is adopted in wavefront reconstruction for the high-resolution adaptive optical system. The number of multiplication and the required space of the iterative algorithm are directly related to the sparseness of both iterative matrix and slope response matrix. In an adaptive optical system, the sparseness of these two matrixes is connected with the system parameters. Therefore, it is necessary to study how to choose the proper parameters for an adaptive optical system when it uses iterative wavefront reconstruction algorithm. In this paper, the sparseness of slope response matrix and iterative matrix are analyzed based on a 613-actuator adaptive optical system. The influence of the Gaussian function index of deformable mirror on the sparsenesses of slope response matrix, iterative matrix, stability and correction qualities of the adaptive optical system are also studied under the condition of constant actuator spacing and coupling coefficient. A larger Gaussian function index results in a lower sparseness of the slope response matrix and the iterative matrix. Too large or too small a Gaussian function index will degrade the stability and the correction quality of an adaptive optical system. Finally, the optimal range of the Gaussian function index is provided by balancing the sparseness of slope response matrix, the correction quality, and the stability of the adaptive optical system.
    • 基金项目: 国家重大科研装备研制项目(批准号: ZDYZ2013-2)、国家自然科学基金(批准号: 11173008)和四川省杰出青年学术技术带头人资助计划(批准号: 2012JQ0012)资助的课题.
    • Funds: Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Province Outstanding Youth Academic Technology Leaders Program, China (Grant NO. 2012JQ0012).
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    Jiang W H, Zhang Y D, Rao C H, Ling N, Guan C L, Li M, Yang Z P, Shi G H 2011 Acta Optica Sinaca 31 9 (in Chinese) [姜文汉, 张雨东, 饶长辉, 凌宁, 官春林, 李梅, 杨泽平, 史国华 2011 光学学报 31 9]

    [2]

    Jiang W H 2006 Chinese Journal of Nature 28 1 (in Chinese) [姜文汉 2006 中国自然杂志 28 1]

    [3]

    Zhang L Q, Gu N T, Rao C H 2013 Acta. Phys. Sin. 62 169501 (in Chinese) [张兰强, 顾乃庭, 饶长辉 2013 物理学报 62 169501]

    [4]

    Ren Z J, Liang X Y, Liu M B, Xia C Q, Lu X M, Li R X, Xu Z Z 2009 Chin. Phys. Lett. 26 124203

    [5]

    Yu L H, Liang X Y, Ren Z J, Wang L, Xu Y, Lu X M, Yu G T 2012 Chin. Phys. B 21 014201

    [6]

    Li X Y, Jiang W H 2003 Acta Optica Sinaca 23 6 (in Chinese) [李新阳, 姜文汉 2003 光学学报 23 6]

    [7]

    Jiang W H, Li H G 1990 Proc. SPIE The Hague, Netherlands, March 01, 1990 p82

    [8]

    Feng L, Fedrigo E, Bechet C 2012 Applied Optics 51 3564

    [9]

    Antonin H B 2010 Proc. SPIE San Diego, CA, August 02, 2009 p1

    [10]

    Luc G, Curtis R, Vogel, Brent L 2002 J. Opt. Soc. Am. A 19 1817

    [11]

    Eric T, Michel T 2010 J. Opt. Soc. Am. A 27 1046

    [12]

    Cheng S Y, Chen S Q, Dong L Z, Liu W J, Wang S, Yang P, Ao M W, Xu B 2014 Acta Phys. Sin. 63 074206 (in Chinese) [程生毅, 陈善球, 董理治, 刘文劲, 王帅, 杨平, 敖明武, 许冰 2014 物理学报 63 074206]

    [13]

    Zhu Y G 2010 Matrix Analysis and Calculation (Beijing: National Defense Industry Press) pp160-183 (in Chinese) [朱元国 2010 矩阵分析与计算(北京: 国防工业出版社)第160-183页]

    [14]

    Curtis R V 2004 Proc. of SPIE Bellingham WA, June 21, 2004 p1327

    [15]

    John M C, John G 2004 Science, The International Journal of High Performance Computing Applications 18 225

    [16]

    Dong L Z, Yang P, Xu B 2009 Applied Physics B 96 527

    [17]

    Ning Y, Yu H, Zhou H, Rao C H, Jiang W H 2009 Acta Phys. Sin. 58 4717 (in Chinese) [宁禹, 余浩, 周虹, 饶长辉, 姜文汉 2009 物理学报 58 4717]

    [18]

    Noll R J 1976 J. Opt. Soc. Am. A 66 207

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出版历程
  • 收稿日期:  2014-10-08
  • 修回日期:  2014-11-12
  • 刊出日期:  2015-05-05

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