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基于引力搜索算法的湍流相位屏生成方法

张冬晓 陈志斌 肖程 秦梦泽 吴浩

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基于引力搜索算法的湍流相位屏生成方法

张冬晓, 陈志斌, 肖程, 秦梦泽, 吴浩

Generation of turbulence phase screen based on gravitational search algorithm

Zhang Dong-Xiao, Chen Zhi-Bin, Xiao Cheng, Qin Meng-Ze, Wu Hao
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  • 本文提出了一种全新的相位屏生成方法, 结合了经典快速傅里叶变换(FFT)模型与稀疏谱模型. 经典的FFT模型由于低频成分的严重缺失, 限制了其在高精度相位屏生成方面的应用, 为此, 本文将相位屏的低频部分单独提取出来, 应用稀疏谱模型生成相应的低频补偿屏, 将二者相加后得到最终的精确相位屏. 结果表明, 补偿屏的模拟精度与低频采样点的分布有关, 且存在一种最优分布使得最终的相位屏结构函数与理论结构函数的误差最小. 为兼顾相位屏生成速度, 本文选取了16个低频采样点, 采样点位置由两个待定参数确定, 并应用引力搜索算法对参数进行优化得到最终的低频采样点分布. 仿真结果表明, 该方法与传统低频补偿方法相比精度提高了1—2个数量级, 且运算速度优于传统方法.
    The new techniques in adaptive optics, free space optical(FSO) communication rely on the use of numerical simulations for atmospheric turbulence to evaluate the performance of the system. The simulation of turbulence phase screen is the heart of numerical simulations which produces random wavefront phase perturbations with the correct statistical properties corresponding to models of optical propagation through atmospheric turbulence. The phase-screen simulation techniques can be roughly divided into fast Fourier transform (FFT) method and matrix-based method. Because of a better performance in computation time, the FFT method is generally used for modeling the performance of a real system. But the classical FFT method has a main deficiency of oversample in low frequency region, which leads to the lost of accuracy. To overcome this deficiency, many methods have been proposed for compensating for the oversample of low frequency components, in the last decades. Essentially, these methods achieve a higher accuracy at the expense of computation time. A good compensation method should take into consideration both accuracy and computation time.   To achieve higher accurcy and lower computational cost simultaneously, we develop a hybrid method to generate turbulence phase screen, i.e. the classical FFT model is mixed with the sparse spectrum model. We first extract the low frequency region from the frequency grid of FFT model, and resample this region with 16 samples. It is found that the accuracy of phase screen is related to the distribution of these samples, and there must be an optimum distribution that can minimize the relative error between expected structure function and theoretical structure function in the low frequency region. So it permits one to use optimization algorithm to find the optimized distribution of low frequency samples. Here an improved gravity search algorithm is adopted in which the memory of each particle is taken into consideration. The optimization parameters are determined after a lot of tests, and the robustness testing shows that the algorithm is effective. To compare with existing subharmonic method, we choose the same parameters of phase screen as those used in the expanded subharmonic method, generate 1000 phase screens for each method, compute the phase structure function, and we also compare our results with those from the theoretical structure function. The comparison result shows that the curve of phase structure function generated by our method is nearly consistent with the theoretical one, the maximum relative error in low frequency region is about 0.063% which is much better than that from the expanded subharmonic method 5%. Finally in this paper, the computational cost is analyzed, showing that the generation speed for our method is at least 4.5 times as fast as that for the Johansson’s method.
      通信作者: 张冬晓, zhang58452sc@163.com
    • 基金项目: 国防科技项目基金(批准号: 2004053)资助的课题.
      Corresponding author: Zhang Dong-Xiao, zhang58452sc@163.com
    • Funds: Project supported by the National Defense Research Program of Science and Technology, China (Grant No. 2004053).
    [1]

    季小玲 2010 物理学报 59 692Google Scholar

    Jin X L 2010 Acta Phys. Sin. 59 692Google Scholar

    [2]

    Fleck J A, Morris J R, Feit M D 1976 Appl. Phys. 10 129

    [3]

    Flatte S M, Wang G Y, Martin J 1993 J. Opt. Soc. Am. A 10 2363Google Scholar

    [4]

    Flatte S M 2000 Opt. Express 10 777

    [5]

    McGlamery B L 1976 Proc. SPIE Int. Soc. Opt. Eng. 74 225

    [6]

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

    [7]

    Roddier N 1990 Opt. Eng. 29 1174Google Scholar

    [8]

    Wallace J, Gebhardt F G 1986 Proc. SPIE 642 261Google Scholar

    [9]

    Roggemann M C, Welsh B M, Montera D, Rhoadamer T A 1995 Appl. Opt. 34 4037Google Scholar

    [10]

    Harding C M, Johnston R A, Lane R G 1999 Appl. Opt. 38 2161Google Scholar

    [11]

    华志励, 李洪平 2012 光学学报 32 0501001

    Hua Z L, Li H P 2012 Acta Optica Sinica 32 0501001

    [12]

    Formwalt B, Cain S 2006 Appl. Opt. 45 5657Google Scholar

    [13]

    Sriram V, Kearney D 2007 Opt. Express 15 13709Google Scholar

    [14]

    Zhang B D, Qin S Q, Wang X S 2010 Chin. Opt. Lett. 8 969

    [15]

    Xiang J 2012 Opt. Express 20 681Google Scholar

    [16]

    王建新, 白福忠, 宁禹, 黄林海, 姜文汉 2011 物理学报 60 209501

    Wang J X, Bai F Z, Ning Y, Huang L H, Jiang W H 2011 Acta Phys. Sin. 60 209501

    [17]

    Vorontsov A M, Paramonov P V, Valley M T, Vorontsov M A 2008 Waves Random Complex Medium 18 91Google Scholar

    [18]

    Herman B J, Strugala L A 1990 Proc. SPIE 1221 183Google Scholar

    [19]

    Lane R G, Glindemann A, Dainty J C 1992 Waves Random Complex Medium 2 209Google Scholar

    [20]

    Johansson E M, Gavel D T 1994 Symposium on Astronomical Telescopes and Instrumentation for the 21st Century Kona, Hawaii, March 13-18 1994 p940391

    [21]

    Sedmak G 2004 Appl. Opt. 43 4527Google Scholar

    [22]

    Charnotskii M 2013 J. Opt. Soc. Am. A 30 479Google Scholar

    [23]

    蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞 2014 物理学报 63 104217Google Scholar

    Cai D M, Wang K, Jia P, Wang D, Liu J X 2014 Acta Phys. Sin. 63 104217Google Scholar

    [24]

    蔡冬梅, 遆培培, 贾鹏, 王东, 刘建霞 2015 物理学报 64 224217Google Scholar

    Cai D M, Ti P P, Jia P, Wang D, Liu J X 2015 Acta Phys. Sin. 64 224217Google Scholar

    [25]

    Xiang J S 2014 Opt. Eng. 53 016110Google Scholar

    [26]

    Rashedi E, Nezamabadi-pour H, Saryazdi S 2009 Information Science 179 2232Google Scholar

    [27]

    Kennedy J, Eberhart R 1995 Proceedings of IEEE International Conference on Neural Networks Perth, November 27, 1995 p1942

    [28]

    李春龙, 戴娟, 潘丰 2012 计算机应用 32 2732

    Li C L, Dai J, Pan F 2012 J. Comput. Appl. 32 2732

    [29]

    陈水利, 蔡国榕, 郭文忠, 陈国龙 2007 长江大学学报(自科版)理工卷 4 1Google Scholar

    Chen S L, Cai G R, Guo W Z, Chen G L 2007 Journal of Yangtze University(Nat. Sci. Ed.) Sci. & Eng. V 4 1Google Scholar

  • 图 1  低频采样点分布

    Fig. 1.  The distribution of low frequency samples.

    图 2  引力搜索算法优化曲线

    Fig. 2.  The optimization curve of GSA.

    图 3  湍流相位屏模拟结果 (a)相位屏二维分布; (b)相位屏三维分布

    Fig. 3.  A realization of turbulence phase screen: (a) Two dimensional distribution; (b) three dimensional distribution.

    图 4  两种方法的相位屏结构函数对比 (a)结构函数曲线; (b)相对误差曲线

    Fig. 4.  Expected structure functions generated by Johansson’s method and our method, where the theoretical structure function is shown for reference: (a) Phase structure functions (b) relative errors.

    图 5  不同L0/L下的相位屏结构函数曲线与理论结构函数曲线

    Fig. 5.  The expected structure functions vs. theoretical structure functions with different L0/L.

    表 1  不同参数及参数值下的最大相对误差

    Table 1.  The maximum relative errors with different parameters.

    参数类型参数值
    最大相对误差
    r0/m0.10.20.30.40.511.5
    εmax0.000630.000630.000630.000630.000630.000630.00063
    L0/m2345102030
    εmax0.073990.166070.230830.258300.000630.965741.49931
    L/m2345102030
    εmax0.000630.232280.258300.230830.073990.023270.00677
    N326412825651210242048
    εmax0.002490.001110.000710.000630.000770.000840.00084
    下载: 导出CSV

    表 2  不同L0/L下的最优参数

    Table 2.  The optimization parameters with different L0/L.

    L0/L(c1, c2)
    1(15.73173, 24.90114)
    5(6.43847, 9.04869)
    10(23.73113, 28.39211)
    100(18.76658, 19.86318)
    200(18.16039, 18.81765)
    300(18.04556, 18.37957)
    inf(16.56943, 15.80313)
    下载: 导出CSV
  • [1]

    季小玲 2010 物理学报 59 692Google Scholar

    Jin X L 2010 Acta Phys. Sin. 59 692Google Scholar

    [2]

    Fleck J A, Morris J R, Feit M D 1976 Appl. Phys. 10 129

    [3]

    Flatte S M, Wang G Y, Martin J 1993 J. Opt. Soc. Am. A 10 2363Google Scholar

    [4]

    Flatte S M 2000 Opt. Express 10 777

    [5]

    McGlamery B L 1976 Proc. SPIE Int. Soc. Opt. Eng. 74 225

    [6]

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

    [7]

    Roddier N 1990 Opt. Eng. 29 1174Google Scholar

    [8]

    Wallace J, Gebhardt F G 1986 Proc. SPIE 642 261Google Scholar

    [9]

    Roggemann M C, Welsh B M, Montera D, Rhoadamer T A 1995 Appl. Opt. 34 4037Google Scholar

    [10]

    Harding C M, Johnston R A, Lane R G 1999 Appl. Opt. 38 2161Google Scholar

    [11]

    华志励, 李洪平 2012 光学学报 32 0501001

    Hua Z L, Li H P 2012 Acta Optica Sinica 32 0501001

    [12]

    Formwalt B, Cain S 2006 Appl. Opt. 45 5657Google Scholar

    [13]

    Sriram V, Kearney D 2007 Opt. Express 15 13709Google Scholar

    [14]

    Zhang B D, Qin S Q, Wang X S 2010 Chin. Opt. Lett. 8 969

    [15]

    Xiang J 2012 Opt. Express 20 681Google Scholar

    [16]

    王建新, 白福忠, 宁禹, 黄林海, 姜文汉 2011 物理学报 60 209501

    Wang J X, Bai F Z, Ning Y, Huang L H, Jiang W H 2011 Acta Phys. Sin. 60 209501

    [17]

    Vorontsov A M, Paramonov P V, Valley M T, Vorontsov M A 2008 Waves Random Complex Medium 18 91Google Scholar

    [18]

    Herman B J, Strugala L A 1990 Proc. SPIE 1221 183Google Scholar

    [19]

    Lane R G, Glindemann A, Dainty J C 1992 Waves Random Complex Medium 2 209Google Scholar

    [20]

    Johansson E M, Gavel D T 1994 Symposium on Astronomical Telescopes and Instrumentation for the 21st Century Kona, Hawaii, March 13-18 1994 p940391

    [21]

    Sedmak G 2004 Appl. Opt. 43 4527Google Scholar

    [22]

    Charnotskii M 2013 J. Opt. Soc. Am. A 30 479Google Scholar

    [23]

    蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞 2014 物理学报 63 104217Google Scholar

    Cai D M, Wang K, Jia P, Wang D, Liu J X 2014 Acta Phys. Sin. 63 104217Google Scholar

    [24]

    蔡冬梅, 遆培培, 贾鹏, 王东, 刘建霞 2015 物理学报 64 224217Google Scholar

    Cai D M, Ti P P, Jia P, Wang D, Liu J X 2015 Acta Phys. Sin. 64 224217Google Scholar

    [25]

    Xiang J S 2014 Opt. Eng. 53 016110Google Scholar

    [26]

    Rashedi E, Nezamabadi-pour H, Saryazdi S 2009 Information Science 179 2232Google Scholar

    [27]

    Kennedy J, Eberhart R 1995 Proceedings of IEEE International Conference on Neural Networks Perth, November 27, 1995 p1942

    [28]

    李春龙, 戴娟, 潘丰 2012 计算机应用 32 2732

    Li C L, Dai J, Pan F 2012 J. Comput. Appl. 32 2732

    [29]

    陈水利, 蔡国榕, 郭文忠, 陈国龙 2007 长江大学学报(自科版)理工卷 4 1Google Scholar

    Chen S L, Cai G R, Guo W Z, Chen G L 2007 Journal of Yangtze University(Nat. Sci. Ed.) Sci. & Eng. V 4 1Google Scholar

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出版历程
  • 收稿日期:  2019-01-16
  • 修回日期:  2019-05-09
  • 上网日期:  2019-07-01
  • 刊出日期:  2019-07-05

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