搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

非均匀采样的功率谱反演大气湍流相位屏的快速模拟

蔡冬梅 遆培培 贾鹏 王东 刘建霞

引用本文:
Citation:

非均匀采样的功率谱反演大气湍流相位屏的快速模拟

蔡冬梅, 遆培培, 贾鹏, 王东, 刘建霞

Fast simulation of atmospheric turbulence phase screen based on non-uniform sampling

Cai Dong-Mei, Ti Pei-Pei, Jia Peng, Wang Dong, Liu Jian-Xia
PDF
导出引用
  • 对大气湍流功率谱非均匀采样可以有效改善传统功率谱反演法低频采样严重不足的缺陷, 实现高精度的大气湍流相位屏的模拟. 但采用的直接求和运算计算复杂度高, 相位屏的模拟速度极慢. 将非均匀快速傅里叶变换(NUFFT)引入到大气湍流相位屏的模拟, 可以实现相位屏的快速模拟. 从随机过程的谱分解出发, 将大气湍流相位随机过程表示为有限谐波分量叠加和的均方极限. 通过一个高斯核函数的卷积, 将非均匀分布的谐波复振幅映射到均匀网格空间, 进而利用快速傅里叶变换, 降低计算复杂度, 加快大气湍流相位屏的模拟速度. 以大气湍流的Kolmogorov 谱为例, 利用NUFFT仿真得到大气湍流相位屏, 并对相位屏的模拟精度、模拟速度和误差进行统计分析. 结果表明, NUFFT的引入可以实现快速、高精度的大气湍流相位屏的模拟.
    The generation of atmosphere turbulence wave-front is important for studying the light propagation and imaging through the atmosphere, and correcting the atmosphere turbulence, such as the adaptive optics system. The power spectral density method generates phase screens quickly for using the fast Fourier transform (FFT). The main drawback to this approach is that lower order aberrations such as tilt are often under represented. The reason is that the low frequency is sampled inadequately. Since the low order aberrations include a major percentage of the atmospheric energy spectrum, the error of simulated phase screens makes this method less desirable to use. To overcome this shortcoming, a non-uniform sampling method is proposed to generate phase screens accurately. Unfortunately, when the sampling is nonuniform, the FFT does not apply directly. Generating such a phase screen is computation intensive which greatly reduces simulation speed. In this paper, we develop a fast, more accurate method to generate atmospheric turbulence phase screens, according to non-uniforming sampling. The nonequispaced fast Fourier transform (NUFFT) arises in a variety of application areas, ranging from medical imaging to radio astronomy to the numerical solution of partial differential equations. Speeding up the simulation of atmospheric turbulence phase screens is possible by using the non-uniform fast Fourier transform. In this paper, the atmospheric turbulence phase screen is decomposed into a series of harmonics. Then the non-uniform distributed harmonics are projected onto over-sampled uniform grid by using the Gaussian kernel function. Atmospheric turbulence phase screen will be generated using the standard fast Fourier transform on the over-sampled uniform grid. The atmospheric turbulence phase screens can be generated quickly. Using Kolmogorov spectrum model in this paper, the phase screens can be generated quickly. The performances of generated phase screens are analyzed through their phase structure functions. The statistical results are in very good agreement with the theoretical values. The relative error curve of simulation phase screens is calculated and analyzed. The more the oversampling grid, the more the relative error is. Compared with the result from the direct harmonics summation method, the error here mainly concentrates in high-frequency region where the sampling frequency points are sparse. However, the atmosphere turbulence phase screen is simulated in high accuracy on the whole. Compared with the time cost of the harmonics summation, the time using NUFFT is decreased to about 800 times. The simulated phase screens indicate that non-uniform fast Fourier transform is able to generate atmospheric turbulence phase screen with high accuracy and fast speed.
      通信作者: 蔡冬梅, dm_cai@163.com
    • 基金项目: 山西省自然科学基金(批准号: 2013011006-4)、中国科学院自适应光学重点实验室基金(批准号: LAOF201301)和微细加工光学国家重点实验室(批准号: KFS4)资助的课题.
      Corresponding author: Cai Dong-Mei, dm_cai@163.com
    • Funds: Project supported by the Natural Science Foundation of Shanxi Province, China (Grant No. 2013011006-4), the Foundation of Key Laboratory of Adaptive Optics, Chinese Academy of Sciences (Grant No. LAOF201301), and the State Key Laboratory of Optical Technologies for Micro-fabrication, China (Grant No. KFS4).
    [1]

    Liu Y Y, L Q B, Zhang W X 2012 Acta Phys. Sin. 61 124201 (in Chinese) [刘杨阳, 吕群波, 张文喜 2012 物理学报 61 124201]

    [2]

    Zhao P T, Zhang Y C, Wang L, Zhao Y F, Su J, Fang X, Cao K F, Xie J, Du X Y 2007 Chin. Phys. B 16 2486

    [3]

    Du J, Ren D M, Zhao W J, Qu Y C, Chen Z L, Geng L J 2013 Chin. Phys. B 22 024211

    [4]

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

    [5]

    Lane R G, Glindeman A, Dainty J C 1992 Waves Random Media 2 209

    [6]

    Sedmak G 1998 Appl. Opt. 37 4605

    [7]

    Cai D M, Wang K, Jia P, Wang D, Liu J X 2014 Acta Phys. Sin. 63 104217 (in Chinese) [蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞 2014 物理学报 63 104217]

    [8]

    Dutt A, Rokhlin V 1993 SIAM J. Sci. Comput. 14 1368

    [9]

    Fessler J A, Sutton B P 2003 IEEE Trans. Signal Process. 14 560

    [10]

    Greengard L, Lee J Y 2004 Siam Rev. 46 443

    [11]

    Roddier N 1990 Opt. Eng. 29 1174

  • [1]

    Liu Y Y, L Q B, Zhang W X 2012 Acta Phys. Sin. 61 124201 (in Chinese) [刘杨阳, 吕群波, 张文喜 2012 物理学报 61 124201]

    [2]

    Zhao P T, Zhang Y C, Wang L, Zhao Y F, Su J, Fang X, Cao K F, Xie J, Du X Y 2007 Chin. Phys. B 16 2486

    [3]

    Du J, Ren D M, Zhao W J, Qu Y C, Chen Z L, Geng L J 2013 Chin. Phys. B 22 024211

    [4]

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

    [5]

    Lane R G, Glindeman A, Dainty J C 1992 Waves Random Media 2 209

    [6]

    Sedmak G 1998 Appl. Opt. 37 4605

    [7]

    Cai D M, Wang K, Jia P, Wang D, Liu J X 2014 Acta Phys. Sin. 63 104217 (in Chinese) [蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞 2014 物理学报 63 104217]

    [8]

    Dutt A, Rokhlin V 1993 SIAM J. Sci. Comput. 14 1368

    [9]

    Fessler J A, Sutton B P 2003 IEEE Trans. Signal Process. 14 560

    [10]

    Greengard L, Lee J Y 2004 Siam Rev. 46 443

    [11]

    Roddier N 1990 Opt. Eng. 29 1174

  • [1] 王明军, 席建霞, 王婉柔, 李勇俊, 张佳琳. 声波扰动对大气湍流内外尺度与折射率功率谱函数的影响分析. 物理学报, 2023, 72(12): 124303. doi: 10.7498/aps.72.20230003
    [2] 艾则孜姑丽·阿不都克热木, 陶志炜, 刘世韦, 李艳玲, 饶瑞中, 任益充. 大气湍流对接收光场时间相干特性的影响. 物理学报, 2022, 71(23): 234201. doi: 10.7498/aps.71.20221202
    [3] 罗文, 陈天江, 张飞舟, 邹凯, 安建祝, 张建柱. 基于阶梯相位调制的窄谱激光主动照明均匀性. 物理学报, 2021, 70(15): 154207. doi: 10.7498/aps.70.20210228
    [4] 闫玠霖, 韦宏艳, 蔡冬梅, 贾鹏, 乔铁柱. 大气湍流信道中聚焦涡旋光束轨道角动量串扰特性. 物理学报, 2020, 69(14): 144203. doi: 10.7498/aps.69.20200243
    [5] 徐启伟, 王佩佩, 曾镇佳, 黄泽斌, 周新星, 刘俊敏, 李瑛, 陈书青, 范滇元. 基于深度卷积神经网络的大气湍流相位提取. 物理学报, 2020, 69(1): 014209. doi: 10.7498/aps.69.20190982
    [6] 邓万涛, 赵刚, 夏惠军, 张茂, 杨艺帆. 非相干合成阵列激光倾斜像差校正方法. 物理学报, 2019, 68(23): 234205. doi: 10.7498/aps.68.20190961
    [7] 张冬晓, 陈志斌, 肖程, 秦梦泽, 吴浩. 基于引力搜索算法的湍流相位屏生成方法. 物理学报, 2019, 68(13): 134205. doi: 10.7498/aps.68.20190081
    [8] 刘李辉, 吕炜煜, 杨超, 麦灿基, 陈德鹏. 部分相干双曲余弦厄米高斯光束在非Kolmogorov大气湍流中的传输特性. 物理学报, 2015, 64(3): 034208. doi: 10.7498/aps.64.034208
    [9] 李晓庆, 王涛, 季小玲. 球差光束在大气湍流中传输特性的实验研究. 物理学报, 2014, 63(13): 134209. doi: 10.7498/aps.63.134209
    [10] 蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞. 功率谱反演大气湍流随机相位屏采样方法的研究. 物理学报, 2014, 63(10): 104217. doi: 10.7498/aps.63.104217
    [11] 李成强, 张合勇, 王挺峰, 刘立生, 郭劲. 高斯-谢尔模光束在大气湍流中传输的相干特性研究. 物理学报, 2013, 62(22): 224203. doi: 10.7498/aps.62.224203
    [12] 李晓庆, 季小玲, 朱建华. 大气湍流中光束的高阶强度矩. 物理学报, 2013, 62(4): 044217. doi: 10.7498/aps.62.044217
    [13] 刘扬阳, 吕群波, 张文喜. 大气湍流畸变对空间目标清晰干涉成像仿真研究. 物理学报, 2012, 61(12): 124201. doi: 10.7498/aps.61.124201
    [14] 李晋红, 吕百达. 部分相干涡旋光束通过大气湍流上行和下行传输的比较研究. 物理学报, 2011, 60(7): 074205. doi: 10.7498/aps.60.074205
    [15] 刘飞, 季小玲. 双曲余弦高斯列阵光束在湍流大气中的光束传输因子. 物理学报, 2011, 60(1): 014216. doi: 10.7498/aps.60.014216
    [16] 黎芳, 唐华, 江月松, 欧军. 拉盖尔-高斯光束在湍流大气中的螺旋谱特性. 物理学报, 2011, 60(1): 014204. doi: 10.7498/aps.60.014204
    [17] 马阎星, 王小林, 周朴, 马浩统, 赵海川, 许晓军, 司磊, 刘泽金, 赵伊君. 大气湍流对多抖动法相干合成技术中相位调制信号的影响. 物理学报, 2011, 60(9): 094211. doi: 10.7498/aps.60.094211
    [18] 季小玲. 大气湍流对径向分布高斯列阵光束扩展和方向性的影响. 物理学报, 2010, 59(1): 692-698. doi: 10.7498/aps.59.692
    [19] 郑巍巍, 王丽琴, 许静平, 王立刚. 带初相位分布的径向基模激光束列阵在湍流大气中的传输特性研究. 物理学报, 2009, 58(7): 5098-5103. doi: 10.7498/aps.58.5098
    [20] 陈晓文, 汤明玥, 季小玲. 大气湍流对部分相干厄米-高斯光束空间相干性的影响. 物理学报, 2008, 57(4): 2607-2613. doi: 10.7498/aps.57.2607
计量
  • 文章访问数:  6016
  • PDF下载量:  256
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-03-27
  • 修回日期:  2015-06-05
  • 刊出日期:  2015-11-05

/

返回文章
返回