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Simulation research and theoretical study on measurement of atmospheric optical turbulence and wind profile using the correlation of gradient-tilt

Peng Zhe Jing Xu Hou Zai-Hong Wu Yi

Simulation research and theoretical study on measurement of atmospheric optical turbulence and wind profile using the correlation of gradient-tilt

Peng Zhe, Jing Xu, Hou Zai-Hong, Wu Yi
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  • In this article, a theoretical method based on the fluctuation of gradient tilt (G-tilt) of active light source is proposed to estimate the horizontal profiles of atmospheric optical turbulence (Cn2) and transverse wind. The G-tilt, related to the average phase gradient, is in the same direction as the average ray direction. And G-tilt angle is considered to be equal to the ratio between the centroid position offset and the focal length. In this method, a theoretical model based on lidar system is set up, in which forward scatter light beams at different distances are taken as beacons. These beacons are detected by a two-aperture telescope. And two light columns, from which we can obtain the information about G-tilt angle, are imaged by these beacons. In order to obtain the turbulence intensity and wind velocity from G-tilt angle with our theoretical model, the differential cross-correlation expressions of G-tilt angle and its derivative are derived in detail. These two expressions are based on the spatial cross-correlation function obtained from Rytov approximation and Taylor's frozen-flow hypothesis for Kolmogorov turbulence. Simultaneously, path weighting functions of Cn2 and wind velocity are derived, and the effects of path weighting functions on the calculation of our method are analyzed. Based on such an analysis, to realize the inversion of turbulence intensity and transverse wind, the matrix transformation algorithm is proposed. We ignore some minimal values of the path weighting functions in our algorithm so that the ill-conditioned matrix is avoided. Besides, numerical simulation is used for preliminarily validating this method. In our simulation, Cn2 varies randomly between 10-15 m-2/3 and 10-14 m-2/3 while wind velocity ranges from -5 m/s to 10 m/s. The sign of the wind velocity represents the direction of wind. According to the simulation results, the horizontal profiles of atmospheric optical turbulence and transverse wind calculated are consistent with their theoretical values no matter whether there exists Gaussian noise. When the ratio between the standard deviation of Gaussian noise we added and the original signal is 0.2, the maximum relative error of logarithmic Cn2 is 3.4%, and the correlation coefficient between the calculated results and theoretical values for Cn2 is 0.8. Besides, the maximum absolute error of wind velocity is 1.82 m/s, and the correlation coefficient between the calculated results and theoretical values for wind velocity is 0.9. Even if the horizontal profiles of atmospheric optical turbulence and transverse wind vary largely, the calculation results of our method remain stable. Therefore, a new idea is provided for measuring atmospheric turbulence and wind.
      Corresponding author: Jing Xu, xujing@aiofm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 41405014).
    [1]

    Vernin J, Munoz-Tunon C 1994 Astron. Astrophys. 284 311

    [2]

    Avila R, Cuevas S 2009 Opt. Express 17 10926

    [3]

    Ziad A, Blary F, Borgnino J, Fanteï-Caujolle Y, Aristidi E, Martin F, Lantéri H, Douet R, Bondoux E, Mékarnia D 2013 Astron. Astrophys. 559 L6

    [4]

    Cheng Z, Tan F F, Jing X, He F, Hou Z H 2016 Acta Phys. Sin. 65 074205 (in Chinese) [程知, 谭逢富, 靖旭, 何枫, 侯再红 2016 物理学报 65 074205]

    [5]

    Jing X, Hou Z H, Wu Y, Qin L A, He F, Tan F F 2013 Opt. Lett. 38 3445

    [6]

    Cui C L, Huang H H, Mei H P, Zhu W Y, Rao R Z 2013 High Power Laser Part. Beams 25 1091 (in Chinese) [崔朝龙, 黄宏华, 梅海平, 朱文越, 饶瑞中 2013 强激光与粒子束 25 1091]

    [7]

    Cheng Z, He F, Jing X, Tan F F, Hou Z H 2016 Acta Opt. Sin. 36 401004 (in Chinese) [程知, 何枫, 靖旭, 谭逢富, 侯再红 2016 光学学报 36 401004]

    [8]

    Tichkule S, Muschinski A 2012 Appl. Opt. 51 5272

    [9]

    Schock M, Spillar E J 1998 Opt. Lett. 23 150

    [10]

    Jing X, Hou Z H, Qin L A, He F, Wu Y 2011 Infrared Laser Eng. 40 1352 (in Chinese) [靖旭, 侯再红, 秦来安, 何峰, 吴毅 2011 红外与激光工程 40 1352]

    [11]

    Sasiela R J 2007 Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Bellingham: SPIE) pp69-102

    [12]

    Wang T, Clifford S F, Ochs G R 1974 Appl. Opt. 13 2602

    [13]

    Rao R Z 2012 Modern Atmospheric Optics (Beijing: Science Press) pp368-433 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第368—433页]

    [14]

    Cai D M, Ti P P, Jia P, Wang D, Liu J X 2015 Acta Phys. Sin. 64 224217 (in Chinese) [蔡冬梅, 遆培培, 贾鹏, 王东, 刘建霞 2015 物理学报 64 224217]

    [15]

    Guo Y M, Ma X Y, Rao C H 2014 Acta Phys. Sin. 63 069502 (in Chinese) [郭友明, 马晓燠, 饶长辉 2014 物理学报 63 069502]

    [16]

    Huang K T 2014 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, the Chinese Academy of Sciences) (in Chinese) [黄克涛 2006 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]

  • [1]

    Vernin J, Munoz-Tunon C 1994 Astron. Astrophys. 284 311

    [2]

    Avila R, Cuevas S 2009 Opt. Express 17 10926

    [3]

    Ziad A, Blary F, Borgnino J, Fanteï-Caujolle Y, Aristidi E, Martin F, Lantéri H, Douet R, Bondoux E, Mékarnia D 2013 Astron. Astrophys. 559 L6

    [4]

    Cheng Z, Tan F F, Jing X, He F, Hou Z H 2016 Acta Phys. Sin. 65 074205 (in Chinese) [程知, 谭逢富, 靖旭, 何枫, 侯再红 2016 物理学报 65 074205]

    [5]

    Jing X, Hou Z H, Wu Y, Qin L A, He F, Tan F F 2013 Opt. Lett. 38 3445

    [6]

    Cui C L, Huang H H, Mei H P, Zhu W Y, Rao R Z 2013 High Power Laser Part. Beams 25 1091 (in Chinese) [崔朝龙, 黄宏华, 梅海平, 朱文越, 饶瑞中 2013 强激光与粒子束 25 1091]

    [7]

    Cheng Z, He F, Jing X, Tan F F, Hou Z H 2016 Acta Opt. Sin. 36 401004 (in Chinese) [程知, 何枫, 靖旭, 谭逢富, 侯再红 2016 光学学报 36 401004]

    [8]

    Tichkule S, Muschinski A 2012 Appl. Opt. 51 5272

    [9]

    Schock M, Spillar E J 1998 Opt. Lett. 23 150

    [10]

    Jing X, Hou Z H, Qin L A, He F, Wu Y 2011 Infrared Laser Eng. 40 1352 (in Chinese) [靖旭, 侯再红, 秦来安, 何峰, 吴毅 2011 红外与激光工程 40 1352]

    [11]

    Sasiela R J 2007 Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Bellingham: SPIE) pp69-102

    [12]

    Wang T, Clifford S F, Ochs G R 1974 Appl. Opt. 13 2602

    [13]

    Rao R Z 2012 Modern Atmospheric Optics (Beijing: Science Press) pp368-433 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第368—433页]

    [14]

    Cai D M, Ti P P, Jia P, Wang D, Liu J X 2015 Acta Phys. Sin. 64 224217 (in Chinese) [蔡冬梅, 遆培培, 贾鹏, 王东, 刘建霞 2015 物理学报 64 224217]

    [15]

    Guo Y M, Ma X Y, Rao C H 2014 Acta Phys. Sin. 63 069502 (in Chinese) [郭友明, 马晓燠, 饶长辉 2014 物理学报 63 069502]

    [16]

    Huang K T 2014 Ph. D. Dissertation (Hefei: Hefei Institutes of Physical Science, the Chinese Academy of Sciences) (in Chinese) [黄克涛 2006 博士学位论文(合肥: 中国科学院合肥物质科学研究院)]

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Publishing process
  • Received Date:  01 December 2016
  • Accepted Date:  08 March 2017
  • Published Online:  20 May 2017

Simulation research and theoretical study on measurement of atmospheric optical turbulence and wind profile using the correlation of gradient-tilt

    Corresponding author: Jing Xu, xujing@aiofm.ac.cn
  • 1. Department of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230026, China;
  • 2. Key Laboratory of Atmospheric Composition and Optical Radiation, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 41405014).

Abstract: In this article, a theoretical method based on the fluctuation of gradient tilt (G-tilt) of active light source is proposed to estimate the horizontal profiles of atmospheric optical turbulence (Cn2) and transverse wind. The G-tilt, related to the average phase gradient, is in the same direction as the average ray direction. And G-tilt angle is considered to be equal to the ratio between the centroid position offset and the focal length. In this method, a theoretical model based on lidar system is set up, in which forward scatter light beams at different distances are taken as beacons. These beacons are detected by a two-aperture telescope. And two light columns, from which we can obtain the information about G-tilt angle, are imaged by these beacons. In order to obtain the turbulence intensity and wind velocity from G-tilt angle with our theoretical model, the differential cross-correlation expressions of G-tilt angle and its derivative are derived in detail. These two expressions are based on the spatial cross-correlation function obtained from Rytov approximation and Taylor's frozen-flow hypothesis for Kolmogorov turbulence. Simultaneously, path weighting functions of Cn2 and wind velocity are derived, and the effects of path weighting functions on the calculation of our method are analyzed. Based on such an analysis, to realize the inversion of turbulence intensity and transverse wind, the matrix transformation algorithm is proposed. We ignore some minimal values of the path weighting functions in our algorithm so that the ill-conditioned matrix is avoided. Besides, numerical simulation is used for preliminarily validating this method. In our simulation, Cn2 varies randomly between 10-15 m-2/3 and 10-14 m-2/3 while wind velocity ranges from -5 m/s to 10 m/s. The sign of the wind velocity represents the direction of wind. According to the simulation results, the horizontal profiles of atmospheric optical turbulence and transverse wind calculated are consistent with their theoretical values no matter whether there exists Gaussian noise. When the ratio between the standard deviation of Gaussian noise we added and the original signal is 0.2, the maximum relative error of logarithmic Cn2 is 3.4%, and the correlation coefficient between the calculated results and theoretical values for Cn2 is 0.8. Besides, the maximum absolute error of wind velocity is 1.82 m/s, and the correlation coefficient between the calculated results and theoretical values for wind velocity is 0.9. Even if the horizontal profiles of atmospheric optical turbulence and transverse wind vary largely, the calculation results of our method remain stable. Therefore, a new idea is provided for measuring atmospheric turbulence and wind.

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