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本文提出了基于光纤湍流传感器阵列的大气光学湍流空间相关函数测量原理, 并确定了具体的测量方案和数据统计方法. 利用光纤湍流传感器阵列在近地面开展了大气光学湍流空间相关特性的实验测量研究, 尽可能全面地展示光学湍流空间相关函数的各种形式. 结果表明, 大气光学湍流的一维空间相关函数主要表现为两种结构形态, 其一, 58.7%基本符合各向同性湍流空间相关函数模型, 其相关函数在一定尺度范围内呈现随尺度的增大而减小的趋势, 当超过该尺度时, 相关系数接近于0; 其二, 另有37.9%表现为与尺度无关, 相关系数维持在0附近小幅度随机振荡. 不难发现:光学湍流的空间相关特性主要取决于湍流的强弱和湍流是否得以充分发展, 同时, 湍流的相干结构将引起空间相关函数的小幅度振荡. 以空间布点探测直接获取光学湍流空间相关函数的方法, 不仅为分析湍流空间结构奠定了实验基础, 同时, 也为进一步建立非K湍流模型提供了理论开端.Atmospheric optical turbulence means refractive index random fluctuation of atmosphere. In this article, according to the concept of correlation function, the measurement principle, measurement schemes, and data processing method of spatial correlation function are given based on a high-quality fiber optical turbulence sensing array. Determining the statistical time and the calculation principle of the spatial correlation is the main point of current research. Emphasis is put on demonstrating the kinds of structural forms and analyzing the impact elements of spatial correlation function in turbulence as clear as possible. Using the sensing array, experimental measurement is promoted in the near ground layer and many forms of correlation functions are revealed. Results show that there are two main structural forms of the spatial correlation function:the first one shows an isotropy-model form, which tends to decrease with the increase of spatial displacement, and then tends to zero after outer scale, the coincidence rate is about 58.7%. The other one tends to oscillate around zero, and the coincidence rate is about 37.9%. By analyzing the probability and impact elements, it is not difficult to know that the spatial correlation of an optical turbulence mainly depends on the intensity and development degree of the optical turbulence; and the coherent structure is an important factor of oscillation in the correlation functions. On the one hand, the value of correlation coefficient is mainly determined by the intensity of the optical turbulence; and on a certain scale, the stronger the turbulence, the bigger the value of correlation coefficient becomes. On the other hand, the variation tendency of correlation function is not only determined by the intensity of turbulence, but also by the development degree of the optical turbulence. When the atmosphere is in advection or anisotropy, its spatial correlation coefficient will oscillate around zero and be unrelated to the spatial displacement. The spatial correlation function obtained by the sensor array set is not only the foundation of analyzing the spatial structure, but also the beginning of giving non-Kolmogorov model of turbulence.
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Keywords:
- atmospheric optical turbulence /
- spatial correlation function /
- fiber optical turbulence sensor /
- structure form
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[11] Xiao S M 2014 Ph. D. Dissertation (Hefei:Hefei Institutes of Physical Science, the Chinese Academy of Sciences) (in Chinese) [肖树妹 2014 博士学位论文(合肥:中国科学院合肥物质科学研究院)]
[12] Kolmogorov A N 1991 Proc. R. Soc. Lond. A 434 9
[13] Hao L, Mei H P, Qian X M, Zhu W Y, Rao R Z 2008 Acta Photonica Sin. 37 2292 (in Chinese) [郝磊, 梅海平, 钱仙妹, 朱文越, 饶瑞中 2008 光子学报 37 2292]
[14] Xiao S M, Mei H P, Qian X M, Rao R Z 2011 Acta Opt. Sin. 31 0201002 (in Chinese) [肖树妹, 梅海平, 钱仙妹, 饶瑞中 2011 光学学报 31 0201002]
[15] Lukin V P 2005 Proceedings of SPIE Bellingham, WA, September 21-22, 2005p598101
[16] She Z S, Jackson E, Orszag S A 1990 Nature 344 226
[17] Nosov V V, Grigoriev V M, Kovadlo P G, Lukin V P, Nosov E V, Torgaev A V 2008 Proceedings of SPIE Krasnoyarsk, Russian, June 22, p729609
[18] Simmons L F G, Salter C, Taylor G I 1938 Proc. Roy. Soc. Lond. A 165 73
[19] Karman T V 1937 Physics 23 98
[20] Townsend A A 1947 Math. Proc. Cambridge. 43 560
[21] Renhorn I G E, Svensson T, Boreman G D 2013 Opt. Eng. 52 026001
[22] Kulikov V A, Andreeva M S, Koryabin A V, Shmalhausen V I 2012 Appl. Optics 51 8505
[23] Consortini A, Innocenti C, Paoli G 2002 Opt. Commun. 214 9
[24] Voistsekhovich V V, Cuevas S 1995 J. Opt. Soc. Am. A 12 2523
[25] Osman K T, Horbury T S 2007 Astrophys. J 654 103
[26] Rao C H, Jiang W H, Ling N 2000 Acta Opt. Sin. 20 1323 (in Chinese) [饶长辉, 姜文汉, 凌宁 2000光学学报 20 1323]
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[1] Rao R Z 2012 Modern Atmospheric Optics (Beijing:Science Press) p155-159 (in Chinese) [饶瑞中 2012 现代大气光学(北京:科学出版社)第155-159页]
[2] Cui L Y, Xue B D, Cao X G, Zhou F G 2014 J. Opt. Soc. Am. A 31 829
[3] Reinhardt C N, Tsintikidis D, Hammel S, Kuga Y, Ritcey J A, Ishimaru A 2012 Opt. Eng. 51 031205
[4] Wu X Q, Wang Y J, Zeng Z Y, Gong Z B 2002 High Power Laser and Particle Beams 14233 (in Chinese) [吴晓庆, 王英俭, 曾宗泳, 龚知本 2002 强激光与粒子束 14233]
[5] Wu X Q, Huang Y B, Mei H P, Shao S Y, Huang H H, Qian X M, Cui C L 2014 Acta Opt. Sin. 34 0601001 (in Chinese) [吴晓庆, 黄印博, 梅海平, 邵士勇, 黄宏华, 钱仙妹, 崔朝龙 2014 光学学报 34 0601001]
[6] Guo Y M, Ma X Y, Rao C H 2013 Acta Phys. Sin. 62 13420701 (in Chinese) [郭友明, 马晓燠, 饶长辉 2013 62 13420701]
[7] Cai D M, Wang K, Jia P, Wang D, Liu J X 2014 Acta Phys. Sin. 63 10421701 (in Chinese) [蔡冬梅, 王昆, 贾鹏, 王东, 刘建霞 2014 63 10421701]
[8] Shraiman B I, Siggia E D 2000 Nature 405 639
[9] Jiang N 1999 Mechanics in Engineering 21 75 (in Chinese) [姜楠 1999 力学与实践 21 75]
[10] Mei H P 2007 Ph. D. Dissertation (Hefei:Hefei Institutes of Physical Science, the Chinese Academy of Sciences) (in Chinese) [梅海平 2006 博士学位论文(合肥:中国科学院合肥物质科学研究院)]
[11] Xiao S M 2014 Ph. D. Dissertation (Hefei:Hefei Institutes of Physical Science, the Chinese Academy of Sciences) (in Chinese) [肖树妹 2014 博士学位论文(合肥:中国科学院合肥物质科学研究院)]
[12] Kolmogorov A N 1991 Proc. R. Soc. Lond. A 434 9
[13] Hao L, Mei H P, Qian X M, Zhu W Y, Rao R Z 2008 Acta Photonica Sin. 37 2292 (in Chinese) [郝磊, 梅海平, 钱仙妹, 朱文越, 饶瑞中 2008 光子学报 37 2292]
[14] Xiao S M, Mei H P, Qian X M, Rao R Z 2011 Acta Opt. Sin. 31 0201002 (in Chinese) [肖树妹, 梅海平, 钱仙妹, 饶瑞中 2011 光学学报 31 0201002]
[15] Lukin V P 2005 Proceedings of SPIE Bellingham, WA, September 21-22, 2005p598101
[16] She Z S, Jackson E, Orszag S A 1990 Nature 344 226
[17] Nosov V V, Grigoriev V M, Kovadlo P G, Lukin V P, Nosov E V, Torgaev A V 2008 Proceedings of SPIE Krasnoyarsk, Russian, June 22, p729609
[18] Simmons L F G, Salter C, Taylor G I 1938 Proc. Roy. Soc. Lond. A 165 73
[19] Karman T V 1937 Physics 23 98
[20] Townsend A A 1947 Math. Proc. Cambridge. 43 560
[21] Renhorn I G E, Svensson T, Boreman G D 2013 Opt. Eng. 52 026001
[22] Kulikov V A, Andreeva M S, Koryabin A V, Shmalhausen V I 2012 Appl. Optics 51 8505
[23] Consortini A, Innocenti C, Paoli G 2002 Opt. Commun. 214 9
[24] Voistsekhovich V V, Cuevas S 1995 J. Opt. Soc. Am. A 12 2523
[25] Osman K T, Horbury T S 2007 Astrophys. J 654 103
[26] Rao C H, Jiang W H, Ling N 2000 Acta Opt. Sin. 20 1323 (in Chinese) [饶长辉, 姜文汉, 凌宁 2000光学学报 20 1323]
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