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依据布里渊散射光谱特征与海洋环境参数之间的耦合关系建立反演模型是布里渊激光雷达系统的测量理论基础。
由布里渊散射机理可知,布里渊散射是一种光子与介质相互作用的非弹性散射。与光子发生相互作用的并非介质粒子,而是介质密度波动。这种密度波动是由于介质粒子自由程的变动引起的,与介质的物理属性,如温度等都有关系。在宏观层面上,它是一种弹性振动,会形成声波场,并会造成介质的折射率在时空上发生周期性的变化。当光进入这个声波场时会因为这种折射率上的变化而产生散射现象。这种密度波动在微观上也能够被表示为声模,即声学声子,因而布里渊散射可以被认为是一种声光相互作用的散射。当布里渊散射发生时,光子通过碰撞会吞并一个声子增加自身能量,或者损耗自身能量进而产生一个声子。这种碰撞产生的声光能量交换会引起散射光频率的改变。在光谱上,这种光频率的变化体现为布里渊散射峰分为斯托克斯峰和反斯托克斯峰,其位置对称地分布在激光中心频率的两侧,相对于激光中心频率发生了一定的偏移。该偏移量被命名为布里渊频移,其物理表达式为[9]:
$${v_B}= - \frac{{{\omega _q}}}{{2\pi }}= \mp \frac{{2n{V_S}}}{{{\lambda _i}}}\sin \frac{\theta }{2}$$ (1) 式中:ωq为声子角频率;n为折射率;Vs为
声速;λi为入射光波长;θ为散射角,而布里渊峰半高处的宽度被定义为布里渊峰的半高线宽,简称布里渊线宽,其物理表达式为[10]: $${\varGamma _B}=\frac{{\varGamma {q^2}}}{\pi }=\frac{1}{{2\pi \rho }} \cdot \left[ {\frac{4}{3}{\eta _s}{\rm{ + }}{\eta _b} + \frac{\kappa }{{{C_V}}}\left( {\gamma - 1} \right)} \right] \cdot {\left( {\frac{{4\pi n}}{{{\lambda _i}}}\sin \frac{\theta }{2}} \right)^2}$$ (2) 式中:Γ为声波阻尼;q为声波波矢;ρ为气体密度;ηs和ηb分别为剪切粘滞系数和体粘滞系数;κ为气体热导率;cV为气体定容比热容。γ=cP/cV为气体的比热容比。由以上可以看出布里渊频移和线宽与入射激光的频率、介质的声速、折射率等参量相关。因此通过测量布里渊频移和线宽即可实现对介质参数的反演。
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对于海水介质来说,折射率和声速都可以表示为关于海水温度、盐度和入射波长的函数,具体可将公式(1)改写为:
$${v_B} = \frac{{2n(T,S,\lambda ){V_s}(T,S,p)}}{{{\lambda _i}}}\sin \frac{\theta }{2}$$ (3) 从公式(3)可以看出,温度和盐度通过影响折射率n和声速Vs来反映到布里渊频移vB变化上;只需要知道与折射率n以及声速Vs与温度T和盐度S之间的关系,就可以得到布里渊频移和温度的联系。
根据海水折射率和声速关于温度、盐度的经验公式可将上式变换为温度关于盐度和布里渊频移的函数,如下所示[9]:
$$ \begin{split} T(S, {v_B})=&{t_0} + {t_1}({v_B} - 7.5) + {t_2}{({v_B} - 7.5)^2} + {t_3}{({v_B} - 7.5)^3} +\\ &{t_4}{({v_B} - 7.5)^6} + S\left[ {{t_5} + {t_6}({v_B} - 7.5) }+\right.\\ &\left. { {t_7}{{({v_B} - 7.5)}^2} + {t_8}{{({v_B} - 7.5)}^3}} \right] \end{split} $$ (4) 式中:T为温度,℃;vB为布里渊频移
,GHz;S为盐度,‰。参数t0-t8的取值可见参考文献[9]。同样的声速作为温度跟盐度的函数,也可以根据公式(3)及(4)得到: $$ \begin{split} {V_S}(S, {v_B})=&c_0^{'} + c_1^{'}({v_B} - 7.5) + c_2^{'}{({v_B} - 7.5)^2} + c_3^{'}{({v_B} - 7.5)^3} + \\ & c_4^{'}{({v_B} - 7.5)^5} + S\left[ {c_5^{'} + c_6^{'}{{({v_B} - 7.5)}^2} +} \right.\\ & \left.{c_7^{'}{{({v_B} - 7.5)}^3}} \right] \end{split} $$ (5) 这里参数c0~c7的取值可见参考文献[9]。
通过以上可知,在假设盐度已知的情况下即可实现对海水温度和声速的反演。其中温度最大拟合误差约为±0.16 ℃,声速拟合误差在±0.05 m/s。当布里渊频移的测量不确定度δvB=±1 MHz时,典型条件下温度测量不确定度为0.19~0.28 ℃,声速反演不确定度为0.234~0.255 m/s。
在2002年,北京师范大学的刘大禾课题组利用F-P扫描干涉仪结合PMT的方式接收后向布里渊散射谱线[11],并从中读取布里渊频移,进而利用公式(5)计算声速,获取了温度为0~30 ℃,盐度为0‰及35‰的多组不同条件下的声速数据,将得到的结果与经典方法测得的声速数据进行比较,其最大误差为13 m/s,最小误差为0.1 m/s,相对偏差小于0.9%,证明了利用布里渊频移反演海水中声速的可行性。
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与布里渊频移类似,布里渊线宽公式中的海水的折射率n、密度ρ、体粘滞系数ηb、剪切粘滞系数ηs等也与海水温度T、盐度S有直接联系,因此,可将公式(2)改写为如公式(6)所示:
$$\begin{split} {\varGamma _B}=&\frac{1}{{2\pi \rho (T,S)}} \cdot \left[ {\frac{4}{3}{\eta _s}(T,S) + {\eta _b}(T,S) + \frac{\kappa }{{{C_p}}}\left( {\gamma - 1} \right)} \right] \cdot \\ &{\left( {\frac{{4\pi n(T,S)}}{{{\lambda _i}}}\sin \frac{\theta }{2}} \right)^2} \end{split}$$ (6) 可得布里渊线宽ΓB与温度T及盐度S之间的联系,进而利用经验拟合可以得到温度的计算公式[12]:
$$T(S, {\varGamma _B})=\sum\limits_{i=0}^5 {{t_i}\varGamma _B^{ - i}} + S({t_6}\varGamma _B^{ - 1} + {t_7}\varGamma _B^{ - 2} + {t_8}\varGamma _B^{ - 3})$$ (7) 其中参数t1~t8可见参考文献[12],同理,当盐度已知时,可以通过布里渊线宽进行海水温度反演。当布里渊线宽测量不确定度ΔΓB=1 MHz时,温度反演不确定度从0.008~0.08 ℃,小于通过布里渊频移反演温度的结果。
具体分析布里渊散射光谱与海水温度盐度的依赖关系可知[13],在较低温度(10 ℃)的条件下,采用线宽反演温度的理论模型会有较好的精度,而对于较高温度 (30 ℃)的条件,采用布里渊频移反演温度的理论模型会有较高的精度,则更适合采用频移测量的方式。
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利用上述模型进行温度或者声速反演时,需要假定盐度已知。事实上,上述模型中布里渊频移vB和布里渊线宽ГB都是海水温度T和盐度S的函数,因而可以利用以上两式建立联立的方程组,将该方程组中的布里渊频移vB和布里渊线宽ГB认定为已知量,把海水的温度T和盐度S认作未知量,通过求解方程组:
$$\left\{ \begin{array}{l} {v_B}={v_B}(T,S) \\ {\varGamma _B}={\varGamma _B}(T,S) \end{array} \right. \Rightarrow \left\{ \begin{array}{l} T=T({v_B},{\varGamma _B}) \\ S=S({v_B},{\varGamma _B}) \end{array} \right.$$ (8) 能够得到温度T和盐度S关于布里渊频移vB和布里渊线宽ГB的表达式,即基于布里渊频移和布里渊线宽的温盐同步反演模型[14]。具体如下:
$$ \begin{split} T({v_B},{\varGamma _B})=&{t_1} + {t_2} \cdot {v_B} + \dfrac{{{t_3}}}{{{\varGamma _B}}} + {t_4} \cdot {v_B}^2 + \dfrac{{{t_5}}}{{\varGamma _B^2}} + \dfrac{{{t_6} \cdot {v_B}}}{{{\varGamma _B}}} + \\ & {t_7} \cdot v_B^3 + \dfrac{{{t_8}}}{{\varGamma _B^3}} + \dfrac{{{t_9} \cdot {v_B}}}{{\varGamma _B^2}} + \dfrac{{{t_{10}} \cdot v_B^2}}{{{\varGamma _B}}} \end{split} $$ (9) $$ \begin{split} S({v_B},{\varGamma _B})=&{s_1} + \dfrac{{{s_2}}}{{{v_B}}} + \dfrac{{{s_3}}}{{v_B^2}} + \dfrac{{{s_4}}}{{v_B^3}} + \dfrac{{{s_5}}}{{v_B^4}} + \dfrac{{{s_6}}}{{v_B^5}} + {s_7} \cdot \ln {\varGamma _B} + \\ & {s_8} \cdot {\ln ^2}{\varGamma _B} + {s_9} \cdot {\ln ^3}{\varGamma _B} + {s_{10}} \cdot {\ln ^4}{\varGamma _B} + {s_{11}} \cdot {\ln ^5}{\varGamma _B} \end{split} $$ (10) 式中:布里渊频移vB和布里渊线宽ГB的单位为GHz,参数t1~t10和s1~s11为常数,具体取值可见参考文献[14]。
该模型的温度的拟合误差在0.08 ℃以内,相对误差少于0.26%,而盐度拟合误差在0.21‰以内,相对误差少于0.57%。相比于以往温度单参数反演模型,温度拟合误差相近,而盐度也在海洋盐度变化范围(1‰以上的变化)内,能够用于分辨海洋盐度的变化。设置δvB=±1 MHz和δГB=±1 MHz,温度和盐度的测量不确定度的平均值分别为0.06 ℃和0.84‰。与单参数反演模型相比,温度拟合误差与分辨率相当,而盐度拟合误差则要明显小于该不确定度,说明该模型的拟合精度已满足目前MHz的测量精度。
在2014年,华中科技大学基于F-P标准具结合ICCD的接收系统,获取布里渊散射谱线[15],得到布里渊频移以及布里渊线宽进行温度、盐度的双参数反演,实验结果表明,温度拟合误差在0.1 ℃以内,盐度拟合误差为0.36‰,充分证明了利用布里渊频移及布里渊线宽进行双参数反演的可行性。
Research progress of ocean environmental laser remote sensing based on Brillouin scattering
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摘要:
布里渊激光雷达是探测海洋环境参数的重要手段之一。首先介绍了布里渊激光雷达系统的基本工作原理,然后从理论基础出发,重点介绍了三种依据布里渊散射光谱特征:布里渊频移、布里渊线宽、以及综合二者与海洋环境参数之间的耦合关系建立的反演模型;其次,作为布里渊激光雷达的关键技术,介绍了多种布里渊散射光谱的测量方法:F-P扫描干涉仪探测、边缘探测、F-P标准具- ICCD探测, 以及多边缘探测。
Abstract:Brillouin lidar is one of the important methods to detect ocean environmental parameters. Firstly, the basic work principle of Brillouin lidar system was introduced. Then, from the theoretical basis, three retrieval models based on the relationship between Brillouin scattering spectrum characteristics: Brillouin shift, Brillouin linewidth, and the combination of them, and ocean environmental parameters were introduced. Secondly, as the key technology of Brillouin lidar, several Brillouin spectrum measurement methods were introduced: the scanning Fabry-Pérot(F-P) interferometer, the edge detection technique, F-P etalon combined with Intensified Charge Coupled Device(ICCD), and multi edge detection technique.
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Key words:
- Brillouin scattering /
- ocean remote sensing /
- ocean environment /
- scattering spectrum
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图 8 利用ESFADOF作为边缘探测技术的激光雷达系统实验装置图。(a)激光光源光源产生方案;(b)激光散射方案以及对应产生的布里渊散射谱线;(c)边缘探测方案以及对应的边缘滤波曲线
Figure 8. Experimental setup of lidar system using ESFADOF as edge detection technology. (a) Laser source generation scheme; (b) Laser scattering scheme and corresponding Brillouin scattering spectrum line; (c) Edge detection scheme and corresponding edge filtering curve
图 9 (a1) 50 000次测量平均后,激光雷达两个管道测量的温度结果同Pt100测量结果的比较,(a2)误差分析;(b)激光雷达两个管道的平均温度偏差与平均次数和采集持续时间之间的关系
Figure 9. (a1) Comparison of the temperature results measured by two lidar tubes and Pt100 after 50 000 measurements, (a2) Error analysis; (b) Relationship between the average temperature deviation, average number and acquisition duration of two lidar tubes
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[1] Hua Dengxin, Wang Jun. The research progress of ocean laser remote sensing technology(invited) [J]. Infrared and Laser Engineering, 2018, 47(9): 0903003. (in Chinese) doi: 10.3788/irla201847.0903003 [2] Lin Mingsen, He Xianqiang, Jia Yongjun, et al. Progress of ocean satellite remote sensing technology in China [J]. Acta Oceanographica Sinica, 2019, 41(10): 99-112. (in Chinese) [3] Yin Xiaobin, Wang Zhenzhan, Liu Yuguang, et al. Comparison of sea surface temperature retrieved by infrared and microwave radiometers [J]. Ocean Bulletin, 2009, 11(2): 1-12. (in Chinese) [4] Yu Xiaolei, Wu Zhaocong. Retrieval of Bohai sea surface temperature using thermal infrared image of HJ-1 satellite [J]. Ocean Technology, 2011(2): 5-10. (in Chinese) [5] 殷晓斌. 海面风矢量、温度和盐度的被动微波遥感及风对温盐遥感的影响研究[D]. 中国海洋大学, 2007. Yin Xiaobin. Passive microwave remote sensing of sea surface wind vector, temperature and salinity and the influence of wind on temperature and Salinity Remote Sensing[D]. Qingdao: Ocean University of China, 2007. (in Chinese) [6] Li Qingxia, Zhang Jing, Guo Wei, et al. Research progress of remote sensing ocean salinity by microwave radiometer [J]. Ocean Technology, 2007, 26(3): 62-67. (in Chinese) [7] Ren Xiuyun, Wang Ling, Tian Zhaoshuo, et al. Study on practical underwater temperature telemetry system based on Raman spectroscopy [J]. Spectroscopy and Spectral Analysis, 2019, 39(3): 120-125. (in Chinese) [8] 张雪娟. 基于拉曼散射的海水盐度测量技术研究[D]. 哈尔滨工业大学, 2017 Zhang Xuejuan. Research on seawater salinity measurement technology based on Raman scattering[D]. Harbin: Harbin Institute of Technology, 2017. (in Chinese) [9] Fry E S, Emery Y, Quan X, et al. Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean [J]. Applied Optics, 1997, 36(27): 6887-6894. doi: 10.1364/AO.36.006887 [10] Fry E, Katz J, Liu D, et al. Temperature dependence of the Brillouin linewidth in water [J]. Journal of Modern Optics, 2002, 49(3-4): 411-418. doi: 10.1080/09500340110088551 [11] Liu D, Xu J, Li R, et al. Measurements of sound speed in the water by Brillouin scattering using pulsed Nd: YAG laser [J]. Optics Communications, 2002, 203(3-6): 335-340. doi: 10.1016/S0030-4018(02)01181-1 [12] Gao W, Lv Z, Dong Y, et al. A new approach to measure the ocean temperature using Brillouin lidar [J]. Chinese Optics Letters, 2006, 4(7): 428-431. [13] Yuan Y, Niu Q, Liang K. Measurement error analysis of Brillouin lidar system using F–P etalon and ICCD [J]. Optics Communications, 2016, 375: 58-62. doi: 10.1016/j.optcom.2016.04.065 [14] Liang K, Ma Y, Yu Y, et al. Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth [J]. Optical Engineering, 2012, 51(6): 066002. doi: 10.1117/1.OE.51.6.066002 [15] Yu Y, Ma Y, Li H, et al. Simulation on simultaneously obtaining ocean temperature and salinity using dual-wavelength Brillouin Lidar [J]. Laser Physics Letters, 2014, 11(3): 036001. doi: 10.1088/1612-2011/11/3/036001 [16] Xu J, Ren X, Gong W, et al. Measurement of the bulk viscosity of liquid by Brillouin scattering [J]. Applied Optics, 2003, 42(33): 6704-6709. [17] Fry E, Katz J, Liu D, et al. Temperature dependence of the Brillouin linewidth in water [J]. Journal of Modern Optics, 2010, 10(3-4): 411-418. [18] Hirschberg J G, Byrne J D, Wouters A W, et al. Speed of sound and temperature in the ocean by Brillouin scattering [J]. Applied Optics, 1984, 23(15): 2624-2628. doi: 10.1364/AO.23.002624 [19] Emery Y, Fry E. Laboratory development of a lidar for measurement of sound velocity in the ocean using Brillouin scattering[C]//Proceedings of SPIE the International Society for Optical Engineering, 1997, 2963: 210-215. [20] Dai R, Gong W, Xu J, et al. The edge technique as used in Brillouin lidar for remote sensing of the ocean [J]. Applied Physics B, Lasers and Optics, 2004, B79(2): 245-248. [21] Rudolf A, Walther T. High-transmission excited-state Faraday anomalous dispersion optical filter edge filter based on a Halbach cylinder magnetic-field configuration [J]. Optics Letters, 2012, 37(21): 4477-4479. doi: 10.1364/OL.37.004477 [22] Rudolf A, Walther T. Laboratory demonstration of a Brillouin lidar to remotely measure temperature profiles of the ocean [J]. Optical Engineering, 2014, 53(5): 051407. doi: 10.1117/1.OE.53.5.051407 [23] Shi J, Ouyang M, Gong W, et al. A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean [J]. Applied Physics B: Lasers and Optics, 2008, 90(3-4): 569-571. doi: 10.1007/s00340-007-2866-5 [24] Huang J, Ma Y, Zhou B, et al. Processing method of spectral measurement using F-P etalon and ICCD [J]. Optics Express, 2012, 20(17): 18568. doi: 10.1364/OE.20.018568 [25] Liang K, Zhang R, Sun Q, et al. Brillouin shift and linewidth measurement based on double-edge detection technology in seawater [J]. Applied Physics B, 2020, 126(10): 160. doi: 10.1007/s00340-020-07509-1 [26] Kai S, Alexandru P, Marco G, et al. Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb: doped fiber amplifier [J]. Sensors, 2008, 8(9): 5820-5831. doi: 10.3390/s8095820
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