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在研究激光在水体中的传播问题时,将光束看作大量光子组成的光子束,于是可以将激光在水体中的传播问题转换成光子束在水体中的传播问题。海水中的粒子具有随机性,光子在水体传播时,会随机地与介质发生碰撞[9]。蒙特卡洛仿真基于计算机的统计实验方法,可模拟大量光子的运动过程并记录光子的状态,不需要过多的近似,可以模拟不同衰减系数情况下水体的吸收和散射特性[10-12]。
文中考虑水体介质多次散射的情况,即水中散射粒子很稠密,同时考虑单次、二次、及更高次的散射和路径上的衰减[13]。水体介质多次散射如图1所示,能适用于绝大多数的海域。
模拟光子在水体中的传播,可以分为六个步骤。(1) 发射条件:波长,能量的确定;(2) 运动轨迹(自由程):传输
$ l $ 距离后,发生碰撞;(3) 散射过程:散射角计算;(4) 碰撞后的运动方向;(5) 新的自由程;(6) 终止条件:接收或消亡。(1)自由程及新的自由程确定
准直光束在介质传播的朗伯-比尔定律[14]:
$$ {{E}_{l}={E}_{0} \cdot {\rm e}}^{-cl} $$ (1) 由公式(1)可推导
$$ l=-\frac{\mathit{\rm ln}\S }{{N}^{1/3}\mathit{\rm ln}(1-\pi {r}^{2} \cdot {N}^{1/3})} $$ (2) 新的自由程为:
$$ {l}_{m+1}=-\frac{\mathit{\rm ln}{\S }_{m+1}}{{N}^{1/3}\mathit{\rm ln}(1-\pi {r}^{2} \cdot {N}^{1/3})} $$ (3) 式中:c为介质光学衰减系数;
$ l $ 为光束传播距离;$ {l}_{m+1} $ 碰撞$ m $ 次后新的光束传播距离;$ {E}_{0} $ 为光束的初始能量;$ {E}_{l} $ 为准直光束传播$ l $ 距离之后的剩余能量;$ r $ 为粒子半径;$ N $ 为关于$ C $ 的对数密度;$ \S $ ,$ {\S }_{m+1} $ 为(0,1)间均匀分布的随机数。(2)散射角及新的运动方向确定
图2是单个光子两次碰撞散射坐标系示意图。光子的初始位置为坐标原点,光子的初始运动方向为
${X}$ 轴正向,发生碰撞后改变方向。光子的初始位置矢量采用直角坐标系,只需要确定转角$ \varphi $ 和散射角$ \theta $ 即可。${{I}}_{0}$ 为初始方向,以入射方向为${x}$ 轴建立坐标系${O}{x}{y}{z}$ ,三个方向余弦分别为$ \mathrm{cos}\mathrm{\alpha }=1 $ ,$\mathit{\rm cos}\beta =0$ ,$\mathit{\rm cos}\gamma = 0$ 。第一次碰撞引起散射过程后,光子运动方向变为$ {I}_{1} $ ,以$ {I}_{1} $ 方向为${x}$ 轴建立坐标系$ {O}'{x}_{1}{y}_{1}{z}_{1} $ ,那么在坐标系$ Oxyz $ 中的方向余弦变为$\mathit{\rm cos}{\alpha }_{1}$ ,$\mathit{\rm cos}{\beta }_{1}$ ,$\mathit{\rm cos}{\gamma }_{1}$ ,其中$ {\alpha }_{1}= {\theta }_{1} $ ,$ {\theta }_{1} $ 为第一次散射角。设
$ {\varphi }_{1} $ 为第一次偏转角,$ \Delta {X}'OY $ 中,$ OY=1 $ ,则$X{O}'= \mathit{\rm csc}{\varphi }_{1}$ ;$ \Delta {X}'O{O}' $ 中,$\mathit{\rm sin}{\theta }_{1}=\dfrac{O{X}'}{O{O}'}=\dfrac{\mathit{\rm csc}{\varphi }_{1}}{O{O}'}$ ,$O{O}'= \mathit{\rm csc}{\varphi }_{1} \cdot \mathit{\rm csc}{\theta }_{1}$ ;$ \Delta YO{O}' $ 中,$\mathit{\rm cos}{\beta }_{1}=\dfrac{1}{O{O}'}=\mathit{\rm sin}{\varphi }_{1} \cdot \mathit{\rm sin}{\theta }_{1}$ 。再求${\gamma }_{1},$ $\mathit{\rm cos}{\gamma }_{1}=\mathit{\rm cos}{\varphi }_{2} \cdot \mathit{\rm cos}{\theta }_{2}$ ,那么$ {I}_{1} $ 在坐标系$ Oxyz $ 的方向余弦为$\left(\mathit{\rm cos}{\theta }_{1},\mathit{\rm sin}{\varphi }_{1} \cdot \mathit{\rm sin}{\theta }_{1},\mathit{\rm cos}{\varphi }_{1} \cdot \mathit{\rm cos}{\theta }_{1}\right)$ 。第二次碰撞引起散射过程后,光子运动方向变为$ {I}_{2} $ ,以$ {I}_{2} $ 方向为$ x $ 轴建立坐标系$ {O}^{''}{x}_{2}{y}_{2}{z}_{2} $ ,散射角为$ {\theta }_{2} $ ,偏转角为$ {\varphi }_{2} $ ,那么在相对系$ {O}'{x}_{1}{y}_{1}{z}_{1} $ 中方向余弦为$\left(\mathit{\rm cos}{\alpha }_{2},\mathit{\rm cos}{\beta }_{2},\mathit{\rm cos}{\gamma }_{2}\right)= \left(\mathit{\rm cos}{\theta }_{2},\mathit{\rm sin}{\varphi }_{2} \cdot \mathit{\rm sin}{\theta }_{2},\mathit{\rm cos}{\varphi }_{2} \cdot \mathit{\rm cos}{\theta }_{2}\right)$ ,需将该方向余弦转换为$ Oxyz $ 中的方向余弦,经过坐标系转换后,$ {I}_{2} $ 在坐标系$ Oxyz $ 中的方向余弦变为:$$ \left\{\begin{array}{l}\mathit{\rm cos}{\alpha }_{2}=\mathit{\rm cos}{\theta }_{1}\mathit{\rm cos}{\theta }_{2}-\mathit{\rm sin}{\varphi }_{2}\mathit{\rm sin}{\theta }_{2}\mathit{\rm sin}{\theta }_{1}\\ \mathit{\rm cos}{\beta }_{2}=\mathit{\rm cos}{\varphi }_{1}\mathit{\rm sin}{\theta }_{1}\mathit{\rm cos}{\theta }_{2}+\mathit{\rm cos}{\varphi }_{1}\mathit{\rm cos}{\theta }_{1}\mathit{\rm sin}{\varphi }_{2}\mathit{\rm sin}{\theta }_{2}+\\ \qquad\quad \mathit{\rm \rm \rm sin}{\varphi }_{1}\mathit{\rm \rm cos}{\varphi }_{2}\mathit{\rm sin}{\theta }_{2}\\ \mathit{\rm cos}{\gamma }_{2}=-\mathit{\rm sin}{\varphi }_{1}\mathit{\rm sin}{\theta }_{1}\mathit{\rm cos}{\theta }_{2}-\mathit{\rm sin}{\varphi }_{1}\mathit{\rm cos}{\theta }_{1}\mathit{\rm sin}{\varphi }_{2}\mathit{\rm sin}{\theta }_{2}+\\ \qquad\quad \mathit{\rm cos}{\varphi }_{1}\mathit{\rm cos}{\varphi }_{2}\mathit{\rm sin}{\theta }_{2}\end{array}\right. $$ (4) 光子在第
${m}$ 次碰撞后,其出射方向相对于前次坐标系为$ \left({\alpha }_{m},{\beta }_{m},{\gamma }_{m}\right) $ ,在第$ m+1 $ 次碰撞后,出射方向相对于第${m}$ 坐标系为$ \left({\alpha }_{m+1},{\beta }_{m+1},{\gamma }_{m+1}\right) $ 。其中:$$ \left\{ \begin{array}{l}\mathit{\rm cos}{\alpha }_{m+1}=\dfrac{\mathit{\rm sin}{\theta }_{m+1}( \mathit{\rm cos}{\gamma }_{m} \cdot \mathit{\rm cos}{\varphi }_{m+1}-\mathit{\rm sin}{\varphi }_{m+1} \cdot \mathit{\rm cos}{\beta }_{m})}{\sqrt{{\mathit{\rm cos}{\alpha }_{m}}^{2}+{\mathit{\rm cos}{\beta }_{m}}^{2}}+{\mathit{\rm cos}{a}_{m}}^{2} \cdot \mathit{\rm cos}{\theta }_{m+1}}\\ \mathit{\rm cos}{\beta }_{m+1} = \dfrac{\mathit{\rm sin}{\theta }_{m+1}( \mathit{\rm cos}{\beta }_{m} \cdot \mathit{\rm cos}{\gamma }_{m} \cdot \mathit{\rm cos}{\varphi }_{m+1} - \mathit{\rm sin}{\varphi }_{m+1} \cdot \mathit{\rm cos}{\varphi }_{m})}{\sqrt{{\mathit{\rm cos}{\alpha }_{m}}^{2} + {\mathit{\rm cos}{\beta }_{m}}^{2}} + {\mathit{\rm cos}{\beta }_{m}}^{2} \cdot \mathit{\rm cos}{\theta }_{m+1}}\\ \mathit{\rm cos}{\gamma }_{m+1}=-\mathit{\rm sin}{\theta }_{m} \cdot \mathit{\rm cos}{\varphi }_{m} \cdot \sqrt{{\mathit{\rm cos}{\alpha }_{m}}^{2}+{\mathit{\rm cos}{\beta }_{m}}^{2}}+\\ \qquad\quad\;\;\;\;\; \mathit{\rm cos}{\gamma }_{m} \cdot \mathit{\rm cos}{\theta }_{m}\end{array}\right. $$ (5) 图 2 单个光子两次碰撞散射坐标系示意图
Figure 2. Schematic diagram of double collision scattering coordinate system of a single photon
(3)光子生存确定
设置光子生存权值阈值为
$ {w}_{Y} $ ,单次散射率为$ {w}_{D} $ ,第m+1次碰撞后光子权值$ {w}_{m+1} $ 为:$$ {w}_{m+1}={w}_{m} \cdot {w}_{D} $$ (6) 若
$ {w}_{m+1} < {w}_{Y} $ ,光子继续运动,若${w}_{m+1}\geqslant {w}_{Y}$ ,光子被吸收。蒙特卡洛光子模拟运动程序图如图3所示。
Simulation and experimental study on laser backscattering characteristics in turbid water
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摘要: 由于水体的吸收和散射作用,光束能量在传播的过程中会产生衰减,激光脉冲会被展宽,制约着水下激光雷达的探测范围和探测精度。文中以浑浊水体环境下水下弱小目标探测为应用背景,建立了水下光子传播的蒙特卡洛仿真模型,模拟了不同衰减系数和散射率的水体后向散射回波信号,并对相应的水体后向散射回波信号变化趋势进行了分析。仿真结果表明:随水体衰减系数的增加,近场水体激光回波信号接收光子数逐渐增多;随水体散射率的增加,回波信号光子消亡速度逐渐降低。开展了不同浊度下的激光雷达回波信号的测试实验,实验结果表明:随水体衰减系数的增加,水体激光后向散射回波幅度逐渐增高,脉冲宽度逐渐展宽。在进行浑浊水体水下弱小目标探测时,随水体衰减系数的增加,应通过逐渐减小激光器能量或接收系统增益来增强水体回波与目标回波之间的差异,以此提高浑浊水体水下弱小目标探测的信噪比。实验验证了理论与仿真结果,为浑浊水体环境下水下弱小目标激光探测系统在不同水质下的激光能量选取、接收系统增益设计等提供理论支撑。Abstract: Due to the absorption and scattering of water, the beam energy will attenuate in the process of propagation, and the laser pulse will be widened, which restricts the detection range and accuracy of underwater lidar. Based on the application background of underwater weak and small target detection in turbid water environment, this paper establishes the Monte Carlo simulation model of underwater photon propagation, simulates the backscattering echo signal of water body with different attenuation coefficients and scattering rates, and analyzes the variation trend of the corresponding backscattering echo signal of water body. The simulation results show that the number of photons received by the laser echo signal of near-field water body gradually increases with the increase of attenuation coefficient of water body; With the increase of water scattering rate, the photon extinction speed of echo signal gradually decreases. The lidar echo signal test experiments under different turbidity are carried out. The experimental results show that with the increase of water attenuation coefficient, the laser backscattering echo amplitude of water gradually increases and the pulse width gradually widens. When detecting dim and small underwater targets in turbid water, with the increase of attenuation coefficient of water, the difference between water echo and target echo should be enhanced by gradually reducing laser energy or receiving system gain, so as to improve the signal-to-noise ratio of dim and small underwater targets in turbid water. The experimental results verify the theory and simulation results, and provide theoretical support for the laser energy selection and the gain design of the receiving system of the underwater weak and small target laser detection system under different water qualities in the turbid water environment.
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Key words:
- Monte Carlo /
- lidar /
- backscattering /
- turbid waters
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[1] Wei Zhen, Shen Na, Zhang Xiangjin. Experimental research and improved algorithm in attenuation model of rain transmission of laser at 532 nm [J]. Infrared and Laser Engineering, 2018, 47(11): 1106004. (in Chinese) doi: 10.3788/IRLA201847.1106004 [2] Kang Wenyun, Song Xiaoquan, Wei Zhen. Weak signal detecting method of laser ranging for space target in daytime [J]. Infrared and Laser Engineering, 2014, 43(9): 3026-3029. (in Chinese) doi: 10.3969/j.issn.1007-2276.2014.09.042 [3] Yang Chaoxiong, Jiang Haibo, Sun Xiuhui, et al. Fabrication of holographic diffuser with large scattering angle realized by multi-angle speckle exposure [J]. Acta Optica Sinica, 2021, 41(16): 1609001. (in Chinese) doi: 10.3788/AOS202141.1609001 [4] Cui Xiaoyu, Tao Yuting, Liu Qun, et al. Software to simulate spaceborne oceanic lidar returns using semianalytic Monte Carlo technique [J]. Infrared and Laser Engineering, 2020, 49(2): 0203009. (in Chinese) doi: 10.3788/IRLA202049.0203009 [5] Zhang Yingluo, Wang Yingmin, Huang Aiping. Influence of suspended particles based on mie theory on underwater laser transmission [J]. Chinese Journal of Lasers, 2018, 45(5): 0505002. (in Chinese) doi: 10.3788/CJL201845.0505002 [6] Shen Fahua, Zhuang Peng, Wang Bangxin, et al. Research on retrieval method of low-altitude wind field for rayleigh-mie scattering doppler lidar [J]. Chinese Journal of Lasers, 2021, 48(11): 1110005. (in Chinese) doi: 10.3788/CJL202148.1110005 [7] Zhao Qiaohua, Wang Xin, Li Junsheng, et al. Characteristic analysis of the fluctuation of the downwelling diffuse attenuation coefficient in meiliang bay of Taihu Lake [J]. Journal of Remote Sensing, 2008(1): 128-134. (in Chinese) doi: 10.11834/jrs.20080117 [8] Chen Huimin, Ma Chao, Qi Bin, et al. Study on backscattering characteristics of pulsed laser fuze in smoke [J]. Infrared and Laser Engineering, 2020, 49(4): 0403005. (in Chinese) doi: 10.3788/IRLA202049.0403005 [9] 黎静. 基于解析蒙特卡洛方法的载波调制水下激光通信研究[D]. 武汉: 华中科技大学, 2013. Li Jing. Research on carrier modulated underwater laser communication based on analytical Monte Carlo method. [D]. Wuhan: Huazhong University of science and technology, 2013. (in Chinese) [10] Shi Shengwei, Wang Jiang'an, Jiang Xingzhou, et al. Analysis of scattering phase function and backscattering signal characteristic of bubble films in ship wake [J]. Acta Optica Sinica, 2008, 28(10): 1861. (in Chinese) doi: 10.3321/j.issn:0253-2239.2008.10.005 [11] Chen Xingsu, Wang Xuefeng, Gao Canguan. Analysis of diffuse light field based on Monte Carlo simulation [J]. Laser Journal, 2016, 37(4): 50-53. (in Chinese) [12] Xu Qirui, Yin Fuchang. Monte Carlo simulation of laser propagation in underwater multipath [J]. Journal of Changchun University of Science and Technology (Natural Science Edition), 2008, 31(1): 81-84. (in Chinese) [13] Kong Xiaojuan, Liu Bingyi, Yang Qian, et al. Simulation of water optical property measurement with shipborne lidar [J]. Infrared and Laser Engineering, 2020, 49(2): 0205010. (in Chinese) doi: 10.3788/IRLA202049.0205010 [14] Yang Yu, Fan Linlin, Zhang Feng, et al. Interventional monitoring method of hemoglobin concentration based on Lambert-Beer law [J]. Journal of Optoelectronics · Laser, 2020, 31(4): 447-452. (in Chinese) [15] Ding Kun, Huang Youwei, Jin Weiqi, et al. Experimental study on the relationship between attenuation coefficient of blue-green laser transmission and the water turbidity [J]. Infrared Technology, 2013, 35(8): 467-471. (in Chinese)