-
舰船尾流的分布特性如图1所示,舰船尾流分布特性一般指舰船尾流场厚度[6]、舰船尾流有效检测长度[7]、舰船尾流的宽度[8]等特性。
图 1 舰船尾流的分布特性。(a) 俯视图;(b) 横向剖面图;(c) 侧向剖面图
Figure 1. Distribution characteristics of ship wake. (a) Top view; (b) Transverse section; (c) Lateral profile
舰船尾流的长度一般为20~50 L (L指船体长度),其持续时间可达10~15 min,舰船尾流的有效检测长度与航速及可检测能力有关[9]。其公式可表示为:
$$ {L}_{T}={C}_{T}\cdot v $$ (1) 式中:
${L}_{T} $ 为可检测舰船尾流的长度;$ v $ 为舰船航速;$ {C}_{T} $ 为常数,代表尾流检测能力。已有的研究及实船测试数据表明舰船尾流的宽度和舰船的船型有关。其具体示意图如图1(a)所示,舰船尾流的起始宽度约为舰船宽度的一半,随后以40°~60°扩散角向两边扩散,到达一定距离后,舰船尾流的宽度大约为舰船的2.5倍。此后,舰船尾流以不大于1°的扩散角向两边扩散,直至舰船尾流消失[10]。其公式可以表示为:
$$ W=\left\{\begin{array}{l}0.5B+2vt\mathrm{tan}\alpha \qquad\qquad\qquad\;\; W\leqslant 2.5B\\ 2.5B+2\mathrm{tan}\beta vt-2B\mathrm{tan}\beta /\mathrm{t}\mathrm{a}\mathrm{n}\alpha \;\;W > 2.5B\end{array}\right. $$ (2) 式中:W为舰船尾流的宽度;B为舰船的宽度;t为航行时间;
$ \alpha $ ,$ \,\beta $ 为舰船尾流的扩散角。舰船尾流的初始厚度与舰船的吃水深度有关。其具体示意图如图1(b)、(c)所示,大型船只为吃水深度的2倍,小型船只为吃水深度的4倍左右,而后又与舰船的航行速度有关,通常为航速越高,舰船尾流越厚,高速航行的舰船可达吃水深度的7倍。尾流达到最大厚度后,气泡主要受自身浮力的影响,舰船尾流的厚度随时间的增加而逐渐降低。典型的舰船尾流分布如表1所示,CSS PAR IIEAU船在航速10 kn时、经过175 s后可达9 m深[11]。
-
尾流气泡目标特性通常指气泡数密度[12]、气泡层厚度[13]、气泡尺度[14]等特征。这里的尾流气泡层厚度特性亦可作为舰船尾流分布特性也可作为气泡目标特性。
舰船尾流气泡数密度主要由螺旋桨工况和舰船航速所决定。一般螺旋桨转速越快,航速越快,初始数密度越大。舰船尾流气泡数密度分布比较均匀,同一深度呈高斯分布。随气泡半径大致呈线性分布,半径越小的气泡其数密度越大。将舰船尾流分为近程尾流与远程尾流,近程尾流一般为舰船到3倍舰船长度左右距离。近程舰船尾流与远程舰船尾流存在明显的气泡特性差异,近程舰船尾流场中气泡受螺旋桨搅动及舰船行驶过后形成的空穴力因素影响较大,气泡尺度较大,一般在1000 μm以下,主要集中在100~500 μm左右,根据表2实际测量结果,气泡数密度可达到106~3×108 m−3,尺度较大的气泡上浮速度较快,且气泡尺度越大,气泡数密度越低[15]。
Bubble
radius/μm1 min/m−3 3 min/m−3 5 min/m−3 1070 4.9×102 4.1×101 - 400 1.79×104 5.6×103 7.8×102 160 4.6×105 1.98×105 9.3×104 80 5.5×106 2.61×106 1.45×106 10-1070 2.83×108 1.32×108 7.16×107 远程舰船尾流场中气泡主要受自身浮力的影响,大尺度气泡上升到海平面消亡,小尺度气泡由于上升缓慢,在海水中存留时间比较长,尺度一般为10~300 μm,其中以40~80 μm居多。根据实际测量,海水背景中的气泡数密度一般为104~105 m−3左右,远程舰船尾流气泡数密度一般可达105~6×106 m−3。随时间的增加,远程舰船尾流数密度逐渐降低到海水背景气泡数密度,其中10~20 μm气泡数密度最大,气泡层厚度一般为2~4 m[17]。
从远程尾流到近程尾流,舰船尾流分布特性及气泡目标特性变化规律为:尾流宽度逐渐减小;气泡群集中尺度逐渐增大;气泡数密度逐渐增大;气泡层厚度逐渐增大,到达最大厚度后开始减小。
-
蒙特卡洛方法是基于光子运动轨迹的计算机模拟,其基本过程是:光子以一个特殊的方向进入介质,确定发生碰撞时光子运动的距离,若发生散射,则由适当的散射相位函数就能选取散射后新的运动方向。若发生吸收,光子便消亡[18]。这些过程随机重复进行,直到光子被接收面所接收。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衰减路径上的衰减[19],能适用于绝大多数海域。
蒙特卡洛模拟可以分为六个步骤,(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。蒙特卡洛光子模拟运动程序图如图2所示。 -
不同舰船的舰船尾流目标特性不同,其回波特性也不尽相同,可利用其回波特性识别反演不同舰船,并探究其信号变化规律。文中采用多尺度、宽数密度、大厚度气泡场进行模拟,将舰船分为大型船只和小型船只,大型船只的航速高于小型船只。以远程舰船尾流气泡场作为探测的基本环境,将探测系统寻找舰船的过程分为搜索阶段和跟踪阶段,从远程尾流到近程舰船尾流过程进行模拟,近程舰船尾流模拟状态会存在于远程舰船尾流模拟中。舰船尾流是一个动态变化的环境,舰船尾流会随时间的增加,受湍流、扰动等非均匀因素影响,气泡会向四周扩散[20]。探测系统可能存在于尾流中或者尾流下,进行水下探测时探测系统以固定姿态运动,即与海平面保持固定距离,探测系统可能存在的运动方式如图3所示。
-
为了仿真模拟大型船只真实情况下的尾流场,仿真条件设置为激光波长532 nm,光子数为106,权值为10−5,接收口径为0.05 m,接收角为5 mrad;水质环境设为纯净海水,衰减系数为0.056 m−1,水体折射率为1.3。大型船只产生的气泡厚度在2~9 m动态变化,气泡尺度主要为20~500 μm动态变化,气泡数密度为105~3×108 m−3动态变化,气泡尺度、数密度、厚度逐渐随时间的增大而增大。仿真条件设置见表3。
表 3 大型船只仿真条件设置
Table 3. Simulation conditions for large vessel
Simulation
conditionsZone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7 Zone 8 Movement
modeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeBubble size/μm 20-80 80-140 140-200 200-260 260-320 320-380 380-440 440-500 Bubble thickness/m 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9 Bubble density/m−3 105-106 106-3×106 3×106-6×106 6×106-107 107-108 108-2×108 2×108-3×108 3×108 -
假设搜索阶段只在区域1进行,将探测搜索阶段大体分为两种情况:(1) 探测系统切入尾流场到0.5 W处;(2) 探测系统从0.5 W处切出尾流场;两种情况对称,其他情况大体包含在这两种情况中。将探测系统可能存在的位置划分为0、0.5、1、1.5、2 m,则位置划分为位置1~5。
(1)探测系统位于尾流场之下
设x=3 m,其余条件不变,得到探测系统从水体背景中切入到尾流场0.5 W处的回波信号图,如图4(a)所示,在位置2时,水体回波凹陷,出现气泡回波,出现气泡回波时间为20~30 ns,接收光子数从2360~2795降为33,气泡回波信号逐渐左移,且气泡回波幅度逐渐增加,脉冲宽度逐渐展宽。此时,气泡回波幅度尚未饱和。情况2下的状态与情况1的状态保持对称,其情况2与此相反,气泡回波幅度逐渐降低,脉冲宽度逐渐变窄。
(2)探测系统位于尾流场之中
现探测系统处于尾流之中,其余条件不变。得到探测系统从水体背景中切入到尾流场0.5 W处的回波信号图,如图4(b)所示,从位置2开始出现变化,回波信号整体先上升后下降,水体初始接收光子数在降低,峰值接收光子数从2700降到2414,气泡回波信号逐渐右移,气泡回波幅度逐渐降低,脉冲宽度逐渐变窄,较水体背景有明显变化。情况2时为气泡回波幅度逐渐增高,脉冲宽度逐渐展宽。出现气泡回波较水体回波降低的原因主要是探测系统位于舰船尾流之中,舰船尾流气泡遮挡了大部分光束,回波信号失去了部分水体的回波信号。
信号强度变化最明显的位置位于0.5 W处,探测系统位于尾流之中与尾流之下探测系统信号变化相反,且探测系统位于尾流之下时,变化更为明显,若信号在一直处于某个阈值之外,则搜索失败,继续保持搜索。
-
跟踪阶段为搜索阶段经系统检测后探测系统的下一个阶段,其已具备比较明显的变化特征,对从探测系统进入跟踪阶段到摧毁目标舰船进行模拟,将区域划分为8个区域,模拟其信号变化,仿真条件见表3。
(1)探测位于尾流场之下
设x=10 m,其余条件不变,其跟踪阶段回波信号图见图5(a),气泡回波信号逐渐左移、幅度持续凹陷、幅度缓慢增加,脉冲宽度逐渐展宽,接收光子数从1 012~2 721范围降为0,出现气泡信号时间范围为22~85 ns,气泡回波自区域2开始饱和,至区域7时,恢复不到原来水体回波信号,较搜索阶段信号变化明显。
(2)探测系统位于尾流场之中
现探测系统在尾流中,其余条件不变。其跟踪阶段回波信号图如图5(b)所示,信号初始接收光子数在降低,在区域2时初始接收光子数为零,大型船只峰值接收光子数从2453降到1683,气泡回波信号整体右移,气泡回波幅度逐渐降低,脉冲宽度逐渐变窄,较搜索阶段有明显变化。
探测系统位于尾流之中与尾流之下探测系统信号变化相反,且探测系统位于尾流之下时,变化更为明显,若信号在一直处于某个阈值之外,则跟踪失败,重新保持搜索。
-
试验目标设置为小型船只,小型船只产生的气泡厚度在1~4 m之间动态变化,气泡数密度在104~107 m−3之间变化,其余条件不变,仿真条件如表4所示。
表 4 小型船只仿真条件设置
Table 4. Small vessel simulation condition settings
Simulation
conditionsZone 1 Zone 2 Zone 3 Zone 4 Movement
modeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeBubble size/μm 20-60 60-100 100-300 300-500 Bubble
thickness/m0-1 1-2 2-3 3-4 Bubble
density/m−3104-105 105-106 106-107 107 -
将探测系统可能存在的位置划分为0、0.25、0.5、0.75、1 m,则位置划分为位置1~5,仿真环境为在区域1进行,其余条件不变。
(1)探测系统位于尾流场之下
设x=3 m,得到探测系统从水体背景中切入到尾流场0.5 W处的回波信号图,如图6(a)所示,信号变化趋势与大型船只变化相同,出现气泡时接收光子数从2443降为323,出现气泡时间范围为7~17 ns,信号变化强度不如大型船只,幅值和脉宽变化较小。
(2)探测系统位于尾流场之中
现探测系统处于尾流之中,得到探测系统从水体背景中切入到尾流场0.5 W处的回波信号图,如图6(b)所示,信号变化趋势与大型船只变化相同,峰值接收光子数从2812降为2482,变化强度不如大型船只,幅值和脉宽变化同样较小。
-
将小型船只跟踪区域划分为四个区域,对四个区域的信号变化进行模拟。仿真条件如表4所示。
(1)探测系统位于尾流场之下
设x=10 m,其余条件不变,其跟踪阶段回波信号图见图7(a),气泡变化趋势与大型船只相同,但出现气泡回波时间较大型船只晚,在50 ns后才出现,出现气泡回波接收光子数从856~1 362范围降为0,出现气泡时间范围为11~33 ns,变化强度不如大型船只。
(2)探测系统位于尾流场之中
现探测系统在尾流中,其余条件不变。其跟踪阶段回波信号图如图7(b)所示,气泡变化趋势与大型船只相同,但幅度和脉宽变化范围不如大型船只,小型船只接收光子数从2510降到了1 960左右,区域4时初始接收光子数为0。
通过仿真分析可得:当激光探测系统位于尾流之下时,大型船只的气泡回波幅度缓慢上升,气泡脉冲宽度显著展宽,且距舰船越近,气泡回波变化越明显。激光探测系统位于尾流之中时,气泡回波幅度逐渐降低,脉冲宽度逐渐变窄。激光探测系统位于尾流之下时与探测系统位于尾流之中时,信号变化相反。小型船只信号变化趋势基本与大型船只保持一致,但尾流激光探测回波强度变低。
Method and experiment of laser detection and tracking of ship wake
-
摘要: 舰船尾流激光探测跟踪是水下航行器对舰船进行探测、识别、跟踪的新手段。论文基于舰船尾流分布特性、气泡目标特性,采用蒙特卡洛仿真方法,实现了多尺度、宽数密度、大厚度舰船尾流气泡群的后向散射回波信号特性仿真,得到了水下航行器载激光探测系统在搜索、跟踪阶段信号的变化趋势,以及不同目标舰船的激光后向回波信号变化强度,可有效模拟激光探测系统对舰船尾流目标特性的真实跟踪状态。对于大型船只,当激光探测系统位于尾流之下时,航行器距舰船目标越近,尾流气泡激光回波越强,脉冲宽度展宽幅度越大;当激光探测系统位于尾流之中时,航行器距舰船目标越近,尾流气泡激光回波越弱,脉冲宽度变窄幅度越大。探测系统位于尾流之下时与探测系统位于尾流之中时,信号变化相反。小型船只信号变化趋势基本与大型船只保持一致,但尾流激光探测回波强度变低。开展了湖泊环境下船舶尾流激光探测跟踪试验,当探测系统在尾流之下时,大型船只尾流激光回波信号信噪比高,小型船只尾流激光难以检测。探测系统位于尾流之中时,大小船只尾流激光探测系统都可实现有效探测。论文可为舰船尾流探测实际工程应用提供支撑。Abstract:
Objective Ship wake laser detection and tracking is a new method for underwater vehicles to detect, identify and track ships. Due to the cavitation effect of the propeller, the breaking of the sea waves and the large amount of air involved in the waterline part of the ship during navigation, the air curtain belt containing a large number of bubbles, namely the ship wake, has formed at the ship's tail, which has very different optical characteristics from the surrounding water environment. Through the study of the laser characteristics of the ship wake, the characteristics of the ship's navigation path and speed in the ocean can be further judged, and then the precise guidance and damage attack of underwater vehicles such as the detection system can be realized. Ship wake is a dynamic changing environment, and the distribution characteristics of ship wake and bubble target characteristics are different in different ships and different environments. To achieve accurate attack on ships, it is necessary to study the distribution characteristics of ship wake and bubble target characteristics. By simulating the changing trend of echo signals under different ship wake conditions, it provides theoretical and simulation support for the ship wake in lakes, ocean and other outfield tracking and detection. Methods The simulation environment is established based on the ship wake distribution characteristics and bubble target characteristics (Fig.1). The Monte Carlo method is used to simulate the multi-scale, wide-number density and large-thickness ship wake bubble group. Through the analysis of the ship wake backscattering echo signal under different conditions, the real state of the detection system under the characteristics of the ship wake target can be effectively simulated. The signal changing trend of the detection system in the search and tracking phase and the echo signal change intensity of different target ships are obtained (Fig.4-7). The experiment of laser tracking and detection of ship wake in lake environment is carried out, and the simulation results are verified (Fig.9-12). Results and Discussions Through the in-depth study of ship wake distribution characteristics and bubble target characteristics, the laser backscattering echo characteristics of different bubble size, bubble number density, bubble layer thickness, and bubble distance are verified by simulation (Tab.1,2). Based on the horizontal/vertical distribution characteristics of bubbles in the wake of ships with different tonnage and speed, the detection ability and tracking method of underwater vehicles at different distances from the wake are studied (Fig.3). The outfield lake test of the laser detection prototype is carried out (Fig.8). The detection device is arranged at different depths to detect the wake of large sand carriers and yachts, which realizes the detection of the wake target under dynamic conditions, and verifies the system detection ability of the underwater vehicle at different distances from the wake (Fig. 9-12). Conclusions Based on the engineering application of laser detection of ship wakes, the manuscript establishes a simulation environment based on the distribution characteristics of ship wakes and target characteristics, and uses the Monte Carlo simulation method to simulate the multi-scale, wide-number density, and large-thickness ship wakes bubble groups. By summarizing and analyzing the backscattering echo signals of ship wakes under corresponding conditions, the real state of the detection system under the characteristics of ship wakes target can be effectively simulated. It is obtained that when the laser detection system is located under the wake, the bubble echo amplitude of large ships slowly rises, the bubble pulse width significantly broadens, and the closer to the ship target, the more obvious the bubble echo changes. When the laser detection system is in the wake, the bubble echo amplitude gradually decreases and the pulse width gradually narrows. When the laser detection system is under the wake and the detection system is in the wake, the signal changes are opposite. The signal changing trend of small ships is basically consistent with that of large ships, but the echo intensity of wake laser detection is lower. An outfield laser backscattering echo experimental system is built to verify that when the detection system is under the wake, the bubble echo signal changes to a slow increase in bubble amplitude and a significant broadening of bubble pulse width. When the detection system is in the wake, the bubble echo amplitude gradually decreases and the pulse width gradually narrows. It can provide support for ship wake detection in practical engineering applications. -
Key words:
- ship wake /
- laser detection /
- target tracking /
- Monte Carlo /
- lake experiment /
- simulation
-
Destroyer
modelSpeed/kn Thickness
at 360 m/mWidth/m Draft Rathborn 10-12 6.5±1.1 - - Hopewell 10 7.7±1.2 12 5.8 Evian 13 4.4±1.1 7.5 2.9 Bubble
radius/μm1 min/m−3 3 min/m−3 5 min/m−3 1070 4.9×102 4.1×101 - 400 1.79×104 5.6×103 7.8×102 160 4.6×105 1.98×105 9.3×104 80 5.5×106 2.61×106 1.45×106 10-1070 2.83×108 1.32×108 7.16×107 表 3 大型船只仿真条件设置
Table 3. Simulation conditions for large vessel
Simulation
conditionsZone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7 Zone 8 Movement
modeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeBubble size/μm 20-80 80-140 140-200 200-260 260-320 320-380 380-440 440-500 Bubble thickness/m 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9 Bubble density/m−3 105-106 106-3×106 3×106-6×106 6×106-107 107-108 108-2×108 2×108-3×108 3×108 表 4 小型船只仿真条件设置
Table 4. Small vessel simulation condition settings
Simulation
conditionsZone 1 Zone 2 Zone 3 Zone 4 Movement
modeIn/under
wakeIn/under
wakeIn/under
wakeIn/under
wakeBubble size/μm 20-60 60-100 100-300 300-500 Bubble
thickness/m0-1 1-2 2-3 3-4 Bubble
density/m−3104-105 105-106 106-107 107 -
[1] Wang Huili, Qi Yi, Liu Huanying. Boundary detection method of infrared image of ship wake [J]. Infrared and Laser Engineering, 2013, 42(2): 524-527. (in Chinese) [2] Wang Ping, Du Yongcheng, Yang Li, et al. Numerical and experimental study on the buoyancy and diffusion law of submarine thermal wake based on overlapping grid technology and VOF model [J]. Infrared and Laser Engineering, 2019, 48(4): 0404002. (in Chinese) doi: 10.3788/irla201948.0404002 [3] Jiang Xin, Chen Wuxiong, Nie Haitao, et al. Real-time ship target detection based on aerial remote sensing images [J]. Optics and Precision Engineering, 2020, 28(10): 2360-2369. (in Chinese) doi: 10.37188/OPE.20202810.2360 [4] Tang Meng, Zhang Yu. Study on polarization characteristics of wake microbubbles detected by laser [J]. Infrared and Laser Engineering, 2020, 49(1): 0105006. (in Chinese) doi: 10.3788/IRLA202049.0105006 [5] Li Yiyue. Turbulence spectrum separation of wind lidar using independent component analysis [J]. Optics and Precision Engineering, 2020, 28(5): 1029-1037. (in Chinese) [6] Zhang Hui, Gao Xiaocheng. Analysis of optical characteristics of ship wake and research on wake detection technology [J]. Ship Science and Technology, 2021, 43(24): 52-54. (in Chinese) [7] Gao Kexin, Jin Liangan, Yuan Zhijiang, et al. Study on bubble number density attenuation model of ship bubble wake [J]. China Test, 2019, 45(8): 61-66. (in Chinese) [8] Jin Liangan, Yan Xuefei, Wang Yong, et al. Study on bubble coalescence in ship wake based on large eddy simulation method and modified bubble equilibrium equation [J]. Science, Technology and Engineering, 2014, 14(24): 141-145. (in Chinese) [9] Chen P, Li X N, Zhang G. Rapid detection to long ship wake in synthetic aperture radar satellite imagery [J]. Journal of Oceanology and Limnology, 2019, 37(5): 1523-1532. (in Chinese) doi: 10.1007/s00343-019-8221-y [10] Li Hai, Jia Hongguang, Chen Zaibin. Analysis and experiment on aerodynamic characteristics of coaxial rotor system [J]. Optics and Precision Engineering, 2021, 29(9): 2140-2148. (in Chinese) doi: 10.37188/OPE.20212909.2140 [11] Zhang Qun, Wang Yingmin. Multi bubble model and finite element analysis in wake [J]. Torpedo Technology, 2014, 22(4): 316-320. (in Chinese) [12] Zhang Yinbo, Li Sining, Jiang Peng, et al. PCA feature extraction and elastic BP neural network for underwater bubble recognition [J]. Infrared and Laser Engineering, 2021, 50(6): 20200352. (in Chinese) doi: 10.3788/IRLA20200352 [13] Gao Jiang, Zhang Jingyuan Yang Li. Research status of ship bubble wake characteristics [J]. Ship Science and Technology, 2008(4): 27-32. (in Chinese) [14] Tian Hengdou, Jin Liangan, Wang Yong, et al. Study on bubble distribution in ship wake considering single bubble motion characteristics [J]. Acta Armamentarii, 2011, 32(9): 1126-1130. (in Chinese) [15] Guo C Y, Wu T C, Zhang Q, et al. Numerical simulation and experimental research on wake field of ships under off-design conditions [J]. China Ocean Engineering, 2016, 30(5): 821-834. (in Chinese) doi: 10.1007/s13344-016-0053-3 [16] Zhang X X, Wu Z S, Su X. Influence of breaking waves and wake bubbles on surface-ship wake scattering at low grazing angles [J]. Chinese Physics Letters, 2018, 35(7): 074101. (in Chinese) doi: 10.1088/0256-307X/35/7/074101 [17] Wang B L, Guo X Y, He C. Numerical simulations of wake signatures around high-speed ships [J]. Journal of Hydrodynamics, 2014, 26(6): 986-989. (in Chinese) doi: 10.1016/S1001-6058(14)60109-8 [18] Li Xiaobo, Li Wei, Sun Tianyu, et al. Analysis and design of onboard interface of Tianwen-1 high-resolution camera [J]. Optics and Precision Engineering, 2022, 30(2): 227-236. (in Chinese) [19] Feng Z F, Wang P P, Yang X, et al. Evaluation of light penetration of LED phototherapy apparatus in skin [J]. Optics and Precision Engineering, 2022, 30(10): 1139-1150. (in Chinese) doi: 10.37188/OPE.20223010.1139 [20] Cheng Yan, Yu Xuelian, Qian Weixian, et al. Ship wake extraction and detection from infrared remote sensing images [J]. Infrared and Laser Engineering, 2022, 51(2): 20210844. (in Chinese) doi: 10.3788/IRLA20210844