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激光雷达作为一种主动光电探测系统， 广泛应用于机载海洋测量[1]、气象监测[2-4]等领域。近年，自动驾驶[5-6]等行业应用激光雷达实现避障和导航。
探测距离为公里级的长距离大气探测激光雷达，以参数反演为应用目的[7]，较多采用望远系统作为接收光学系统，激光器发出的光脉冲与大气中的空气分子、气溶胶和云等相互作用形成后向散射光，后向散射光经望远系统被探测器接收形成后向散射回波信号，对后向散射回波信号进行算法反演得到大气的相关廓线信息[8]，精准的后向散射回波信号建模对参数反演至关重要。图1所示是采用卡塞格林望远系统的激光雷达 [9]，次反射镜对回波信号存在遮挡。
图 1 望远式长距离激光雷达光机结构示意图
Figure 1. Schematic diagram of optical and mechanical structure for LiDAR using telescopic system
自动驾驶等行业应用的警戒激光雷达以获取目标距离和告警为应用目的，通过对回波信号进行“阈值检测”[10]获取目标距离并告警 [11]。警戒激光雷达在恶劣气象环境（雾、粉尘等）下工作时，激光雷达出射的激光入射到水滴或粉尘上会发生散射，后向散射光形成后向散射回波，前向散射光在遇到物体后被反射形成目标回波，后向散射回波会对目标回波的检测造成干扰，因此，抑制后向散射回波对警戒激光雷达至关重要，这一点与大气探测激光雷达不同。警戒激光雷达的探测距离在10−1千米量级，对探测距离要求相对较低，警戒激光雷达的接收光学系统由望远系统简化为单透镜。图2给出采用单透镜作为接收光学系统的旁轴激光雷达和同轴激光雷达的典型光机结构示意图，旁轴激光雷达的反射镜和同轴激光雷达的发射单透镜对回波信号存在遮挡。
图 2 单透镜接收警戒激光雷达光机结构示意图
Figure 2. Schematic diagram of optical and mechanical structure for warning LiDAR using single lens receiver
一方面，针对面目标探测的激光雷达回波信号强度与距离平方成反比[12]，导致近场信号强度比远场信号强度大几个数量级，响应动态范围极大。另一方面，激光雷达发射模块光机结构遮挡部分的接收视场、发射光学系统和接收光学系统非共轴等因素会影响近场信号[13]，导致回波信号强度并不随距离增加而单调递减，而是随距离增加呈现先增大后减小的现象。上述两方面对大气探测激光雷达和警戒激光雷达具有不同的影响，下面分别阐述。
对大气探测激光雷达而言：一方面，针对“响应动态范围极大”的问题，可以从硬件电路控制和光学方法两个方面进行“响应动态范围压缩”， 在大气探测不是很计较经济成本的前提下也可以采用高性能探测器和存储器来采集和存储大动态范围的回波信号，因此“响应动态范围压缩”对大气探测激光雷达而言不是瓶颈问题。另一方面，光机结构遮挡导致回波信号随距离增加先增大后减小，此时如果仍然按照距离平方反比反演参数，会造成参数反演的偏差，因此，必须通过“基于光机结构参数进行激光雷达回波建模”修正后向散射回波信号，从而精确反演大气参数，大气探测激光雷达研究重点在对后向散射回波信号进行精准建模，从而“利用后向散射回波信号”实现精确的大气参数反演。通过高性能硬件电路控制方式实现激光雷达响应动态范围压缩[14-16]存在稳定性不足、串扰强、延迟高、工艺难度大等弊端，且对优质进口芯片的依赖性强。因此，高稳定性光学方法成为该项研究的重点突破方向[17]。2013年，张冰娜等提出一种复合自动增益控制技术，采用电子学自动增益和接收光学系统通光口径自动调节结合的方式，通过标定实现光学调节[18]。2015年，李松等提出一种激光雷达回波能量动态范围压缩的实验调整方法，通过在实验中调节发射光轴和接收光轴的夹角、并同时调节探测器的离焦程度实现动态范围压缩[17]。上述两种光学实验调整方案都能取得较好的动态范围压缩效果，但是对经验具有很强的依赖性。如果能基于光机结构参数建立激光雷达回波的理论模型，则能在激光雷达初始设计阶段对影响激光雷达响应的光机结构参数进行理论分析和优化设计。为了对利用光机结构特性对激光雷达后向散射回波信号进行建模的方法进行定量描述，引入重叠因子(overlap) [9]的概念，重叠因子定义为探测器的有效接收能量与介质散射/目标反射回波总能量的比值 [19-20]。2005年，Stelmaszczykk对采用望远接收系统的收发旁轴大气探测激光雷达进行重叠因子建模，仅考虑光机结构参数的影响，没有考虑光斑能量分布的非均匀性 [20]。2014年，王威等对采用望远接收系统的收发旁轴大气探测激光雷达进行重叠因子建模，考虑了光斑能量分布和光机结构参数两方面的影响，可应用于任意指定激光强度分布和光机结构参数的大气探测激光雷达重叠因子求解[21]。2020年，张寅超等推导了大气探测同轴激光雷达的重叠因子计算公式，用薄透镜代替望远镜进行分析计算，通过对均匀发射激光光束区域的视场函数积分与激光光束截面积的比值得到重叠因子[13]。上述研究均针对大气探测激光雷达，研究的侧重点在于通过重叠因子修正后向散射回波信号，以便“利用后向散射回波信号”精确反演大气参数。
对警戒激光雷达而言：一方面，如前所述“警戒激光雷达在恶劣气象环境（雾、粉尘等）下工作时，激光雷达出射的激光入射到水滴或粉尘上会发生散射，后向散射光形成后向散射回波，前向散射光在遇到物体后被反射形成目标回波”，由于后向散射光程较短，前向散射经目标反射后光程较长，因此后向散射回波在前，目标回波在后[22]，“近场信号强度远大于远场信号强度”会进一步增强后向散射回波，这导致实施“阈值检测”时将后向散射回波误检测为目标，从而导致激光雷达误告警。另一方面，光机结构对近场信号存在影响，逆向利用这一属性，通过“基于光机结构参数(重叠因子)进行激光雷达回波建模”，探索通过光机结构优化实现近场信号压缩，从而抑制恶劣气象环境(雾、粉尘等)下的后向散射回波、而不影响目标回波，从而较少警戒激光雷达误告警。
警戒激光雷达重叠因子建模研究的侧重点在于“抑制后向散射回波”， 通过光机参数优化抑制近场信号、进而抑制恶劣气象环境下的后向散射形成的虚假回波信号，从而获取利于实施“阈值检测”的回波信号、准确检测出目标，而不是把后向散射回波误检为目标。这与大气探测激光雷达研究基于“精准的后向散射回波建模”来反演大气参数存在本质的不同。
针对警戒激光雷达重叠因子建模实现响应动态范围压缩鲜有文献报道，为了解决警戒激光雷达应用中的实际问题，文中针对同轴警戒激光雷达，利用同轴遮挡和激光光斑能量分布非均匀性对重叠因子的影响，提出了一种基于重叠因子的同轴警戒激光雷达动态范围压缩方法。首先，基于同轴激光雷达的光机结构和激光光斑能量分布的概率密度函数，建立激光雷达方程修正模型。然后，针对实际商用警戒激光雷达，对响应曲线进行实测和仿真，验证文中模型的有效性，进而仿真分析发射透镜半径、光阑半径、激光发散角、接收透镜焦距四个参数对响应曲线的影响。
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根据辐射传输理论，当目标满足朗伯体特性、发射激光脉冲与目标表面正交、目标面积大于激光脉冲发散角所形成的光斑面积时，激光雷达方程可表达为[12, 23]：
$$ E\left( h \right) = \frac{{{\eta _o}\rho \left( h \right){T_a}{{\left( h \right)}^2}{A_r}}}{{\pi {h^2}}}{P_t} $$ (1) 式中：h为目标与激光雷达间的距离；E(h)为激光雷达接收到的回波信号；Pt为激光雷达发射的激光功率；ηo为 光学系统的效率；ρ(h)为距离h处目标的反射率；Ta(h)为单程大气透过率；Ar=πD2/4为光学系统的有效接收面积，D为接收透镜口径。
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图3所示的同轴激光雷达，发射透镜通过外圈机构镶嵌在接收透镜的中心，外圈机构起到光阑的作用。激光通过发射透镜发射出去，发射激光被发射视场内的待测目标反射形成回波信号，回波信号通过接收透镜被探测器接收。
图 3 同轴激光雷达的发射透镜和接收透镜
Figure 3. Emission lens and receiving lens of coaxial LiDAR
同轴激光雷达发射视场和接收视场如图4所示。发射透镜上方、边界线01和边界线02之间的区域为发射视场、即激光发散角。接收透镜上方、边界线11和边界线21、边界线12和边界线22之间的区域为接收视场。
图 4 同轴激光雷达发射视场和接收视场
Figure 4. Emission and receiving fields of view for coaxial LiDAR
实际上，光阑会对接收视场造成遮挡，图4中光阑会对接收视场的边界线11和边界线12造成遮挡，实际的接收视场如图5所示，将边界线11修正为边界线31，边界线12修正为边界线32。通常，接收透镜半径D/2大于R + b × tank，其中R为光阑半径，b为光阑的高度，k为接收视场角，由接收透镜焦距和探测器光敏面积决定。一般接收视场角k大于激光发散角t，因此接收视场外侧边界线不会影响发射视场与接收视场的交叠，可以将边界线21简化为边界线41，将边界线22简化为边界线42，简化后的视场交叠示意图如图6所示。由于光阑的遮挡，只有在发射视场和接收视场交叠时，待测目标反射的回波信号才能被接收透镜接收，距离激光雷达h处的“有效接收范围”为发射视场与接收视场交叠的区域。
图 5 考虑遮挡时同轴激光雷达视场交叠示意图
Figure 5. Schematic diagram of overlapping field of view for coaxial LiDAR considering occlusion
图 6 同轴激光雷达视场交叠简化示意图
Figure 6. Simplified diagram of overlapping field of view for coaxial LiDAR
根据发射视场与接收视场的交叠程度把距离h划分为盲区、过渡区和明区。其中，盲区为发射视场与接收视场不交叠的区域，过渡区为发射视场和接收视场部分交叠的区域，明区为发射视场与接收视场完全交叠的区域。
盲区的边界距离h1为盲区-过渡区的交界面与激光雷达(发射透镜)之间的距离，过渡区的边界距离h2为过渡区与明区的交界面与激光雷达(发射透镜)之间的距离。根据几何关系，可得h1和h2的计算式：
$$ {h}_{1}=\frac{R-d}{\mathrm{tan}\,t+\mathrm{tan}\,k}{，}{h}_{2}=\frac{R}{\mathrm{tan}\,k} $$ (2) 由于光阑对接收视场的遮挡，激光雷达的“有效接收范围”随待测目标距离h变化而变化。假设x1(h)是距离h处接收视场的内侧边界与光轴的距离，x2(h)是发射视场的半径，则：
$$ \begin{gathered} {x_1}\left( h \right) = \tan \, k\left( {\frac{R}{{\tan \, k}} - h} \right){\text{ }} \\ {x_2}\left( h \right) = d + h\tan \,t \\ \end{gathered} $$ (3) 当h ≤ h1，即待测目标在盲区时，发射视场和接收视场不交叠，接收透镜不能接收到回波信号，此时有效接收范围为0；当 h1 < h < h2，即待测目标在过渡区时，发射激光被反射后和接收视场部分交叠，此时有效接收范围为环形区域，环形区域的内圆半径为x1(h)、外圆半径为x2(h)；当h ≥ h2，即待测目标在明区时，发射激光被反射后的回波信号被接收视场全部接收，此时相当于x1(h) 为0，明区的有效接收范围为半径为x2(h)的圆形区域。
当激光光斑能量分布均匀时，可用“有效接受范围”的归一化面积作为重叠因子f(h)：
$$ f\left( h \right){\text{ = }}\left\{ {\begin{array}{*{20}{c}} {\dfrac{0}{{\pi x_2^2}} = 0,}&{h \leqslant {h_1}} \\ {\dfrac{{\pi x_2^2 - \pi x_1^2}}{{\pi x_2^2}},}&{{h_1} < h < {h_2}} \\ {\dfrac{{\pi x_2^2}}{{\pi x_2^2}} = 1,}&{{h_2} \leqslant h} \end{array}} \right. $$ (4) 然而，实际的激光光斑能量分布往往并不均匀，因此，不能直接用“有效接收范围”的归一化面积作为重叠因子，需要考虑激光光斑的能量分布来确定重叠因子，进而用重叠因子修正激光雷达方程。
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基于“有效接收范围”内激光光斑能量分布的概率密度函数，计算“有效接收范围”内能量分布概率密度函数的积分，并用能量分布概率密度函数在半径为x2(h)的圆形区域的积分进行归一化，得到重叠因子。通过重叠因子对激光雷达方程进行修正，得到激光雷达方程的修正模型。
以高斯光束为例，图7是一种基模高斯光束光斑能量分布示意图，距离h处的激光光斑能量分布的概率密度函数满足：
图 7 基模高斯光束光斑能量分布示意图
Figure 7. Schematic diagram of spot energy distribution of fundamental mode Gaussian laser
$$ P D F\left( {h,r} \right) = {E_0}\frac{{\omega \left( 0 \right)}}{{\omega \left( h \right)}}\exp \left( { - {{{r^2}} \mathord{\left/ {\vphantom {{{r^2}} {{\omega ^2}\left( h \right)}}} \right. } {{\omega ^2}\left( h \right)}}} \right) $$ (5) 式中：E0为距离h = 0处激光光斑中心的能量；r为距离h处激光光斑横截面内某点与光轴的距离；ω(h)为距离h处的激光光束束腰半径，对于图6的激光雷达，ω(h) = x2(h)。
距离h处的总光能量Etotal(h)是激光光斑能量分布的概率密度函数在半径为x2(h)的圆形区域的积分，为：
$$ {E_{total}}\left( h \right) = \int_{ - {x_2}}^{{x_2}} {P D F\left( {h,r} \right)} {\rm{d}}r $$ (6) 有效接收光能量Eeff(h)是激光光斑能量分布的概率密度函数在“有效接收范围”内的积分，为：
$$ {E_{eff}}\left( h \right) = \left\{ {\begin{array}{*{20}{c}} {0,}&{h < {h_1}} \\ {\displaystyle\int_{ - {x_2}}^{{x_2}} {P D F\left( {h,r} \right)}{\rm{ d}}r - \displaystyle\int_{ - {x_1}}^{{x_1}} {P D F\left( {h,r} \right)} {\rm{d}}r,}&{{h_1} < h < {h_2}} \\ {\displaystyle\int_{ - {x_2}}^{{x_2}} {P D F\left( {h,r} \right)} {\rm{d}}r,}&{h \geqslant {h_2}} \end{array}} \right. $$ (7) 用距离h处总光能量Etotal(h)对Eeff (h)进行归一化，得重叠因子f(h)如公式(8)所示：
$$ f\left( h \right){\text{ = }}\frac{{{E_{eff}}\left( h \right)}}{{{E_{total}}\left( h \right)}}{\text{ = }}\left\{ {\begin{array}{*{20}{c}} {0,}&{h < {h_1}} \\ {\frac{{\displaystyle\int_{ - {x_2}}^{{x_2}} {P D F\left( {h,r} \right)} {\rm{d}}r - \displaystyle\int_{ - {x_1}}^{{x_1}} {P D F\left( {h,r} \right)} {\rm{d}}r}}{{\displaystyle\int_{ - {x_2}}^{{x_2}} {P D F\left( {h,r} \right)} {\rm{d}}r}},}&{{h_1} < h < {h_2}} \\ {1,}&{h \geqslant {h_2}} \end{array}} \right. $$ (8) 将公式(8)所示重叠因子f(h)与公式(1)所示的面目标激光雷达方程相乘，建立激光雷达方程修正模型，获取修正信号Ec(h)为：
$$ {E_c}\left( h \right) = \frac{{{\eta _o}\rho \left( h \right){T_a}{{\left( h \right)}^2}{A_r}}}{{\pi {h^2}}}{P_t} \cdot f\left( h \right) $$ (9) -
利用保定市天河电子技术有限公司GL-1130型号警戒激光雷达(参数如表1所示)采集响应曲线，并基于GL-1130的参数进行仿真计算，通过对比分析实测和仿真响应曲线，验证文中模型的有效性。
表 1 GL-1130警戒激光雷达参数
Table 1. Parameters for GL-1130 warning LiDAR
Parameter Value Radius of emitting lens d/mm 5.75 Radius of aperture R/mm 7 Laser divergence angle(emission field of view) 2t/mrad 6 Diameter of receiving lens D/mm 30 Focal length of receiving lens f/mm 40 Diameter of APD φ/mm 0.5 Receiving field of view 2k = φ/f /mrad 13 为了定量分析，将实测和仿真响应曲线均进行归一化处理。基于模型仿真响应曲线，除了表1的光学参数和机械结构参数，还需激光雷达的出射能量Pt、光学系统的接收效率ηo、目标的反射率ρ(h)、大气的单程透过率Ta(h)等参数。这四个参数均不影响重叠因子f(h)，故取Pt=1、ηo=1、ρ(h) =1、Ta(h) =1的仿真响应曲线。
响应曲线的实验原理及测试现场见图8，将激光雷达置于测试轨道一端，将靶标置于测试轨道的可移动小车上，固定激光雷达的参数设置，采集靶标在不同距离处的回波信号，并依据回波信号绘制响应曲线。
图 8 带透光罩和旋转反射镜的响应曲线实验原理及测试现场
Figure 8. Response curve test principle and test site with light transmission hood and rotating mirror
在实际测量时，目标与激光雷达发射透镜之间的距离L=L1+L2+L3。其中，L1为目标与透光罩之间的距离，L2=48.17 mm为透光罩与旋转反射镜之间的距离，L3=12.03 mm为旋转反射镜和发射透镜之间的距离。L2和L3可根据激光雷达光学、机械设计参数确定。但实际测量时激光与透光罩的交点Q并不易确定，因此目标与透光罩之间的距离L1也不易确定。
为了实验方便，在实际测试响应曲线时，摘掉激光雷达的透光罩和旋转反射镜，如图9所示放置激光雷达，直接测量目标到发射透镜的距离。
图 9 不带透光罩和旋转反射镜的响应曲线测试实验原理及测试现场
Figure 9. Response curve test principle and test site without light trans-mission hood and rotating mirror
表2给出了实测不同距离回波的归一化峰值，并仿真了相应距离处修正前后回波的归一化峰值及重叠因子。因为实测数据在小于215 mm的距离未测到信号，215 mm以内的距离为激光雷达盲区，所以从215 mm距离开始仿真。修正前数据根据公式(1)仿真得到，修正后数据根据公式(1)~(9)仿真得到。激光雷达实测的信号值是0~128之间的整数值、用最大值进行归一化得到(0,1)范围的小数，不同距离仿真数据在小数点后三位有差别，综上，选择数据保留到小数点后三位。理论上，修正前回波强度随距离增加单调递减。仿真数据中，修正前回波之所以在215 mm处信号取最大值1，是因为用215处的信号值对其他距离的信号值进行归一化。根据表2绘制的响应曲线如图10所示。
表 2 归一化激光雷达响应曲线实测数据和仿真数据
Table 2. Measured data and simulation data of nor-malized LiDAR response curve
Distance
h/mmMeasured
dataSimulation data
before correctionCorrected
simulation dataOverlap
factor0 - - - - 215 0.533 1.000 0.250 0.084 653 0.779 0.562 0.938 0.559 810 0.859 0.457 0.991 0.726 895 0.940 0.413 1.000 0.811 983 0.975 0.374 0.998 0.894 1096 1.000 0.332 0.983 0.993 1369 0.995 0.261 0.779 1.000 1739 0.827 0.207 0.618 1.000 2389 0.635 0.159 0.475 1.000 2969 0.501 0.137 0.408 1.000 4028 0.338 0.114 0.341 1.000 5052 0.231 0.102 0.306 1.000 6205 0.166 0.094 0.281 1.000 7047 0.117 0.090 0.269 1.000 
图 10 归一化激光雷达响应曲线
Figure 10. Normalized LiDAR response curve
比较分析实测、仿真数据：实测数据在1096 mm处出现回波强度峰值，并向两侧减小；修正前仿真数据的回波强度随着目标距离单调递减、与实测数据不符；在重叠因子的影响下，修正后仿真数据在895 mm出现回波强度峰值、与实测峰值位置1096 mm较为接近，且修正后回波强度向峰值两侧减小、与实测数据的变化趋势类似；过渡区与明区的交界面与激光雷达(发射透镜)之间的距离h2的仿真结果为1104 mm，在明区距离之外，重叠因子取值为1并保持不变，表2中实测距离取离散值，1096~1369 mm之间的重叠因子未进行仿真，因此，表2中重叠因子数值从1369 mm距离开始取1并随着距离增加恒定为1。考虑激光雷达制造过程中的加工装调误差等因素的影响，实际峰值位置应略大于修正模型预测的895 mm，与实测的1096 mm更为接近。修正后仿真数据和实测数据的Pearson相关系数为0.9085，表明仿真响应曲线与实测响应曲线相关性较强， 有效证明了文中所建模型的有效性。
根据模型，发射透镜半径d、光阑半径R、激光发散角2t、接收视场角2k是影响重叠因子的四个参数。接收APD直径φ和接收透镜焦距f决定接收视场角2k，商业产品化APD直径一般有0.8 mm和0.5 mm两个规格，文中系统选择0.5 mm直径，因此接收视场角2k取决于接收透镜焦距f。接收透镜直径D不影响重叠因子，只决定系统的有效接收面积。因此，仿真分析发射透镜半径d、光阑半径R、激光发散角2t、接收透镜焦距f四个参数对响应曲线的影响。仿真中的其他参数取值为Pt=1、ηo=1、ρ(h) =1、Ta(h) =1、D=30 mm，仿真结果如图11所示。可以看出，发射透镜半径d增加、激光发散角2t减小或接收透镜焦距f增大，可以略微压缩响应曲线的动态范围，但不显著；光阑半径R增大可以显著压缩响应曲线的动态范围。因此，在激光雷达的光机设计阶段可以考虑通过增加光阑半径实现回波信号动态范围的压缩。通过增大警戒激光雷达的光阑半径，可以有效压缩近距离相对于远距离的响应，从而实现后向散射回波相对于目标反射回波的压缩，从而减小恶劣气象环境对警戒激光雷达告警的影响。同时，光阑半径增大会带来APD有效接收的回波信号总体强度降低的问题，此问题可以通过增大接收透镜的口径解决。
图 11 不同参数设置的归一化响应曲线仿真
Figure 11. Normalized response curve simulated with different parameter settings
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文中针对警戒同轴激光雷达响应动态范围压缩问题，提出了一种基于重叠因子的同轴警戒激光雷达动态范围压缩方法。基于同轴遮挡和激光光斑能量分布的概率密度函数，建立了激光雷达方程修正模型，并采用商用警戒激光雷达进行响应曲线测试，实测曲线和仿真曲线具有较高的相关性，验证了文中修正模型的有效性。仿真分析了发射透镜半径d、光阑半径R、激光发散角2t、接收透镜焦距f四个参数对响应曲线的影响，仿真结果表明，光阑半径R是影响响应曲线的最主要因素，增大光阑半径可以显著压缩响应曲线的动态范围。该模型已用于指导现有警戒激光雷达产品的优化、尤其是港口、矿山等恶劣气象环境下(雾、粉尘)应用的警戒激光雷达的优化设计，具有重要实际指导意义和广泛的应用前景，天河电子相关激光雷达产品已经投入市场应用。
光阑半径增大会带来APD有效接收的回波信号总体强度降低的问题，这一问题可以通过增大接收透镜的口径解决，但接收透镜口径的增大又会造成激光雷达整体体积、质量的增加。因此，实际激光雷达的设计生产中，应综合考虑性能指标、有效载荷等因素，进行总体设计。
A dynamic range compression method for coaxial warning LiDAR based on overlap factor
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摘要: 针对警戒激光雷达近场信号过饱和与雨、雾等天气形成的近距离虚假信号造成“虚警”或“漏警”的问题，研究了一种基于重叠因子的同轴警戒激光雷达动态范围压缩方法。由经典激光雷达方程以及同轴遮挡和激光光斑能量分布的概率密度函数，建立了激光雷达方程修正模型；针对商用警戒激光雷达进行了响应曲线测试，并与基于激光雷达方程修正模型仿真的响应曲线进行对比分析，验证模型的有效性；仿真分析了发射透镜半径、光阑半径、激光发散角、接收透镜焦距四个参数对响应曲线的影响，结果表明：光阑半径是影响响应曲线的最主要因素，增大光阑半径可以显著压缩近场信号，进而压缩响应曲线的动态范围。论文建立的激光雷达方程修正模型对激光雷达初始设计具有重要指导意义及广泛的应用前景。Abstract:
Objective The warning LiDAR used in industries such as autonomous driving and smart mining obtains target distance and alerts by threshold detection of echo. When an warning LiDAR works in an adverse environment (fog, dust, etc.), the emitted laser pulse will be scattered when it hits water drops or dust. Backscattered light will form backscattering echo, and forwardscattered light will be reflected when encountering an object to form a target reflection echo. Backscattering echo will interfere with the detection of target reflection echo. Therefore, backscattering echo compression is essential for the warning LiDAR. Methods For the detection of surface targets, the intensity of the LiDAR echo is inversely proportional to the square of the distance, resulting in the intensity of the near-distance echo being several orders of magnitude greater than the intensity of the far-distance echo. Because the optical path of the backscattering echo is shorter than that of the target reflection, the backscattering echo is in front of the target reflection echo. The optical and mechanical structure of the LiDAR transmission module obstructing the receiving field of view can affect the near-distance responsibility, resulting in the echo strength not monotonically decreasing with distance, but first increasing and then decreasing with distance. By reverse utilizing this attribute, we can model the LiDAR echo based on the optical and mechanical structural parameters (overlap factor) to achieve near-distance echo compression, thereby compressing backscattering echo in adverse environments (fog, dust, etc.) without affecting target reflection echo, and thus reducing false alarm rate. A dynamic range compression method for coaxial warning LiDAR based on overlap factor is proposed utilizing the influence of coaxial occlusion and non-uniformity of laser spot energy distribution on overlap factor (Fig.4-7). Results and Discussions LiDAR with parameters in Tab.1 is used to measure response curve and parameters in Tab.1 is used to get simulated response curve. Table 2 presents datas of the measured normalized response curves, simulated normalized response curves, and overlap factors. The response curve plotted according to Tab.2 is shown (Fig.10). Comparative analysis of measured data and simulation data is conducted. The measured data showed a peak echo intensity at 1 096 mm and decreased to both sides; The echo intensity of the simulated data before correction monotonically decreases with the target distance and does not match the measured data; The simulated data after correction showed a peak echo intensity at 895 mm, which was closer to the measured peak position of 1 096 mm. Moreover, the corrected echo intensity decreased towards both sides of the peak and showed a similar trend to the measured data. Considering the influence of factors such as processing and adjustment errors in the manufacturing process of LiDAR, the actual peak position should be slightly larger than the predicted 895 mm by the modified model, which is closer to the measured 1 096 mm. The Pearson correlation coefficient between the corrected simulation data and the measured data is 0.908 5, indicating a strong correlation between the simulation response curve and the measured response curve, effectively proving the effectiveness of the model built in this paper. Based on the above conclusions, simulation analysis is conducted to investigate the effects of four parameters on the response curve, which are the radius of the transmitting lens d, the radius of the aperture R, the divergence angle of the laser 2t, and the focal length of the receiving lens f. The simulation results show that an increase in the radius d of the transmitting lens, a decrease in the laser divergence angle 2t, or an increase in the focal length f of the receiving lens can slightly compress the dynamic range of the response curve, but not significantly; Increasing the aperture radius R can significantly compress the dynamic range of the response curve. Conclusions Therefore, in the optical and mechanical design stage of LiDAR, it is possible to effectively compress the response at near distance relative to far distance by increasing the aperture radius of the warning LiDAR, thereby achieving compression of the backscattering echo relative to the target reflection echo to reduce the impact of adverse weather conditions on warning LiDAR. This model has been used to guide the optimization of existing warning LiDAR products, especially for the optimization design of warning LiDAR applications in adverse weather environments such as autonomous driving and smart mining. It has important practical guidance significance and broad application prospects. -
Key words:
- LiDAR /
- response curve /
- dynamic range compression /
- fundamental mode Gaussian laser
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图 1 望远式长距离激光雷达光机结构示意图
Figure 1. Schematic diagram of optical and mechanical structure for LiDAR using telescopic system
图 2 单透镜接收警戒激光雷达光机结构示意图
Figure 2. Schematic diagram of optical and mechanical structure for warning LiDAR using single lens receiver
图 5 考虑遮挡时同轴激光雷达视场交叠示意图
Figure 5. Schematic diagram of overlapping field of view for coaxial LiDAR considering occlusion
图 6 同轴激光雷达视场交叠简化示意图
Figure 6. Simplified diagram of overlapping field of view for coaxial LiDAR
图 7 基模高斯光束光斑能量分布示意图
Figure 7. Schematic diagram of spot energy distribution of fundamental mode Gaussian laser
图 8 带透光罩和旋转反射镜的响应曲线实验原理及测试现场
Figure 8. Response curve test principle and test site with light transmission hood and rotating mirror
图 9 不带透光罩和旋转反射镜的响应曲线测试实验原理及测试现场
Figure 9. Response curve test principle and test site without light trans-mission hood and rotating mirror
图 11 不同参数设置的归一化响应曲线仿真
Figure 11. Normalized response curve simulated with different parameter settings
表 1 GL-1130警戒激光雷达参数
Table 1. Parameters for GL-1130 warning LiDAR
Parameter Value Radius of emitting lens d/mm 5.75 Radius of aperture R/mm 7 Laser divergence angle(emission field of view) 2t/mrad 6 Diameter of receiving lens D/mm 30 Focal length of receiving lens f/mm 40 Diameter of APD φ/mm 0.5 Receiving field of view 2k = φ/f /mrad 13 
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表 2 归一化激光雷达响应曲线实测数据和仿真数据
Table 2. Measured data and simulation data of nor-malized LiDAR response curve
Distance
h/mmMeasured
dataSimulation data
before correctionCorrected
simulation dataOverlap
factor0 - - - - 215 0.533 1.000 0.250 0.084 653 0.779 0.562 0.938 0.559 810 0.859 0.457 0.991 0.726 895 0.940 0.413 1.000 0.811 983 0.975 0.374 0.998 0.894 1096 1.000 0.332 0.983 0.993 1369 0.995 0.261 0.779 1.000 1739 0.827 0.207 0.618 1.000 2389 0.635 0.159 0.475 1.000 2969 0.501 0.137 0.408 1.000 4028 0.338 0.114 0.341 1.000 5052 0.231 0.102 0.306 1.000 6205 0.166 0.094 0.281 1.000 7047 0.117 0.090 0.269 1.000
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