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图1(a)是文中实现浅水层前后两个表面光回波信号偏振分离的原理图。发射系统发出水平线偏振状态的激光脉冲,当到达水面时,一部分发生反射,由于水面具有很好的保偏特性,反射光保持水平线偏振态;另一部分光继续传播到底面,由于底面存在细沙,比较粗糙,具有较强的退偏特性,因此该反射光的偏振态同时存在水平分量和垂直分量。反射光经过接收系统中的偏振分光棱镜(PBS)后,Gm-APD1探测水平偏振分量,Gm-APD2探测垂直偏振分量。显然,Gm-APD2探测的是底面的反射信号。对于Gm-APD1,虽然在水平分量的光路中,同时存在前后表面的反射信号,但是,水面的反射信号相比底面而言很强,底面的反射信号非常微弱。Gm-APD存在着死时间,45 ns,当水面的较强信号触发Gm-APD1时,就无法响应紧邻的底面的回波信号。因此,Gm-APD1仅探测水面的反射信号。最终,系统实现了前后两个表面回波信号的偏振分离探测,突破了激光脉宽的硬性约束。
图 1 (a) 实现偏振分光的原理图;(b) 方案流程图
Figure 1. (a) Schematic diagram for realizing polarization splitting; (b) Flow chart of program
偏振光在传输过程中,一般采用穆勒矩阵和斯托克斯参量来描述偏振态的变化[23]。笔者所在课题组统一规定水平方向表示为0°,并且始终沿着光束传播方向观察。那么,水平线偏振光的斯托克斯参量可以表示为
${\left[ {\begin{array}{*{20}{c}} 1&1&0&0 \end{array}} \right]^{\rm{T}}}$ ,竖直线偏振光表示为${\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0&0 \end{array}} \right]^{\rm{T}}}$ 。对于起偏角为${\theta _p}$ 的线性起偏器,可以用穆勒矩阵${{{M}}_{{\rm{Pol}}}}\left( {{\theta _p}} \right)$ 表示;对于快轴方位角为$\;\beta $ ,延迟量为$\delta $ 的波片,可以用穆勒矩阵${{{M}}_{{\rm{VWP}}}}\left( {\beta ,\delta } \right)$ 表示,两者的具体表示如下:$${{{M}}_{{\rm{Pol}}}}\left( {{\theta _p}} \right) = \frac{1}{2}\left[ {\begin{array}{*{20}{c}} 1&{\cos 2{\theta _p}}&{\sin 2{\theta _p}}&0 \\ {\cos 2{\theta _p}}&{{{\cos }^2}2{\theta _p}}&{\sin 2{\theta _p}\cos 2{\theta _p}}&0 \\ {\sin 2{\theta _p}}&{\sin 2{\theta _p}\cos 2{\theta _p}}&{{{\sin }^2}2{\theta _p}}&0 \\ 0&0&0&0 \end{array}} \right]$$ (1) $${{{M}}_{{\rm{VWP}}}}\left( {\beta ,\delta } \right) = \left[ {\begin{array}{*{20}{c}} 1&0&0&0 \\ 0&{{{\cos }^2}2\beta {\rm{ + }}{{\sin }^2}2\beta \cos \delta }&{\left( {1 - \cos \delta } \right)\sin 2\beta \cos 2\beta }&{ - \sin 2\beta \sin \delta } \\ 0&{\left( {1 - \cos \delta } \right)\sin 2\beta \cos 2\beta }&{{{\sin }^2}2\beta + {{\cos }^2}2\beta \cos \delta }&{\cos 2\beta \sin \delta } \\ 0&{\sin 2\beta \sin \delta }&{ - \cos 2\beta \sin \delta }&{\cos \delta } \end{array}} \right]$$ (2) 假设激光器产生的偏振态为
${{{S}}_{{\rm{laser}}}}$ ,经过1/2波片和格兰泰勒棱镜之后,产生一束严格的水平线偏振光${{{S}}_T}$ ,$${{{S}}_T} = {{{M}}_{{\rm{Pol}}}}\left( 0 \right){{{M}}_{{\rm{VWP}}}}\left( {\beta ,\pi } \right){{{S}}_{{\rm{laser}}}}{\rm{ = }}{\left[ {\begin{array}{*{20}{c}} 1&1&0&0 \end{array}} \right]^{\rm{T}}}$$ (3) 对于一些非偏振光学元件,例如反射镜、各种透镜和滤波片等,它们的退偏振效应忽略不计。而对于表面粗糙的物体,它们的退偏振效应较显著,甚至可能完全退偏。完整的穆勒矩阵可以描述三种偏振特性。双向衰减特性,它描述与偏振有关的强度衰减;相位延迟特性,它描述与偏振有关的位相变化;退偏特性,它描述偏振光退化为非偏振光的程度。在文中,笔者只考虑浅水层底面对入射光的退偏特性,衰减特性将包含在激光雷达方程中衰减系数中,见后文分析。那么,此时底面的穆勒矩阵就可以简化为一个标准化对角阵[23]:
$${{{M}}_{{\rm{target}}}} = \left[ {\begin{array}{*{20}{c}} 1&0&0&0 \\ 0&a&0&0 \\ 0&0&b&0 \\ 0&0&0&c \end{array}} \right]$$ (4) 经过前面的分析,大家知道Gm-APD1探测的是从浅水层水面反射回来的水平线偏振光信号。激光雷达能量方程表示激光器输入和探测器输出之间的能量衰减。对于一个实际的系统,在水平分量光路中,激光雷达能量方程的衰减为一个定值,假设为常数
${G_1}$ 。那么,Gm-APD1探测到的为水平线偏振光分量,而且它的斯托克斯参量表示为:$${{{S}}_{R1}} = {G_1}{{{M}}_{{\rm{Pol}}}}\left( 0 \right){{{S}}_T}{\rm{ = }}{\left[ {\begin{array}{*{20}{c}} {{G_1}}&{{G_1}}&0&0 \end{array}} \right]^{\rm{T}}}$$ (5) Gm-APD2探测的是从浅水层底面反射回来的垂直分量的信号光分量。同理,在垂直分量的光路中,激光雷达能量方程的衰减系数也为一个定值,假设为常数
${G_2}$ 。实际上,衰减系数${G_1}$ 和${G_2}$ 已经包含了前文中描述的目标的穆勒矩阵中的衰减特性。那么,此时,Gm-APD2探测到的垂直线偏振光分量的斯托克斯参量表示为:$$\begin{split} {{{S}}_{R2}} = {G_2}{{{M}}_{{\rm{Pol}}}}\left( {\dfrac{\pi }{2}} \right){{{M}}_{{\rm{target}}}}{{{S}}_T} =\left[ {\dfrac{{1 - a}}{2}{G_2}\;\; - \dfrac{{1 - a}}{2}{G_2}\;\;{{0\;\;0}}} \right] \end{split} $$ (6) 斯托克斯是一个间接测量值,需要根据直接测量值、强度值解算得到。强度值和斯托克斯参量的关系如下所示:
$${I_1} = \left[ {\begin{array}{*{20}{c}} 1&0&0&0 \end{array}} \right]{{{S}}_{R1}} = {G_1}$$ (7) $${I_2} = \left[ {\begin{array}{*{20}{c}} 1&0&0&0 \end{array}} \right]{{{S}}_{R2}} = \frac{{1 - a}}{2}{G_2}$$ (8) 公式(7)、(8)分别表示两个Gm-APD探测的信号,信号强度分别与各偏振支路的衰减系数有关。对于实际的系统,这两个衰减系数是一个常数。综上所述,从理论上分析了该光学系统能够在空间上实现超薄浅水层水面和底面信号的完全分离,并分别被两个Gm-APD探测,突破了激光脉冲宽度的限制。
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图1(b)为笔者提出方案的流程图,由于Gm-APD激光雷达存在距离漂移误差,将引起距离像的畸变,因此,必须对两个偏振支路的信号分别进行距离漂移误差抑制,从而获取浅水层的高精度距离信息。下面将介绍信号复原质心算法抑制距离漂移误差的原理。
距离漂移误差存在,本质上是由于Gm-APD的非线性响应模型。根据Gm-APD的泊松概率响应模型[18],若在时间轴上对其分成若干个小区间,其在第i个子区间内的触发概率为:
$$P\left( i \right) = \left\{ {1 - \exp \left[ { - {N_{sn}}(i)} \right]} \right\}\exp \left[ { - \sum\nolimits_{j = i - d}^{i - 1} {{N_{sn}}\left( j \right)} } \right]$$ (9) 式中:
${N_{sn}}\left( i \right) = {N_s}\left( i \right) + {N_n}\left( i \right)$ ,${N_s}\left( i \right)$ 表示第i个子区间内的信号光电子数,${N_n}\left( i \right)$ 表示第i个子区间内的噪声光电子数;d表示Gm-APD的死时间长度所对应的子区间个数。根据统计学原理,在实验测量中,当探测次数达到一定数量时,触发概率可以由下式近似得到:
$$P\left( i \right) \approx \frac{{K\left( i \right)}}{M}$$ (10) 式中:K(i)表示Gm-APD在第i个区间的雪崩次数,即Gm-APD在探测过程中直接输出的光子计数分布。笔者发现,输入和输出并不是一个线性关系。因此,如果直接采用光子计数分布去进行测距,必然存在误差,表现为距离漂移误差。详细的理论分析在笔者团队之前的研究工作[24-25]中已经阐述。
鉴于此,笔者采用回波信号光电子数复原法[16],可以反推得到回波信号光电子数的分布
${N_s}^\prime \left( i \right)$ ,$$\begin{array}{*{20}{r}} {{N_s}^\prime \left( i \right) = - \ln \left\{ {1 - \dfrac{{K\left( i \right)}}{M}\exp \left[ {\displaystyle\sum\limits_{j = i - d}^{i - 1} {{N_s}\left( j \right)} + \displaystyle\sum\limits_{j = i - d}^{i - 1} {{N_n}\left( j \right)} } \right]} \right\}} \\ { - {N_n}(i)} \end{array}$$ (11) 此时,光电子数分布与入射到Gm-APD的光信号呈线性关系,用其去表征信号不会引入距离漂移误差,从而实现距离漂移误差的抑制。
对于信号区间
${T_1} \sim {T_m}$ 内所有的信号光电子数${N_s}^\prime \left( i \right)$ 求和,可以得到入射光的强度信息为:$$I = \sum\nolimits_{i = {T_1}}^{{T_m}} {{N_s}^\prime \left( i \right)} $$ (12) 对恢复后的回波信号光电子数分布
${N_s}^\prime \left( i \right)$ ,采用质心算法,得到目标的飞行时间信息如下:$$t = \Delta t\frac{{ \displaystyle\sum\nolimits_{i = {T_1}}^{{T_m}} {i{N_s}^\prime (i)} }}{{ \displaystyle\sum\nolimits_{i = {T_1}}^{{T_m}} {{N_s}^\prime (i)} }}$$ (13) 式中:
$\Delta t$ 为文中实验中光子计数板卡的时间分辨率,164 ps。Gm-APD1探测的浅水层水面的距离表示为:
$${R_1} = \frac{c}{2}{t_1}$$ (14) 式中:
$c = 3 \times {10^8}$ m/s,表示真空中的光速。Gm-APD2探测的浅水层底面的距离表示为:
$${R_2} = {R_1} + \frac{c}{{2n}}\left( {{t_2} - {t_1}} \right)$$ (15) 式中:n为水的折射率,
$n = 1.333$ 。综上分析,首先利用信号复原算法,根据Gm-APD的光子计数分布图恢复到信号光电子数分布图;再利用质心算法获取信号光电子数分布图的的质心,作为目标的激光脉冲飞行时间,从而获取距离值。采用信号复原质心算法进行数据处理后,从理论上能够避免距离漂移误差的引入,从而实现高精度的距离信息获取。
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图2表示文中设计的双Gm-APD光子计数偏振激光雷达系统示意图。信号发生器(Signal generator)产生一个2 kHz的TTL信号去触发激光器发射激光脉冲,激光波长为1064 nm,通过倍频晶体(FDC)转换为532 nm,也就是系统的工作波长。分束器(BS)将发射光分成两部分,其中一部分入射到高速PIN探测器,其输出作为光子计数板卡(DPC-230 Photon Correlator Card)的计时起始信号;另一部分激光通过1/2波片(HWP)和格兰泰勒棱镜(Polarizer)的组合,产生水平线偏振光,再经过X-Y扫描系统(X-Y scanning)照射目标。当水平线偏振光照射到浅水层时,将返回两束信号光。一束是从浅水层水面反射回的水平线偏振光,此信号较强;另一束是穿过水体后,从粗糙的底面返回的包含水平和垂直分量的信号光,此信号较弱。两束信号光全部经过接收光学系统(Receiving system)接收,采用窄带滤波片(NBPF)滤除杂散背景光,采用衰减片组(Attenuators)衰减成光子量级信号强度。信号光子经过偏振分光棱镜(PBS)偏振分光后分别采用光纤准直器(Optical fiber collimator)收集,Gm-APD1探测水平偏振分量的信号光子,Gm-APD2探测垂直偏振分量的信号光子被。光子计数卡采集两者的输出信号,获取信号光子计数分布图。采用信号复原质心算法抑制距离漂移误差后,由计算机(Computer)解算得到高精度距离信息并显示目标的距离像。
图 2 双Gm-APD偏振激光雷达系统示意图(FDC:倍频晶体;PIN:高速PIN探测器;BS:分光片;HWP:1/2波片;Polarizer:格兰泰勒棱镜;PBS:偏振分光棱镜;NBPF:窄带滤波片;Gm-APD:Gm-APD探测模块)
Figure 2. Schematic diagram of the double Gm-APDs polarization lidar system(FDC, Frequency doubling crystal; PIN, High-speed PIN detector; BS, Beam splitter; HWP, Half wave plate; Polarizer, Glan-Taylor prism; PBS, Polarization beam splitting prism; NBPF, Narrow band pass filter; Gm-APD, Gm-APD detecting module)
图3(a)为在实验室内搭建的双Gm-APD偏振激光雷达系统。图3(b)为实验中的超薄浅水层目标,深度渐变,从4.5 cm变化到8 cm,并且底面覆盖了黑、白沙子,探测距离为5 m。实验中的扫描成像点数为44×44。文中实验中所采用的器件及其参数如表1所示。
图 3 (a) 实验室中搭建的双Gm-APD偏振激光雷达系统;(b) 实验室设计的浅水层目标
Figure 3. (a) Double Gm-APD polarization lidar system in the laboratory; (b) Shallow water layer designed in the laboratory
在调节水平线偏振态激光发射过程中,激光器发射的是某一线偏振态的激光,通过1/2波片去改变线偏振态方向,旋转1/2波片的快轴角度,使得出射的水平线偏振光的强度达到最大。这是为了提高激光的能量利用率,适应将来的远距离探测。
表 1 实验中采用的器件及其参数
Table 1. Performance parameters of the devices in our experiment
Devices Performance parameters Semiconductor laser Wavelength, 1064 nm; Pulse width, 6 ns; Repetition frequency, 2 kHz; Work wavelength of the system, 532 nm. Receiving telescope Field of view, <70 mrad; Diameter of telescope, 50 mm. Gm-APD module Laser components GmbH, COUNT-100C-FC; Photon detection efficiency, 70%@532 nm; Dead time, 45 ns; Dark count rate, 100 Hz; Maximum count rate, 20 MHz; Temporal jittering, 1000 ps; Length of TTL output pulse, 15 ns; High level, 3 V. Photon correlator card Becker & Hickl GmbH, DPC-230; Collection time, 60 s; Operating mode,“Multicaler”; Time duration of time-bin, 164 ps.
Study of wide-pulse photon counting polarization lidar to detect shallow water layer (Invited)
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摘要: 由于受激光脉冲宽度的限制,传统激光雷达无法实现几十厘米的浅水层测量。设计了一个双Gm-APD光子计数偏振激光雷达系统,采用宽脉冲获取薄浅水层的高精度距离像。浅水层的表面光滑,能够保偏;底面粗糙,将发生退偏。根据该偏振现象,通过发射水平线偏振光,接收系统中采用一个偏振分光棱镜将前后表面信号光分离,然后分别被两个Gm-APD探测。该系统不受信号光的脉冲宽度限制,并充分利用Gm-APD的死时间机制,针对超薄浅水层实现三维深度测量。利用基于穆勒矩阵和斯托克斯参量表示的偏振传输原理,理论分析了双Gm-APD偏振激光雷达的分光原理。采用信号复原质心算法抑制距离漂移误差获取高精度距离信息。对于深度从4.5cm变化到8 cm渐变的薄浅水层,底面覆盖了黑、白沙子,探测距离为5 m,在实验上采用6 ns激光脉冲获取了薄浅水层的高精度距离像,测距精度为0.8 cm,有效验证了方案的可行性。该方案能够为机载海洋测绘激光雷达的浅水层测量提供一定借鉴。Abstract: Due to the limitation of laser pulse width, traditional lidar cannot achieve shallow water measurement of tens of centimeters. A polarization lidar with dual Geiger-mode avalanche photodiodes (Gm-APD) was designed to achieve high-precision depth image of shallow water layer by using a wide laser pulse. The surface of the shallow water layer was smooth and had good polarization-maintaining characteristics, whereas the bottom surface was rough and had certain depolarization characteristics. According to this feature, by emitting horizontal linearly polarized light, a polarization beam splitting prism was used in the receiving system to separate the front and rear surface signal lights, and then they were detected by two Gm-APDs respectively. The system was not limited by the pulse width of signal light, and made full use of the dead time mechanism of Gm-APD to realize the depth measurement of ultra-thin shallow water. Using the principle of polarization transmission of the Stokes parameter and Muller matrix, the principle of light splitting of the dual Gm-APD polarization lidar was theoretically analyzed. Signal restoration & center-of-mass algorithm method was used to restrain the range walk error to obtain high range precision. The thin shallow water layer had a gradient from 4.5 cm to 8 cm in depth, and the bottom surface of which was covered with black and white sand. In the experiment, a 6 ns width laser pulse was used to obtain a high-precision depth image of the thin shallow water layer at the detection distance of 5 m with the accuracy of 0.8 cm. This effectively verifies the feasibility of the scheme. This scheme can provide certain reference for the measurement of shallow ocean water layer in in airborne lidar bathymetry systems.
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Key words:
- lidar /
- photon counting /
- depth image /
- polarization /
- range walk error
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图 2 双Gm-APD偏振激光雷达系统示意图(FDC:倍频晶体;PIN:高速PIN探测器;BS:分光片;HWP:1/2波片;Polarizer:格兰泰勒棱镜;PBS:偏振分光棱镜;NBPF:窄带滤波片;Gm-APD:Gm-APD探测模块)
Figure 2. Schematic diagram of the double Gm-APDs polarization lidar system(FDC, Frequency doubling crystal; PIN, High-speed PIN detector; BS, Beam splitter; HWP, Half wave plate; Polarizer, Glan-Taylor prism; PBS, Polarization beam splitting prism; NBPF, Narrow band pass filter; Gm-APD, Gm-APD detecting module)
图 5 实验中得到的浅水层距离像。(a) 距离漂移误差抑制前;(b) 图(a)另一视角下的视图;(c) 距离漂移误差抑制后;(d) 图(c)另一视角下的视图
Figure 5. Depth image of the shallow water layer obtained in the experiment. (a) Before the restraint of range walk error; (b) Depth image under another view of (a); (c) After the restraint of range walk error; (d) Depth image under another view of (c)
图 6 实验数据点的距离误差分布直方图。(a) 图5(a)中浅水面的各像素点;(b) 图5(a)中底面的各像素点;(c) 图5(c)中浅水面的各像素点;(d) 图5(c)中底面的各像素点
Figure 6. Histogram of range error distribution of experimental data points. (a) Pixels of the shallow water surface in Fig.5(a); (b) Pixels of the bottom surface in Fig.5(a); (c) Pixels of the shallow water surface in Fig.5(c); (d) Pixels of the bottom surface in Fig.5(c)
表 1 实验中采用的器件及其参数
Table 1. Performance parameters of the devices in our experiment
Devices Performance parameters Semiconductor laser Wavelength, 1064 nm; Pulse width, 6 ns; Repetition frequency, 2 kHz; Work wavelength of the system, 532 nm. Receiving telescope Field of view, <70 mrad; Diameter of telescope, 50 mm. Gm-APD module Laser components GmbH, COUNT-100C-FC; Photon detection efficiency, 70%@532 nm; Dead time, 45 ns; Dark count rate, 100 Hz; Maximum count rate, 20 MHz; Temporal jittering, 1000 ps; Length of TTL output pulse, 15 ns; High level, 3 V. Photon correlator card Becker & Hickl GmbH, DPC-230; Collection time, 60 s; Operating mode,“Multicaler”; Time duration of time-bin, 164 ps. -
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