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风是水汽、气溶胶、碳循环以及海气交换的主要动力，是影响人类生产生活的重要因素。实时的高精度高时空分辨率的风场数据在改进气候模型、研究全球气候变化、促进大气热力学及动力学研究、提高天气预报的准确性、保障航空航天器的起飞和着落安全、提高风能利用率等方面有着重要的应用。多普勒激光雷达是近30多年来发展起来的一种新型大气风场遥感探测设备，在时空分辨率、角度方位和机动性等方面相对于传统的声雷达和微波雷达有较大的提高，而且还可探测晴天条件下的三维风场，是目前对三维风场进行高精度、高时空分辨率遥感探测的最有效工具之一。因此，对多普勒激光雷达技术的研究具有重要的意义。由于风场测量的重要性，国内外很多大学和研究机构都开展了对多普勒激光雷达技术的研究，根据探测体制的不同可分为两类：相干探测[1-4]和直接探测[5-11]。然而，目前的多普勒激光雷达，无论采用的是相干探测体制，还是直接探测体制，其发射源均采用的是窄线宽、稳频的单纵模激光器。只能采用单纵模激光器的局限，造成了现有的多普勒激光雷达系统对工作环境的要求比较苛刻，一旦环境条件不满足就可能影响系统的探测性能，甚至无法正常工作，这就严重制约了多普勒激光雷达的产业化应用及机载和星载应用。
尝试将多纵模激光器用做高光谱分辨率气溶胶激光雷达、测温激光雷达以及多普勒激光雷达等的发射源是当前研究的前沿热点之一。这是因为多纵模激光器若能作为这些激光雷达系统的发射光源，则不仅可以降低系统成本、减小系统体积、提高系统的稳定性和环境适应性，而且可以提高系统待测参数的测量精度。2008年，巩马理等人对多纵模激光用作F-P干涉仪双边缘多普勒激光雷达发射源的可行性做了初步的分析研究[12]，主要是对频率匹配条件的讨论，未涉及频率匹配误差、实际系统性能分析等问题。2013年，Bruneau等人搭建了一套基于M-Z干涉仪的多纵模测风激光雷达系统，并实现了对边界层风场的探测[13]。2015年，Jin等和Ristori等提出了多纵模高光谱分辨率激光雷达技术构想，并进一步对可调谐M-Z干涉仪多纵模高光谱分辨率激光雷达技术做了深入研究[14-15]。2018年，华灯鑫课题组做了进一步研究，所设计的紫外域多纵模高光谱分辨率激光雷达能实现10 km高度内的气溶胶光学参量精细探测[16-17]。2017年，浙江大学刘东课题组利用设计的宽视场迈克耳逊干涉仪开展多纵模高光谱分辨率激光雷达气溶胶探测技术和理论研究[18-19]。由此可见，目前国内外对多纵模激光雷达的研究主要集中在高光谱分辨率气溶胶激光雷达，对多纵模多普勒激光雷达的研究报道还非常少。文中主要探索基于双F-P干涉仪的多纵模米散射多普勒激光雷达技术，包括风速探测原理、理论分析、频率匹配要求及雷达系统性能仿真分析。
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基于双FPI和多纵模激光的米散射大气风场探测原理如图1所示，图1(b)是图1(a)的局部放大图。采用一体化的双FPI，FPI-1和FPI-2的自由谱间距（FSR）相同，两者的频谱峰峰间隔为200 MHz；多纵模激光发射波长为λ=1064 nm，其纵模间隔与干涉仪的FSR匹配，且各纵模的中心频率被锁定在FPI-1和FPI-2频谱的交叉位置。多纵模脉冲激光发射至大气中，遇到大气中运动的气溶胶和分子，总的后向散射光谱为所有单纵模的米和瑞利散射谱的叠加，而散射频谱将发生多普勒频移和展宽，多普勒频移量νd与气溶胶和分子的宏观运动速度（即矢量风速）V有关，即νd=2Vr/λ，Vr=Vcos$\phi $为径向风速，$\phi $为矢量风速方向与光束发射方向的夹角。为了测得多普勒频移量（径向风速），大气后向散射光先分出小部分用作能量监测，大部分再均分为两束分别入射至FPI-1和FPI-2。不同径向风速情况下，等分的米散射光经过FPI-1和FPI-2后透射信号的比值将明显不同，利用FPI-1和FPI-2透射信号的比值与多普勒频移量的函数关系，可以反演得到径向风速。借助能量监测通道的信号可以反演获得后向散射比，并进一步用于修正风速反演结果。
图 1 基于双FPI和多纵模激光的大气风速探测原理。(a) 相对频率范围−14~+14 GHz；(b) 相对频率范围−5.25~+5.25 GHz
Figure 1. Atmospheric wind speed detection principle based on dual FPI and MLM laser. (a) Relative frequency range −14-+14 GHz; (b) Relative frequency range −5.25-+5.25 GHz
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根据风速探测原理设计的多普勒激光雷达接收系统光路如图2所示。假定入射至双FPI接收系统的总大气后向散射光子数为N0，包含分子瑞利散射光子数Nm和气溶胶米散射光子数Na。总后向散射光信号由准直镜准直后，经过分束片1（BS-1），小部分散射信号被反射，光子数为Ne；大部分散射信号透过BS-1后，再经过分束片2（BS-2），被平均分成透反射两部分。透射部分入射至FPI-1，透过FPI-1的信号光子数为N1；反射部分经由45°反射镜反射后，入射至FPI-2，透过FPI-2的信号光子数为N2。
频率为ν的单色光平行光以θ角入射至FPI-i的透过率函数为：
$$ {h_i}(\nu - {\nu _i}) = {\eta _i}\left\{ {1 + 2\sum\limits_{n = 1}^\infty {R_{e,i}^n\cos \left[ {\frac{{2\pi n(\nu - {\nu _i})\cos \theta }}{{{\nu _{FSR}}}}} \right]} } \right\} $$ (1) 式中：i=1, 2；ηi=[1−A/(1−Ri)]2 (1−Ri)/(1+Ri)为FPI-i的平均透过率，Ri为FPI-i平板的实际反射率，A为FPI-i平板的吸收损耗系数；Re,i为FPI-i平板的有效反射率；νi为FPI-i的中心频率；νFSR为FPI-i的自由谱间距。
图 2 基于双FPI和多纵模激光的多普勒激光雷达接收系统光路
Figure 2. Optical path of Doppler lidar receiving system based on dual FPI and MLM laser
多纵模激光入射到大气中后，多纵模中的每条单纵模谱线的回波函数仍可用高斯线型近似，只是各条纵模的强度受到激光介质增益曲线的调制。因此，多纵模激光的气溶胶米散射(j=a)和分子瑞利散射(j=m)总的归一化回波谱函数为[18]：
$$ {G_j}(\nu ) = \sum\limits_q {{C_q}} \exp \left[ { - \frac{{{{(\nu - {\nu _0} - {\nu _d} - q\varLambda )}^2}}}{{\Delta \nu _j^2}}} \right]\bigg/ \sum\limits_q {{C_q}} \Delta {\nu _j}\sqrt \pi $$ (2) 式中：Δva=δv/(4 ln2)1/2为单个纵模米散射谱1/e高度处谱宽，δv为发射激光单个纵模的半高谱宽；Δvm=(Δva2+Δvr2)1/2为单个纵模瑞利散射谱1/e高度处谱宽，Δvr=(8kT/Mλ2)1/2为瑞利散射谱宽增量，k为玻尔兹曼常数，T为大气温度，M为大气分子平均质量，λ发射激光波长；ν0为发射激光中心频率；q是以选定的中心频率ν0（中心频率的q为0）为参考的纵模序数；νd 为多普勒频移量； Λ为纵模间隔；Cq为各条谱线的相对强度（规定ν0处相对强度为1）。
经准直镜准直后，全发散角为2θ0的米和瑞利散射光正入射至双FPI的透过率分别为：
$$ {T_{ij}}({\nu _0} + {\nu _d}) = 2\theta _0^{ - 2}\int_{ - \infty }^{ + \infty } {\int_0^{{\theta _0}} {{G_j}(\nu ){h_i}(\nu - {\nu _i})\sin \theta {\rm d}\theta } } {\rm d}\nu $$ (3) 将公式(1)、(2)代入公式(3)积分得：
$$ {T_{ij}}({\nu _0} + {\nu _d}) = {\eta _i}(1 + 2{\sigma _{ij}}) $$ (4) 其中
$$ \begin{split} {\sigma _{ij}} =& \sum\limits_q {\sum\limits_{n = 1}^\infty {{C_q}R_{e,i}^n} \cos \left[ {\frac{{2\pi n({\nu _0} + {\nu _d} + q\varLambda - {\nu _i})}}{{\nu _{FSR}'}}} \right]} \cdot \\ & \exp [ - {(\pi n\Delta {\nu _j}/\nu _{FSR}')^2}] \cdot \\ & \sin c\left[ {\frac{{2n({\nu _0} + {\nu _d} + q\varLambda - {\nu _i})}}{{\nu _{FSR}'}}\frac{{1 - \cos {\theta _0}}}{{1 + \cos {\theta _0}}}} \right] \bigg/\sum\limits_q {{C_q}} \end{split} $$ (5) 式中：ν′FSR=2νFSR/(1+cosθ0)。当满足条件Λ=pν′FSR，p=1,2,···时，上式可简化为：
$$ \begin{split} {\sigma _{ij}} = & \sum\limits_{n = 1}^\infty {R_{e,i}^n} \cos \left[ {\frac{{2\pi n({\nu _0} + {\nu _d} - {\nu _i})}}{{\nu _{FSR}'}}} \right] \cdot \\ & \exp \left[ { - {{\left( {\frac{{\pi n\varDelta {\nu _j}}}{{\nu _{FSR}'}}} \right)}^2}} \right] \cdot \sin c\left[ {\frac{{2n({\nu _0} + {\nu _d} - {\nu _i})}}{{\nu _{FSR}'}}\frac{{1 - \cos {\theta _0}}}{{1 + \cos {\theta _0}}}} \right] \end{split} $$ (6) 该式和采用单纵模光源获得的结果一致。
由此，两个边缘通道（i=1, 2）和一个能量监测通道探测器接收到的高度z处的大气后向散射光电子数为：
$$ \begin{split} {N_i} =& {a_i}[{N_a}({\textit{z}}){T_{ia}}({\nu _0} + {\nu _d} - {\nu _1}) +\\ & {N_m}({\textit{z}}){T_{im}}({\nu _0} + {\nu _d} - {\nu _i},T)]\\[-10pt] \end{split} $$ (7) $$ {N_e} = {a_3}[{N_a}({\textit{z}}) + {N_m}({\textit{z}})] $$ (8) 式中：a1，a2，a3为校准常数；T为z高度处的大气温度；Na(z)、Nm(z)分别为激光雷达接收机接收到垂直高度z~z+Δz之间的米和瑞利后向散射光电子数，Δz为垂直距离分辨率；Na(z)和Nm(z)可由激光雷达方程得到。由公式(7)~(8)可得：
$$ \begin{split} ({a_3}{N_i})/({a_i}{N_e}) =& {T_i}({\nu _d},{R_\beta },T) = \\ & [(1 - R_\beta ^{ - 1}){T_{ia}}({\nu _0} + {\nu _d} - {\nu _i}) + R_\beta ^{ - 1}{T_{im}}({\nu _0} + {\nu _d} - {\nu _i},T)] \end{split} $$ (9) 式中：Rβ=(βa+βm)/βm为后向散射比。联立上述两个方程，得到：
$$ \left\{ {\begin{array}{*{20}{c}} {{T_1}({\nu _d},{R_\beta },T) - ({a_3}{N_1})/({a_1}{N_e}) = 0} \\ {{T_2}({\nu _d},{R_\beta },T) - ({a_3}{N_2})/({a_2}{N_e}) = 0} \end{array}} \right. $$ (10) 式中：Ti为FPI-i的有效透过率。对公式(9)采用非线性迭代方法可同时反演风速和后向散射比。根据误差传递公式，得到风速测量误差εV和后向散射比测量误差εR分别为：
$$ {\varepsilon _V} = \frac{{\sqrt {\theta _{R1}^2SNR_2^{ - 2} + \theta _{R2}^2SNR_1^{ - 2}} }}{{\left| {{\theta _{V1}}{\theta _{R2}} - {\theta _{R1}}{\theta _{V2}}} \right|}} $$ (11) $$ {\varepsilon _R} = \frac{{\sqrt {\theta _{V1}^2SNR_2^{ - 2} + \theta _{V2}^2SNR_1^{ - 2}} }}{{\left| {{\theta _{V1}}{\theta _{R2}} - {\theta _{R1}}{\theta _{V2}}} \right|}} $$ (12) 式中：θVi=(1/Ti)∂Ti/∂V=(2/λTi)∂Ti/∂νd为Ti的速度灵敏度，θRi=(1/Ti)∂Ti/∂Rβ为Ti的后向散射比灵敏度；SNRi为Ti的探测信噪比（i=1,2）
$$ SN{R_i} = {\left[ {\frac{{{N_i} + {\eta _i}{a_i}{N_b} + {N_d}}}{{N_i^2}} + \frac{{{N_e} + {a_3}{N_b} + {N_d}}}{{N_e^2}}} \right]^{ - 1/2}} $$ (13) 式中：Nb为雷达接收到的天空背景光电子数；Nd为对应测量时间内探测器产生的暗计数。
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米散射多普勒激光雷达主要是利用大气气溶胶米散射信号进行风速测量，故选定雷达系统的工作波长为1064 nm。参考单纵模双FPI干涉仪米散射多普勒激光雷达的优化结果[8]，选取FPI-i的参数νFSR=3.5 GHz，Re,i=0.836，Ri=0.841，ν21=ν2−ν1=200 MHz，A=0.2%，入射光束发散角2θ0=1 mrad；发射激光单个纵模谱宽δv=60 MHz，纵模间隔Λ=3.5 GHz。假定激光介质增益曲线为高斯分布，即Cq=exp[−(qΛ)2/ΔvL2]，
ΔvL为1/e高度处激光辐射谱宽，设为18 GHz。利用上述参数仿真得到双FPI的米散射信号透过率和大气温度为290 K时的瑞利散射信号透过率，如图3所示。可以看出：T1a和T2a随多普勒频移量的变化而变化明显，而T1m和T2m随多普勒频移量的变化而几乎不变，即对风速测量而言，瑞利散射信号类似于白噪声。 
图 3 双FPI米散射信号透过率和瑞利散射信号透过率
Figure 3. Mie-signal transmittance and Rayleigh-signal transmittance of dual FPI
图3是假定发射激光的纵模间隔Λ与FPI的FSR严格匹配（Λ=pν′FSR, p=1,2,···）时的理想结果。然而，实际Λ与FSR可能失配，即存在匹配误差ΔνFSR=|Λ−νFSR|。这是多纵模激光雷达才有的误差，它将引起风速测量误差增大，甚至导致无法测量。从前文理论分析可知，当不存在匹配误差时，采用多纵模激光可获得与单纵模激光一致的理论结果。图4给出了存在不同匹配误差时，发射激光入射至双FPI的透过率曲线。可以看出，随着匹配误差增大，双FPI的透过率曲线线宽增大、峰值降低，风速测量灵敏度减小。图5给出了透过率曲线峰值随匹配误差的变化。显然，当Λ与FSR完全匹配时，透过率曲线峰值达到最大。该变化曲线可以用于Λ与FSR匹配校准[20]，方法与文献[15-16]相似。2022年，浙江大学刘东课题组深入分析了激光纵模间隔Λ与鉴频器的FSR失匹配的深层机制，并提出了有效的抑制方法[21]。当Λ与FSR满足匹配条件后，多纵模激光发射频率和FPI透过率曲线的锁定方法，与单纵模激光器和FPI之间的频率锁定方法完全一致[8]。
图 4 不同匹配误差时，发射激光入射至双FPI的透过率曲线
Figure 4. Transmittance curves of emitted laser incident on dual FPI with different matching errors
图 5 FPI透过率峰值随匹配误差的变化曲线
Figure 5. Curve of FPI transmittance peak changing with matching error
图6给出了在不同的后向散射比情况下，存在匹配误差时的风速测量误差ε′V与完全匹配时的测量误差εV相比所增加的百分数EV=(ε′V−εV)/εV×100%随匹配误差和径向风速大小变化的等高线图。从图中可以看出：在低风速区域，EV随匹配误差增大而迅速增大；匹配误差不变时，EV随风速增大而缓慢减小。当Rβ=1.5，ΔνFSR=10 MHz，径向风速为0 m/s和20 m/s时，风速测量误差增加的百分数EV分别为3.8%和1.9%；当ΔνFSR=25 MHz，径向风速为0 m/s和20 m/s时，EV分别为37.6%和20.7%，如图6(a)所示。当Rβ=2，ΔνFSR=10 MHz，径向风速为0 m/s和20 m/s时，EV分别为4.1%和2.4%；ΔνFSR=25 MHz，径向风速为0 m/s和20 m/s时，EV分别为39.2%和23.3%，如图6(b)所示。当Rβ=5，ΔνFSR=10 MHz，径向风速为0 m/s和20 m/s时，EV分别为4.4%和2.9%；当ΔνFSR=25 MHz，径向风速为0 m/s和20 m/s时，EV分别为41%和26.6%，如图6(c)所示。由此可知，只需将匹配误差控制在10 MHz以下，EV将小于5%，匹配误差对风速测量的影响很小。
图 6 不同后向散射比时，风速误差增大的百分比随匹配误差和径向风速大小变化的等高线图
Figure 6. Contour map of the percentage of increase in wind speed error with the matching error and radial wind speed for different backscatter ratios
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文中选择Nd:YAG固体脉冲激光器作为多纵模激光雷达发射源，以美国Continuum公司Powerlite 8050产品为例，其无种子注入时的线宽为1 cm−1（30 GHz），当纵模间隔为3.5 GHz时，辐射线宽内将会同时出现九个纵模。发射激光经过八倍扩束镜将发散角压至0.625 mrad，通过导光反射镜、二维扫描系统以设定的角度指向大气被测区域。大气后向散射回波信号光由卡塞格林望远镜接收并耦合到100 m长多模光纤，接收视场角为0.1 mrad，然后通过1×2光纤耦合器FC-2进入接收机进行频率检测。发射激光在扩束前由分束片BS-0分出1%，并经FC-1导入50 m长光纤，利用其在光纤中的后向散射光作为参考光，然后也通过FC-2进入接收机进行频率检测及频率锁定。由参考光与回波信号光的频率差值即可得到径向风速的大小。通过设置合适的光纤长度，将两路光信号在时序上分开。进入到接收机中的光信号经过准直镜、干涉滤光片后，被BS-1分成两束。反射光束由雪崩光电二极管APD-E接收，用于能量探测。透射光束再由BS-2均分成两束，分别正入射至双FPI的两个通道，透射光再分别由APD-1和APD-2接收。三个APD探测器的输出信号由多通道采集卡采集，再由计算机进行数据处理、存储以参数反演和结果显示。激光器、扫描仪、探测器、采集卡、FPI等系统单元均通过RS232串口由计算机控制。系统主要技术参数见表1。基于双FPI多纵模米散射多普勒激光雷达结构图如图7所示。
表 1 基于双FPI的多纵模多普勒激光雷达系统参数
Table 1. Parameters of MLM Doppler lidar system based on dual FPI
Parameter Value Parameter Value Wavelength 1064 nm Laser energy/pulse 550 mJ Laser mode number 9 Laser mode interval 3.5 GHz Laser mode linewidth 60 MHz Laser repetition frequency 50 Hz Beam diameter 7 mm Pulse width 7-9 ns Beam divergence 0.5 mrad Beam expander ×8 Telescope/scanner aperture 25 cm Telescope focal length 625 mm Scan range 360°×90° Field of view 0.1 mrad Optical efficiency >85% Zenith angle 30° FPI free spectral range 3.5 GHz FPI-1 and FPI-2 separation 0.2 GHz FWHM of FPI-1, FPI-2 0.2 GHz Defect finesse of FPI 71 Effective reflectivity of FPI 0.836 Loss coefficient of FPI 0.2% Actual reflectivity of FPI 0.841 Dual FPI aperture 60 mm Fiber core diameter 62.5 μm Fiber NA 0.22 Solar filter bandwidth 0.5 nm APD quantum efficiency 18%
@1064Filter peak transmission >60% Detector dark count 100 counts/s BS-1, BS-2 splitting ratio (R/T) 20/80
, 50/50Multiscaler sampling rate 200 MHz 
图 7 基于双FPI多纵模米散射多普勒激光雷达结构图
Figure 7. Structure diagram of MLM Mie Doppler lidar based on dual FPI
设定探测径向距离分辨率为30 m，时间分辨率为30 s，激光发射天顶角为30°，白天直接太阳辐射强度取0.688 W·sr−1·m−2·nm−1 @1064 nm，激光雷达比取35。大气参数采用1976美国标准大气模型，同时在标准气溶胶模型的3.5~4.5 km高度附近加入了模拟的淡积云。模拟得到的大气分子和气溶胶后向散射系数如图8(a)所示，对应的后向散射比如图8(b)所示。由图8(b)可以看出，在4 km处后向散射比达到了90。
图 8 模拟的大气参数随高度的变化廓线。(a) 大气分子和气溶胶后向散射系数；(b) 后向散射比
Figure 8. Profile of simulated atmospheric parameters with altitude. (a) Backscatter coefficients of atmospheric molecules and aerosols; (b) Backscatter ratio
采用表1所示的系统参数和上述模拟得到的大气参数，对基于双FPI的多纵模多普勒激光雷达系统的探测性能进行仿真。图9(a)和图9(b)分别给出了径向风速测量误差和后向散射比相对测量误差（εR/Rβ）随高度的变化廓线。从图9(a)和图9(b)可以分别看出：在0~10 km高度、0~50 m/s的径向风速范围内，系统白天和晚间的径向风速测量误差分别小于1.50 m/s和1.02 m/s；系统白天和晚间的后向散射比相对测量误差在4 km云层出现的高度附近达到最大，均为12.13%，而在没有云层的情况下，系统白天和晚间的后向散射比相对测量误差分别小于6.57%和4.53%。在白天与夜晚，系统均可保证较高的参数测量精度。
图 9 参数测量误差随高度变化的仿真廓线。(a) 径向风速；(b) 后向散射比
Figure 9. Simulation profile of parameter measurement error changing with altitude. (a) Wind speed; (b) Backscatter ratio
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提出了一种基于多纵模激光器和双FPI的米散射多普勒激光雷达技术。分析了该技术的风场探测原理，推导出了径向风速和后向散射比测量误差公式等一系列理论公式。深入分析发现：当满足频率匹配条件时，多纵模测风等效于各个单模测风的叠加，结论与单纵模测风完全相同；频率匹配误差将引起风速测量误差增大，但只要将频率匹配误差控制在10 MHz以下，匹配误差对风速测量精度的影响就小于5%，而这一点很容易通过系统校准来实现。进一步对基于该技术的多普勒激光雷达系统的探测性能进行了仿真，仿真结果也表明了系统全天候均具有较高的风速和后向散射比探测精度。这些结论充分说明了该技术具备可行性。
Multi-longitudinal-mode Mie scattering Doppler lidar technology based on dual Fabry-Perot interferometer
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摘要: 提出了基于双法布里-珀罗干涉仪（FPI）的多纵模米散射多普勒激光雷达技术，分析了探测原理，并导出了径向风速和后向散射比测量误差公式。该技术要求多纵模激光源的纵模间隔与双FPI的自由谱间距相匹配，并将各纵模的中心频率锁定在双FPI周期性频谱曲线的交叉点附近。详细分析了频率匹配误差引起的风速测量误差。在低风速区域，由频率匹配误差造成的风速测量误差增加的百分数EV随匹配误差的增大而迅速增大；频率匹配误差不变时，EV随风速增大而缓慢减小；当频率匹配误差小于10 MHz时，EV将小于5%。设定合理的大气模式和系统参数，对基于双FPI的多纵模米散射多普勒激光雷达的探测性能进行了仿真分析。结果表明：在0~10 km高度、0~50 m/s的径向风速范围内，当距离分辨率为30 m、时间分辨率为30 s、激光发射天顶角为30°时，系统白天和晚间的径向风速测量精度分别优于1.50 m/s和1.02 m/s；在无云条件下，系统白天和晚间的后向散射比相对测量精度分别优于6.57%和4.53%。Abstract:
Objective Doppler lidar is one of the most powerful tools for the remote sensing of the three-dimensional wind field in the atmosphere at present. It is widely used in wind power generation, weather forecast, aviation safety, atmospheric science research and other fields. The traditional coherent detection or direct detection Doppler lidar requires a single-longitudinal-mode laser source with narrow linewidth, resulting in the shortcomings of the existing Doppler lidar system such as high cost, poor environmental adaptability, low laser energy utilization, which seriously restricts their industrialization and the airborne and spaceborne applications. Therefore, it is of great significance and scientific value to explore and study the technology of multi-longitudinal-mode (MLM) Doppler lidar using MLM laser as the emission source. For this purpose, the MLM Mie Doppler lidar technology based on dual Fabry-Perot interferometer (FPI) is proposed and studied. Methods The detection principle of MLM Mie Doppler lidar based on dual FPI is analyzed (Fig.1). The theoretical formulas of radial wind speed and backscatter ratio measurement errors are derived, and the matching relationship between the longitudinal mode interval of the MLM laser source and the free spectral spacing of the dual FPI is analyzed, as well as the wind speed measurement error caused by the mismatch between the two. The lidar system structure (Fig.7) and parameters (Tab.1) are designed, and the detection performance of the designed lidar system is simulated using the 1976 USA atmospheric model and simulated cumulus clouds. Results and Discussions The frequency matching condition between the longitudinal mode interval of the MLM laser source and the free spectral spacing of the dual FPI is that the former is an integral multiple of the latter. When the frequency matching condition is satisfied, the MLM wind measurement is equivalent to the superposition of each single-longitudinal-mode (SLM) wind measurement. In the low wind speed region, the percentage of the wind speed measurement error EV caused by the frequency matching error increases rapidly with the increase of the matching error; When the frequency matching error remains unchanged, EV decreases slowly with the increase of wind speed; When the frequency matching error is less than 10 MHz, EV will be less than 5% (Fig.6). The simulation results of lidar detection performance show that, in the range of 0-10 km altitude and 0-50 m/s radial wind speed, when the range resolution is 30 m, the time resolution is 30 s and the zenith angle of laser emission is 30°, the radial wind speed measurement accuracy of the lidar system is better than 1.50 m/s and 1.02 m/s in daytime and nighttime respectively; Under cloudless conditions, the relative measurement accuracy of the backscatter ratio in daytime and nighttime is better than 6.57% and 4.53%, respectively (Fig.9). Conclusions A Mie Doppler lidar technology based on multimode laser and dual FPI is proposed and studied. This technology requires that the longitudinal mode interval of the laser source should match the free spectral spacing of the dual FPI, and the center frequency of each longitudinal mode should be locked near the intersection of the dual FPI periodic spectrum curves. When the frequency matching condition is satisfied, the MLM wind measurement is equivalent to the superposition of each SLM wind measurement. The frequency matching error will increase the wind speed measurement error, but as long as the frequency matching error is controlled below 10 MHz, the impact of the matching error on the wind speed measurement accuracy is less than 5%, which can be easily achieved through system calibration. The simulation results show that the Doppler lidar system based on this technology has high detection accuracy of wind speed and backscatter ratio in all weather. These conclusions fully demonstrate the feasibility of this technology. -
Key words:
- lidar /
- atmospheric wind /
- multi-mode pulse laser /
- Fabry-Perot interferometer /
- Mie scattering
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图 1 基于双FPI和多纵模激光的大气风速探测原理。(a) 相对频率范围−14~+14 GHz；(b) 相对频率范围−5.25~+5.25 GHz
Figure 1. Atmospheric wind speed detection principle based on dual FPI and MLM laser. (a) Relative frequency range −14-+14 GHz; (b) Relative frequency range −5.25-+5.25 GHz
图 2 基于双FPI和多纵模激光的多普勒激光雷达接收系统光路
Figure 2. Optical path of Doppler lidar receiving system based on dual FPI and MLM laser
图 3 双FPI米散射信号透过率和瑞利散射信号透过率
Figure 3. Mie-signal transmittance and Rayleigh-signal transmittance of dual FPI
图 4 不同匹配误差时，发射激光入射至双FPI的透过率曲线
Figure 4. Transmittance curves of emitted laser incident on dual FPI with different matching errors
图 5 FPI透过率峰值随匹配误差的变化曲线
Figure 5. Curve of FPI transmittance peak changing with matching error
图 6 不同后向散射比时，风速误差增大的百分比随匹配误差和径向风速大小变化的等高线图
Figure 6. Contour map of the percentage of increase in wind speed error with the matching error and radial wind speed for different backscatter ratios
图 7 基于双FPI多纵模米散射多普勒激光雷达结构图
Figure 7. Structure diagram of MLM Mie Doppler lidar based on dual FPI
图 8 模拟的大气参数随高度的变化廓线。(a) 大气分子和气溶胶后向散射系数；(b) 后向散射比
Figure 8. Profile of simulated atmospheric parameters with altitude. (a) Backscatter coefficients of atmospheric molecules and aerosols; (b) Backscatter ratio
图 9 参数测量误差随高度变化的仿真廓线。(a) 径向风速；(b) 后向散射比
Figure 9. Simulation profile of parameter measurement error changing with altitude. (a) Wind speed; (b) Backscatter ratio
表 1 基于双FPI的多纵模多普勒激光雷达系统参数
Table 1. Parameters of MLM Doppler lidar system based on dual FPI
Parameter Value Parameter Value Wavelength 1064 nm Laser energy/pulse 550 mJ Laser mode number 9 Laser mode interval 3.5 GHz Laser mode linewidth 60 MHz Laser repetition frequency 50 Hz Beam diameter 7 mm Pulse width 7-9 ns Beam divergence 0.5 mrad Beam expander ×8 Telescope/scanner aperture 25 cm Telescope focal length 625 mm Scan range 360°×90° Field of view 0.1 mrad Optical efficiency >85% Zenith angle 30° FPI free spectral range 3.5 GHz FPI-1 and FPI-2 separation 0.2 GHz FWHM of FPI-1, FPI-2 0.2 GHz Defect finesse of FPI 71 Effective reflectivity of FPI 0.836 Loss coefficient of FPI 0.2% Actual reflectivity of FPI 0.841 Dual FPI aperture 60 mm Fiber core diameter 62.5 μm Fiber NA 0.22 Solar filter bandwidth 0.5 nm APD quantum efficiency 18%
@1064Filter peak transmission >60% Detector dark count 100 counts/s BS-1, BS-2 splitting ratio (R/T) 20/80
, 50/50Multiscaler sampling rate 200 MHz 
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