光子学报  2019, Vol. 48 Issue (10): 1001001  DOI: 10.3788/gzxb20194810.1001001 0

### 引用本文

PAN Ting-yu, SUN Dong-song, ZHAO Ruo-can, et al. Parameter Design and Performance Analysis of Bistatic Helium Lidar System[J]. Acta Photonica Sinica, 2019, 48(10): 1001001. DOI: 10.3788/gzxb20194810.1001001.

### 文章历史

(中国科学技术大学 地球和空间科学学院, 合肥 230026)

Parameter Design and Performance Analysis of Bistatic Helium Lidar System
PAN Ting-yu , SUN Dong-song , ZHAO Ruo-can , LAN Jia-xin , HAN Yu-li , CHEN Ting-di , XUE Xiang-hui , TANG Lei
(School of Earth and Space Science, University of Science and Technology of China, Hefei 230026, China)
Foundation item: The National Natural Science Foundation of China (Nos. 41774193, 41574180)
Abstract: According to the atmospheric continuous laser beam imaging technology, the corresponding resolution range for the distance between separated transmitter and receiver on bistatic helium lidar system is obtained, as well as the relationship between the single-row CCD pixels and the altitude, and the variation curve of resolution range with different altitudes. Moreover, the corresponding relation between the number of photons received by the system's single-row pixels and the altitude under different metastable helium densities is analyzed, and the signal to noise ratio and relative error varied with altitude are obtained. The simulation results indicate that the signal to noise ratio can be improved by increasing the integration time. In the range of altitude from 400 km to 1 000 km, when the integration time is 2 h and the range resolution is 50 km, the signal to noise ratio is in the range from 10 to 65 and the relative error is less than 10%. These results prove that adopting the bistatic helium resonance fluorescence lidar system can detect the metastable helium density of the 200~1 000 km thermosphere, which provides a reference for further perfecting and optimizing the scheme of the bistatic helium resonance fluorescence lidar system.
Key words: Atmospheric optics    Helium density lidar    Resonance fluorescence    Metastable helium    Thermosphere    Remote sensing    Numerical simulation
OCIS Codes: 010.0280;010.3640;280.3640
0 引言

1 亚稳态氦密度激光雷达探测原理 1.1 亚稳态氦跃迁谱线

 图 1 LS耦合下亚稳态氦1 083.0 nm共振辐射线 Fig.1 Resonance radiation of metastable helium 1 083.0 nm under LS coupling

1.2 氦共振荧光激光雷达系统结构及激光雷达方程

 图 2 氦激光雷达系统结构 Fig.2 Structure of the helium lidar system

 图 3 氦激光雷达系统收发装置示意图 Fig.3 Schematic diagram of the helium lidar system transceiver

 ${I_{{{\rm{R}}_1}}} = \frac{{{P_{\rm{L}}}{T_1}E(z)}}{{R_1^2{\rm{d}}{\omega _1}}} = \frac{{{P_{\rm{L}}}{T_1}E(z)}}{{R_1^2 \cdot {\rm{ \mathsf{ π} }} \cdot {{\left( {\tan \frac{{{\theta _{\rm{L}}}}}{2}} \right)}^2}}}$ (1)
 ${I_{{{\rm{R}}_2}}} = \frac{{{P_{\rm{L}}}{T_1}E(z)}}{{R_1^2 \cdot {\rm{ \mathsf{ π} }} \cdot {{\left( {\tan \frac{{{\theta _{\rm{L}}}}}{2}} \right)}^2}}} \cdot \frac{V}{{R_2^2}} \cdot {T_2}E(z) \cdot \left[ {\frac{{{\sigma _{{\rm{eff}}}}}}{{4{\rm{ \mathsf{ π} }}}}{N_{\rm{c}}}(z){R_{\rm{B}}}} \right]$ (2)

 ${N_{\rm{S}}} = \frac{{{\lambda _0}}}{{hc}} \cdot \frac{{{P_{\rm{L}}}{T_1}E(z)}}{{R_1^2 \cdot {\rm{ \mathsf{ π} }} \cdot {{\left( {\tan \frac{{{\theta _{\rm{L}}}}}{2}} \right)}^2}}} \cdot \frac{V}{{R_2^2}} \cdot {T_2}E(z) \cdot \left[ {\frac{{{\sigma _{{\rm{eff}}}}}}{{4{\rm{ \mathsf{ π} }}}}{N_{\rm{c}}}(z){R_{\rm{B}}}} \right] \cdot {A_{\rm{R}}} \cdot \eta \cdot \tau + {n_{\rm{B}}}\tau$ (3)

 ${R_1} = \frac{{z(n)}}{{\sin {\beta _{\rm{L}}}}}$ (4)
 ${R_2} = \frac{{z(n)}}{{\sin {\beta _{\rm{R}}}(n)}}$ (5)

 ${N_{\rm{S}}}(n) = \frac{{{P_{\rm{L}}}\tau {\lambda _0}}}{{hc}} \cdot \frac{{V(n) \cdot {A_{\rm{R}}}}}{{{\rm{ \mathsf{ π} }}{{\left( {\tan \frac{{{\theta _{\rm{L}}}}}{2}} \right)}^2}{{\left[ {\frac{{z(n)}}{{\sin {\beta _{\rm{L}}}}}} \right]}^2}{{\left[ {\frac{{z(n)}}{{\sin {\beta _{\rm{R}}}(n)}}} \right]}^2}}} \cdot \left[ {\frac{{{\sigma _{{\rm{eff}}}}}}{{4{\rm{ \mathsf{ π} }}}}{N_{\rm{c}}}(z){R_{\rm{B}}}} \right] \cdot \left[ {\eta {T^2}{E^2}(z)} \right] + {n_{\rm{B}}}\tau$ (6)

1.3 分支比和消光系数

 ${R_{\rm{B}}}(\lambda ) = \frac{{{I_{{\rm{ul}}}}}}{{\sum {{I_{{\rm{ul}}}}} }}$ (7)

 $E(z) = \exp \left[ { - \int_{{z_{{\rm{bottom}}}}}^z {{\sigma _{{\rm{eff }}}}} (\lambda ){N_{\rm{c}}}(z){\rm{d}}z} \right)$ (8)

1.4 背景光强

 图 4 SRI瑞利激光雷达系统观测的单位时间背景噪声光子数随θSZA变化曲线 Fig.4 Variation curve of background noise photons per unit time with θSZA observed by SRI Rayleigh lidar
 ${N_{\rm{B}}} = 4.25\exp \left[ { - 0.79\left( {{\theta _{{\rm{SZA}}}} - 95} \right)} \right]$ (9)

 ${N_{\rm{B}}} = \frac{{{E_{\rm{B}}} \cdot {A_{\rm{R}}} \cdot \frac{{\rm{ \mathsf{ π} }}}{4} \cdot {\theta _{{\rm{VO}}{{\rm{V}}^2}}} \cdot \eta \cdot \Delta \lambda \cdot 2 \cdot \Delta z}}{{h \cdot v \cdot c \cdot {\rm{ \mathsf{ π} }}}}$ (10)

 图 5 背景光强度随太阳天顶角SZA变化曲线 Fig.5 Variation curve of background intensity with solar zenith angle
2 氦激光雷达系统的探测性能分析

 $z(n) = \frac{D}{{\frac{1}{{\tan \left( {{\beta _{\rm{L}}}} \right)}} + \frac{1}{{\tan \left[ {{\beta _{\rm{R}}}(n)} \right]}}}}$ (11)

n个像素列的最高高度为

 ${z_1}(n) = \frac{D}{{\frac{1}{{\tan \left( {{\beta _{\rm{L}}} + \frac{{{\theta _{\rm{L}}}}}{2}} \right)}} + \frac{1}{{\tan \left( {{\beta _{\rm{R}}}(n) + \frac{{{\theta _{{\rm{FOV}}}}}}{{2N}}} \right)}}}}$ (12)

n个像素列的最低高度为

 ${z_2}(n) = \frac{D}{{\frac{1}{{\tan \left( {{\beta _{\rm{L}}} - \frac{{{\theta _{\rm{L}}}}}{2}} \right)}} + \frac{1}{{\tan \left( {{\beta _{\rm{R}}}(n) - \frac{{{\theta _{{\rm{FOV}}}}}}{{2N}}} \right)}}}}$ (13)

n个像素列的距离分辨率为

 $\Delta z(n) = {z_1}(n) - {z_2}(n) = \frac{D}{{\frac{1}{{\tan \left( {{\beta _{\rm{L}}} + \frac{{{\theta _{\rm{L}}}}}{2}} \right)}} + \frac{1}{{\tan \left( {{\beta _{\rm{R}}}(n) + \frac{{{\theta _{{\rm{FOV}}}}}}{{2N}}} \right)}}}} - \frac{D}{{\frac{1}{{\tan \left( {{\beta _{\rm{L}}} - \frac{{{\theta _{\rm{L}}}}}{2}} \right)}} + \frac{1}{{\tan \left( {{\beta _{\rm{R}}}(n) - \frac{{{\theta _{{\rm{FOV}}}}}}{{2N}}} \right)}}}}$ (14)

 图 6 不同收发装置距离对应的距离分辨率分布曲线 Fig.6 Variation curve of resolution range with the distance between separated transmitter and receiver

 图 7 单列像素元与高度对应关系 Fig.7 The altitude range for various CCD pixel numbers
 图 8 不同高度的距离分辨率 Fig.8 The resolution range for various altitudes

 图 9 亚稳态氦密度随高度变化曲线 Fig.9 Variation curve of metastable He densities with altitude
 图 10 接收光子数与高度对应关系 Fig.10 Simulated return counts with altitude

 ${N_{{\rm{S\_Ray}}}} = \frac{{{P_{\rm{L}}}\tau {\lambda _0}}}{{hc}} \cdot \frac{{{V_{{\rm{Ray}}}} \cdot {A_{\rm{R}}}}}{{{\rm{ \mathsf{ π} }}{{\left( {\tan \frac{{{\theta _{{\rm{L}}\_{\rm{Ray}}}}}}{2}} \right)}^2}{{\left( {\frac{{{z_{\rm{R}}}}}{{\sin {\beta _{{\rm{L}}\_{\rm{Ray}}}}}}} \right)}^2}{{\left( {\frac{{{z_{\rm{R}}}}}{{\sin {\beta _{{\rm{R}}\_{\rm{Ray}}}}}}} \right)}^2}}} \cdot \left( {{N_{{\rm{C}}\_{\rm{Ray}}}}{\sigma _{{\rm{Ray}}}}} \right) \cdot \eta T_{\rm{R}}^2 + {n_{\rm{B}}}\tau$ (15)

 $\frac{{{N_{\rm{S}}}(n) - {n_{\rm{B}}}\tau }}{{{N_{{\rm{S}}\_{\rm{Ray}}}} - {n_{\rm{B}}}\tau }} = {\left( {\frac{{\sin {\beta _{\rm{L}}}\sin {\beta _{\rm{R}}}\tan \frac{{{\theta _{{\rm{L}}\_{\rm{Ray}}}}}}{2}}}{{\sin {\beta _{{\rm{L}}\_{\rm{Ray}}}}\sin {\beta _{{\rm{R}}\_{\rm{Ray}}}}\tan \frac{{{\theta _{\rm{L}}}}}{2}}}} \right)^2}\frac{{V(n)z_{\rm{R}}^4}}{{{V_{{\rm{Ray}}}}z{{(n)}^4}}}\frac{{{N_{\rm{C}}}(n){\sigma _{{\rm{eff}}}}{R_{\rm{B}}}}}{{4{\rm{ \mathsf{ π} }}{N_{{\rm{C}}\_{\rm{Ray}}}}{\sigma _{{\rm{Ray}}}}}}\frac{{{T^2}E{{(z)}^2}}}{{T_{\rm{R}}^2}}$ (16)

 $\frac{{{N_{\rm{C}}}(n)}}{{{N_{{\rm{C}}\_{\rm{Ray}}}}}} = \frac{{{N_{\rm{S}}}(n) - {n_{\rm{B}}}\tau }}{{{N_{{\rm{S}}\_{\rm{Ray}}}} - {n_{\rm{B}}}\tau }} \cdot {\left( {\frac{{\sin {\beta _{{\rm{L}}\_{\rm{Ray}}}}\sin {\beta _{{\rm{R}}\_{\rm{Ray}}}}}}{{\sin {\beta _{\rm{L}}}\sin {\beta _{\rm{R}}}}}} \right)^2} \cdot \frac{{{V_{{\rm{Ray}}}}}}{{V(n)}} \cdot \frac{{z_{\rm{R}}^4}}{{z{{(n)}^4}}} \cdot \frac{{4{\rm{ \mathsf{ π} }}{\sigma _{{\rm{Ray}}}}}}{{{\sigma _{{\rm{eff}}}}{R_{\rm{B}}}}} \cdot \frac{1}{{E{{(z)}^2}}}$ (17)

 ${\left( {\frac{{\sin {\beta _{{\rm{L}}\_{\rm{Ray}}}}\sin {\beta _{{\rm{R}}\_{\rm{Ray}}}}}}{{\sin {\beta _{\rm{L}}}\sin {\beta _{\rm{R}}}}}} \right)^2} = {C_{\rm{R}}}$ (18)

 ${N_{\rm{C}}}\left( n \right) = {N_{{\rm{C}}\_{\rm{Ray}}}} \cdot \frac{{{N_{\rm{S}}}(n) - {n_{\rm{B}}}\tau }}{{{N_{{\rm{S}}\_{\rm{Ray}}}} - {n_{\rm{B}}}\tau }} \cdot \left[ {{C_{\rm{R}}} \cdot \frac{{{V_{{\rm{Ray}}}}}}{{V(n)}} \cdot \frac{{z_{\rm{R}}^4}}{{z{{(n)}^4}}}} \right] \cdot \frac{{4{\rm{ \mathsf{ π} }}{\sigma _{{\rm{Ray}}}}}}{{{\sigma _{{\rm{eff}}}}{R_{\rm{B}}}}} \cdot \frac{1}{{E{{(z)}^2}}}$ (19)

 $SNR(z) = \frac{{{N_{\rm{S}}}(z) - {n_{\rm{B}}} \cdot \tau }}{{\sqrt {{N_{\rm{S}}}(z)} }}$ (20)

 图 11 氦激光雷达系统接收信噪比随高度分布曲线 Fig.11 Variation curve of SNR with altitude

 图 12 三种光电探测器信噪比随高度变化对比曲线 Fig.12 Variation curve of SNR with altitude of the three photo detectors

 ${\sigma _{\rm{N}}} = \sqrt N$ (21)

 $\frac{{{\sigma _{\rm{N}}}}}{N} = \frac{{\sqrt {{N_{\rm{S}}}(z)} }}{{{N_{\rm{S}}}(z) - {n_{\rm{B}}} \cdot \tau }} = \frac{1}{{ SNR (z)}}$ (22)

 图 13 氦激光雷达系统密度相对误差随高度分布曲线 Fig.13 Relative error distribution curve of helium lidar system density with altitude
3 结论

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