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Optical System and Detection Range Analysis of Synthetic Aperture Ladar
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摘要: 该文对合成孔径激光雷达(Synthetic Aperture Ladar, SAL)光学系统和作用距离进行了分析。根据SAL成像特点，提出了SAL使用非成像衍射光学系统的概念，并引入相控阵模型对其性能进行分析。通过在压缩光路中馈源和主镜两处使用二元光学器件，在口径300 mm条件下将2°接收视场信号收入光纤，对所需的相位参数和对应的波束方向图进行了计算仿真。给出了SAL作用距离方程，分析了相干探测和信号积累增益，明确了SAL具有良好的微弱信号探测能力的结论。针对实际应用需求，给出了一个远距离高分辨率机载SAL系统参数和工作模式。5 cm分辨率时，在连续条带成像模式下，其作用距离可达5 km，幅宽可达1.5 km；在滑动聚束成像模式下，作用距离可达10 km，幅宽可达1 km。Abstract: Optical system and detection range of Synthetic Aperture Ladar (SAL) are analyzed. According to the imaging characteristics of SAL, the concept that SAL uses non-imaging diffractive optical system are proposed, meanwhile, the phased array model is introduced to analyze its performance. In the condition of using binary optical element on the feeder and primary mirror, the phaser parameters and beam pattern are presented using simulation. The signal of 2° view field is introduced into fiber with the 300 mm aperture telescope and compressed optical path. The radar detection range equation of SAL is introduced, coherent detection and signal accumulation gain are analyzed, the conclusion is SAL has good ability of detecting weak signal. Aiming at application requirement, system parameters and working modes of airborne SAL are given with high resolution and long detection range. With 5 cm resolution, the airborne SAL can achieve 5 km detection range with 1.5 km swath in strip-map imaging mode and 10 km detection range with 1 km swath in sliding spotlight imaging mode.
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图 2 SAL视场中目标信号方向，距离和时间关系
Figure 2. The relationship among object signal direction, range and time in the view field of SAL
图 4 基于相控阵的宽视场信号收入光纤示意图
Figure 4. Diagram of introducing wide view field signal into fiber based on phased array
图 5 1维纳米光波导阵+空间高阶相位形成器件的宽视场信号收入光纤示意图
Figure 5. Diagram of introducing wide view field signal into fiber based on nanophotonic waveguide array and space higher-order phaser
图 6 光纤准直器+空间高阶相位形成器件的宽视场信号收入光纤示意图
Figure 6. Diagram of introducing wide view field signal into fiber based on fiber collimator and space higher-order phaser
图 7 理想2阶相位和对应的波束方向图展宽情况
Figure 7. Desired second-order phase and the related broading beam pattern
图 8 8值化2阶相位和对应的波束方向图展宽情况
Figure 8. Second-order phase with 8 quantization bits and the related broading beam pattern
图 9 16值化2阶相位和对应的波束方向图展宽情况
Figure 9. Second-order phase with 16 quantization bits and the related broading beam pattern
图 10 SAL主镜和宽视场馈源都采用二元光学器件的衍射光学系统示意图
Figure 10. Diagram of diffractive optical system in which the binary optical element is used both on the feeder and primary mirror
图 11 衍射主镜需形成的移相量、折叠相位曲线和波束方向图
Figure 11. The phase, folded phase and beam pattern of the diffractive primary mirror
图 12 8值化主镜相位和波束方向图
Figure 12. The primary mirror phase with 8 quantization bits and the related beam pattern
图 13 机载SAL扫描方式(通过扫描将距离向观测幅宽扩大2倍示意图)
Figure 13. Scanning model of airborne SAL (Double the swath through scanning)
图 14 机载SAL条带成像模式扫描顺序和对应的波束覆盖范围示意图
Figure 14. Scanning order of airborne SAL strip-map imaging model and related beam scope
表 1 机载SAL条带成像模式扫描参数
Table 1. Scanning parameters of airborne SAL with strip-map imaging model
序号 雷达位置 扫描时间(s) 顺轨扫描范围(°) 顺轨扫描角速度(°/s) 交轨扫描范围(°) 交轨扫描角速度(°/s) 1 
0 $ \to $1 $0\to 2.7\to - 0.6$ 6.0 $ - 5\to - 3$ 2 2 1 $ \to $2 $ - 0.6\to 1.5\to - 1.2$ 4.8 $ - 3\to - 1$ 2 3 2 $ \to $3 $ - 1.2\to 0.3\to - 1.8$ 3.6 $ - 1\to 1$ 2 4 3 $ \to $4 $ - 1.8\to - 0.9\to - 2.4$ 2.4 $1\to 3$ 2 5 4 $ \to $6 $ - 2.4\to - 2.1\to 2.6$ 2.5 $3\to 5\to 3$ 2 6 6 $ \to $7 $2.6\to - 2.7\to 1.8$ 9.8 $3\to 1$ 2 7 7 $ \to $8 $1.8\to - 2.7\to 1.2$ 8.4 $1\to - 1$ 2 8 8 $ \to $9 $1.2\to - 2.7\to 0.6$ 6.8 $ - 1\to - 3$ 2 9 9 $ \to $10 $0.6\to - 2.7\to 0$ 6.0 $ - 3\to - 5$ 2 
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表 2 作用距离5 km机载SAL系统参数
Table 2. System parameters of airborne SAL with 5 km detection range
参数 数值 参数 数值 飞行高度 $H$(km) 2.5 飞行速度 $v$(m/s) 50 平均入射角 $\theta $(°) 60 脉冲重复频率(kHz) 50 顺轨/交轨波束宽度 ${\theta _{\rm{a}}}$, ${\theta _{\rm{c}}}$(mrad) 0.3, 35.0 目标散射系数 ${\sigma _0}$ 0.1 地距向瞬时幅宽 $\Delta R$(m) 350 距离/方位分辨率 ${\rho _{\rm{r}}}$, ${\rho _{\rm{a}}}$(m) 0.05, 0.05 顺轨/交轨扫描范围 $\Delta {\theta _{\rm{c}}}$, $\Delta {\theta _{\rm{a}}}$(°) $ \pm 3$, $ \pm 5$ 双程大气损耗 ${\eta _{{\rm{ato}}}}$ 0.4 最近/最远斜距 $R$(km) 4.35, 5.92 接收望远镜口径 $D$(mm) 300 顺轨/交轨扫描角速度大小 ${\omega _{\rm{a}}}$, ${\omega _{\rm{c}}}$ 如表1所示 发射光学系统损耗 ${\eta _{\rm{t}}}$ 0.9 顺轨/交轨扫描周期 ${T_{\rm{a}}}$, ${T_{\rm{c}}}$ 如表1所示 接收光学系统损耗 ${\eta _{\rm{r}}}$ 0.8 地距向扫描幅宽(km) 1.5 匹配损耗 ${\eta _{\rm{m}}}$ 0.5 激光波长 $\lambda $(μm) 1.55 其他光学损耗 ${\eta _{{\rm{oth}}}}$ 0.8 发射峰值功率 ${P_{\rm{t}}}$(W) 400 量子效率 ${\eta _{\rm{D}}}$ 0.5 脉冲宽度 ${T_{\rm{p}}}$(μs) 5 电子学系统损耗 ${\eta _{{\rm{ele}}}}$ 0.5 信号带宽 ${B_{\rm{r}}}$(GHz) 4 电子学噪声系数 ${F_{\rm{n}}}$(dB) 3 目标后向散射立体角 $\varOmega $ ${\rm{{{π}} }}$ 图像信噪比 ${{\rm SNR}_{\min }}$(条带模式)(dB) 10.3
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表 3 作用距离10 km机载SAL系统参数
Table 3. System parameters of airborne SAL with 10 km detection range
参数 数值 参数 数值 飞行高度 $H$(km) 3.3 目标散射系数 ${\sigma _0}$ 0.1 入射角(°) 70 距离/方位分辨率 ${\rho _{\rm{r}}}$, ${\rho _{\rm{a}}}$(m) 0.05, 0.05 顺轨/交轨波束宽度 ${\theta _{\rm{a}}}$, ${\theta _{\rm{c}}}$(mrad) 0.3, 35.0 双程大气损耗 ${\eta _{{\rm{ato}}}}$ 0.25 最近/最远斜距 $R$(km) 9.21, 10.13 接收望远镜口径 $D$(mm) 300 地距向瞬时幅宽(km) 1 发射光学系统损耗 ${\eta _{\rm{t}}}$ 0.9 飞行速度 $v$(m/s) 50 接收光学系统损耗 ${\eta _{\rm{r}}}$ 0.8 激光波长 $\lambda $(μm) 1.55 匹配损耗 ${\eta _{\rm{m}}}$ 0.5 发射峰值功率 ${P_{\rm{t}}}$(W) 400 其他光学损耗 ${\eta _{{\rm{oth}}}}$ 0.8 脉冲宽度 ${T_{\rm{p}}}$(μs) 5 量子效率 ${\eta _{\rm{D}}}$ 0.5 脉冲重复频率(kHz) 50 电子学系统损耗 ${\eta _{{\rm{ele}}}}$ 0.5 信号带宽 ${B_{\rm{r}}}$(GHz) 4 电子学噪声系数 ${F_{\rm{n}}}$(dB) 3 目标后向散射立体角 $\varOmega $ ${\rm{{{π}} }}$ 图像信噪比 ${{\rm SNR}_{\min }}$(滑动聚束模式)(dB) 10
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