Research on the method for improving the performance of differential wavefront sensing based on adaptive optics technology
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摘要:
空间引力波探测计划拟在太空中使用3颗卫星建立等边三角形的星座结构，通过激光外差干涉的方法实现中低频段引力波信号的探测。激光捕获跟瞄技术用于实现卫星间光束的高精度对准,实现三条双向激光链路的构建。差分波前传感（DWS）技术是激光跟瞄阶段的核心，是实现纳弧度级角度分辨的关键。为充分验证激光捕获跟瞄系统的在轨可行性，需对原理样机开展地面长距离验证实验。然而光束在大气中的传输会严重影响DWS技术的角度测量能力，亟需寻求干扰的抑制方案。为此本文首先通过数值仿真的手段，系统分析了大气对DWS的影响，首次提出引入自适应光学技术补偿大气对DWS信号的干扰，之后设计并搭建了基于DWS信号及波前测量的双控制回路激光跟瞄实验系统。引入了像差扰动开展实验，实验结果表明，在0.1 Hz−1 Hz频段，同频段性能可提升约10倍，充分说明了自适应光学系统可以有效提高DWS在大气环境下的测量能力，为后续的激光捕获跟瞄系统长距离大气环境地面验证奠定了基础。
Abstract:The Space Gravitational Wave detection program intends to use three satellites in space to establish an equilateral triangle constellation structure, and realize the detection of gravitational wave signals in the middle and low frequency bands by laser heterodyne interference. Laser capture and pointing technology is used to achieve high-precision alignment of beams between satellites, and the construction of three bidirectional laser links is realized. Differential wavefront sensing (DWS) technology is the core of laser tracking and pointing stage, and it is the key to achieve nanoradian Angle resolution. In order to fully verify the on-orbit feasibility of the laser capture and tracking system, it is necessary to carry out long-distance ground verification experiments on the principle prototype. However, the transmission of light in the atmosphere will seriously affect the Angle measurement ability of DWS technology, and it is urgent to find a scheme to suppress the interference. Therefore, this paper systematically analyzes the influence of atmosphere on DWS by means of numerical simulation, and proposes the introduction of adaptive optics technology to compensate the interference of atmosphere on DWS signal for the first time. Then, a laser tracking and pointing experimental system with dual control loops based on DWS signal and wavefront measurement is designed and built. The experimental results show that in the 0.1 Hz−1 Hz frequency band, the performance of the same frequency band can be improved by about 10 times, which fully demonstrates that the adaptive optics system can effectively improve the measurement ability of DWS in the atmospheric environment, laying a foundation for the subsequent long-distance ground verification of laser capture and pointing system in atmospheric environment.
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图 3 Shack-Hartmann波前传感器原理图
Figure 3. Schematic diagram of Shack-Hartmann wavefront sensor
图 4 测角误差与像差系数的关系
Figure 4. Relationship between angular error and aberration coefficient
图 9 yaw方向相角转化系数标定
Figure 9. Calibration of yaw direction phase Angle conversion coefficient
图 10 pitch方向相角转化系数标定
Figure 10. Calibration of pitch direction phase Angle conversion coefficient
图 16 无干扰内环频谱对比图
Figure 16. Comparison of spectrum in the inner loop without interference
图 17 无干扰外环频谱对比图
Figure 17. Comparison of spectrum of the outer loop without interference
表 1 Zernike多项式的前15项
Table 1. The first 15 terms of Zernike polynomials
j n m Zj(ρ,θ) 1 0 0 1 2 1 1 $ 2\rho \text{cos}\theta $ 3 1 1 $ 2\rho \text{sin}\theta $ 4 2 0 $ \sqrt{3}(2{\rho }^{2}-1) $ 5 2 2 $ \sqrt{6}{\rho }^{2}\sin 2\theta $ 6 2 2 $ \sqrt{6}{\rho }^{2}\cos 2\theta $ 7 3 1 $ \sqrt{8}(3{\rho }^{3}-2\rho )\text{sin}\theta $ 8 3 1 $ \sqrt{8}(3{\rho }^{3}-2\rho )\text{cos}\theta $ 9 3 3 $ \sqrt{8}{\rho }^{3}\sin 3\theta $ 10 3 3 $ \sqrt{8}{\rho }^{3}\cos 3\theta $ 11 4 0 $ \sqrt{5}(6{\rho }^{4}-6{\rho }^{2}+1) $ 12 4 2 $ \sqrt{10}(4{\rho }^{4}-3{\rho }^{2})\cos 2\theta $ 13 4 2 $ \sqrt{10}(4{\rho }^{4}-3{\rho }^{2})\sin 2\theta $ 14 4 4 $ \sqrt{10}{\rho }^{4}\cos 4\theta $ 15 4 4 $ \sqrt{10}{\rho }^{4}\sin 4\theta $ 
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表 2 实验系统基本参数
Table 2. Table of key parameters of the experimental system
参数 数值 激光波长(λ) 1064 nm测量光扩束倍数 3 扩束后光斑大小 7.8 mm 光阑大小 5 mm WFS光斑大小 3.3 mm QPD光斑大小 1.5 mm DM光斑大小 10 mm
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表 3 哈特曼波前传感器基本参数
Table 3. Hartmann wavefront sensor parameter
参数 数值 RMS值（波前敏感性） l/100 rms @ 633 nm 子孔径数目 47×35 CCD的分辨率 1440 ×1080 Pixels像元尺寸 5.0 µm×5.0 µm 通光孔径 9 mm 每个微透镜对应的子孔径大小 7.20 mm×5.40 mm 微透镜阵列间距 150 µm 微透镜阵列焦距 5.6 mm 微透镜阵列的几何形状 圆形 最高采样率 880 fps
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表 4 变形镜基本参数
Table 4. Deformable mirror parameters
参数 数值 口径大小及形状 圆形，直径为14 mm 镜面分段数 一共40个，24个在瞳孔内，16个在瞳孔外 镜面涂层 银 驱动电压 0~300 V 平均反射率
450 nm - 2 µm
2 - 20 µm
>97.5%
>96.0%相对于参考球面初始均方值 200 nm 初始主要畸变 直径为18 mm的凹球面 最大冲程 24.5 µm
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表 5 快速反射镜基本参数
Table 5. Basic parameters of the fast mirror
参数 数值 角度变化范围 2 mrad 分辨率 0.05 μrad 重复精度（10%偏摆角） 0.15 μrad 重复精度（100%偏摆角） 1.5 μrad
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