Measurement of atmospheric coherence length for extended targets based on wavefront structure function
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摘要:
为测量大气相干长度这一表征大气湍流对自由空间光通信链路性能影响的重要指标，本文提出了一种将扩展目标作为信息源的新策略，即结合波前结构函数法与扩展目标偏移量算法直接对大气相干长度进行估计。现有的差分像运动监测器等方法通常依赖于导星目标，但在水平通信链路中难以设置合适的导星目标，其实际应用效果受到显著限制。因此，将扩展目标作为直接测量的信息源，为大气相干长度测量提供了一种可行的解决方案。本文首先回顾了现有主流算法的原理及研究现状，分析了现有算法对导星目标的依赖性及其在水平链路应用中的局限性。在此基础上，提出一种将改进归一化互相关算法与波前结构函数法相结合的测量方案，用于扩展目标场景估计大气相干长度。与传统测量方法相比，该方法能够在水平链路基于扩展目标条件下有效开展测量，同时显著减少了系统的复杂度和设备成本。为验证所提方法的有效性与测量精度，本文设计开展了仿真与实验研究。结果表明，该方法测得的相干长度值与差分像运动监测器法及波前相位方差法高度一致，测量精度误差约为4%。这一结果证明了该方法在大气相干长度评估中的有效性，可为提升自由空间激光通信的可靠性提供有效参考。
Abstract:To measure the atmospheric coherence length, an important parameter that characterizes the impact of atmospheric turbulence on the performance of free-space optical communication links, we propose a novel strategy for measuring atmospheric coherence length by taking extended targets as the information source. Specifically, the method integrates the wavefront structure function approach with the extended target offset algorithm to directly estimate the atmospheric coherence length. Traditional methods, such as the Differential Image Motion Monitor (DIMM), typically rely on guide star targets, which are difficult to set appropriately in horizontal communication links, thereby limiting their effectiveness in practical applications. In contrast, employing extended targets as direct detection targets provides a feasible solution for measuring atmospheric coherence length. The paper first reviews the principles and current research status of mainstream algorithms, emphasizing the reliance of existing algorithms on guide star targets and their limitations in horizontal links. Subsequently, we propose a new measurement scheme that combines the improved normalized cross-correlation algorithm with the wavefront structure function method to estimate atmospheric coherence length under extended targets scenarios. In comparison to traditional measurement methods, our approach can realizes coherence length measurement based on extended targets in horizontal links, thereby significantly reducing system complexity and equipment costs. To validate the effectiveness and measurement accuracy of the proposed method, both simulations and experiments were designed and conducted. The results demonstrate that the coherence length values measured by this method are highly consistent with those obtained using the DIMM method and the wavefront phase variance method, with a measurement accuracy error of approximately 4%. This indicates that the proposed method can effectively assess atmospheric coherence length, thereby providing a valuable reference for enhancing the reliability of free-space laser communication systems.
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图 1 DIMM测量大气相干长度原理图
Figure 1. Schematic diagram of the principle of atmospheric coherence length measurement with DIMM
图 2 模拟湍流屏实验结果。(a)不同r0下SU算法生成的湍流相位屏；(b)不同强度湍流相位屏对应的远场衍射图案
Figure 2. Experimental result of simulated turbulence screens. (a) Turbulence phase screens generated by the SU algorithm under different r0; (b) far-field diffraction patterns corresponding to phase screens with different turbulence intensities
图 3 仿真湍流精确验证及实验结果。(a)湍流相位屏平均结构函数与理论期望值以及两者RMSE；(b)前20阶Zernike系数方差统计分布的时域统计值与理论值
Figure 3. Experimental results of accuracy validation of simulated turbulence screens. (a) The average structure function of the turbulent phase screen compared to the theoretical expected value (left), as well as the RMSE between them (right); (b) the temporal statistical values and theoretical values of variances distribution of the first 20 orders of Zernike coefficients
图 5 相干长度仿真结果。(a)加入湍流前后的SHWFS子孔径阵列图像（x1和x2为用于计算的子孔径）；(b)不同湍流条件下，每200帧波前结构函数测得的r0曲线；(c)加入不同标准差的高斯噪声后的r0曲线
Figure 5. Coherence length simulation results. (a) Sub-aperture array images of the SHWFS before and after the introduction of turbulence (x1 and x2 represent the sub-apertures used for calculation); (b) curves of r0 measured form the wavefront structure functions every 200 frames under different turbulence conditions; (c) r0 curve with added Gaussian noise of different standard deviations
图 6 实验光路设计图及实际光路图
Figure 6. Schematic diagram of the experimental optical path and the actual optical path
图 7 不同尺寸下点源场景和扩展场景测得D/r0值
Figure 7. Measured D/r0 values for point source and extended scene under different pitches
图 8 三种方法测得相干长度结果对比
Figure 8. Comparison of coherence length results measured by the three methods
表 1 符合Kolmogorov理论的畸变波前各阶Zernike系数方差
Table 1. Variance of Zernike coefficients for each orders of distorted wavefront conforming to Kolmogorov theory
阶数 方差(rad2) 阶数 方差(rad2) 1 0.4479 (D/r0)5/36 0.0061 (D/r0)5/32 0.4480 (D/r0)5/37 0.0062 (D/r0)5/33 0.0230 (D/r0)5/38 0.0062 (D/r0)5/34 0.0230 (D/r0)5/39 0.0062 (D/r0)5/35 0.0232 (D/r0)5/310 0.0024 (D/r0)5/3
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