基于主成分分析法的大气湍流相位畸变表征和还原影响因素分析

王姜菩真; 王志强; 张京会; 乔春红; 范承玉

doi:10.37188/CO.EN-2024-0035

基于主成分分析法的大气湍流相位畸变表征和还原影响因素分析

王姜菩真^{1, 2, 3,},
王志强^{1, 3, ,},
张京会^{1, 4},
乔春红^{1, 4},
范承玉^{1, 3, ,}

1.
中国科学院合肥物质科学研究院安徽光学精密机械研究所中国科学院大气光学重点实验室, 安徽合肥 230031
2.
中国科学技术大学研究生院科学岛分院, 安徽合肥 230026
3.
南湖之光实验室, 中国人民解放军国防科技大学, 湖南长沙 410073
4.
金宝搏188软件怎么用与物质相互作用全国重点实验室, 中国科学院合肥物质科学研究院安徽光学精密机械研究所, 安徽合肥 230031

详细信息

中图分类号: TP394.1;TH691.9
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出版历程
- 收稿日期: 2024-11-14
- 修回日期: 2024-12-11
- 录用日期: 2025-01-06
- 网络出版日期: 2025-01-21

Influencing factor of the characterization and restoration of phase aberrations resulting from atmospheric turbulence based on Principal Component Analysis

doi: 10.37188/CO.EN-2024-0035

WANG Jiang-pu-zhen^{1, 2, 3
,},
WANG Zhi-qiang^{1, 3
, ,},
ZHANG Jing-hui^{1, 4},
QIAO Chun-hong^{1, 4},
FAN Cheng-yu^{1, 3
, ,}

1.
Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
2.
Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, China
3.
Nanhu Laser Laboratory, National University of Defense Technology, Changsha 410073, China
4.
State Key Laboratory of Laser Interaction with Matter, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China

Funds: Supported by the National Natural Science Foundation of China (No. 12273084); Science and Technology Innovation Fund for Key Laboratories of the Chinese Academy of Sciences (No. CXJJ-225028)

More Information

Author Bio:
WANG Jiang-pu-zhen (1998—), female, born in Jinan, Shandong Province, currently, as a doctoral candidate at University of Science and Technology of China (USTC). Her research interests are on the correction of phase aberrations resulting from atmospheric turbulence. E-mail: puzhen98@mail.ustc.edu.cn

WANG Zhi-qiang (1990—), male, born in Bo-zhou, Anhui Province, PH.D, Associate Research Professor, he received his Ph.D from University of Science and Technology of China (USTC) in 2018, he mainly engaged in the field of laser beam propagation through random media and computational imaging. E-mail: zqwang@aiofm.ac.cn

FAN Cheng-yu (1965—), male, Ph.D., he is a researcher and doctoral supervisor at the Hefei Institutes of Physical Science, University of Science and Technology of China (USTC). His research primarily focuses on theoretical and experimental studies of atmospheric propagation of continuous and pulsed lasers, as well as investigations into the strong turbulence effects on laser propagation through the atmosphere. E-mail: cyfan@aiofm.ac.cn

Corresponding author: zqwang@aiofm.ac.cn; cyfan@aiofm.ac.cn

摘要

摘要:
为了有效表征、还原大气湍流造成的相位畸变，解决传统Zernike多项式方法引起的相位还原高频信息不足问题，提出了基于主成分分析法的畸变相位特征表征、还原方法，对可能影响主成分精度从而影响还原效果的因素进行研究。首先建立了几组包含满足Von-Karman功率谱畸变相位的原始数据集，并生成了D/r₀采样间隔分别为1和10的样本空间。接着，建立了不同湍流强度下畸变相位的测试集数据。之后从不同原始数据集中提取对应的主成分，并分别使用相同项数的主成分与Zernike多项式对同一组测试集畸变相位进行还原。最终对比还原结果，分析原始数据样本量和D/r₀采样间隔对主成分精度的影响。实验结果表明：更大的D/r₀采样间隔可以在原始数据量有限的情况下保证主成分的泛化能力和鲁棒性，从而在实际应用中快速实现模型的高精度部署；在测试集D/r₀=24的相对湍流较强的环境下，使用34阶主成分可以将校正后光斑Strehl比从原始的0.007提升至0.1585，而同样使用34阶Zernike还原后的光斑Strehl比仅为0.0215，几乎没有校正效果。可以看出基于主成分分析法的大气湍流相位畸变表征和还原方法优于Zernike多项式法，可以为基于模型和深度学习的自适应光学校正提供参考。
- 相位畸变 /
- 大气湍流 /
- 主成分分析法 /
- Zernike多项式
Abstract:
Restoration of phase aberrations is crucial for addressing atmospheric turbulence in light propagation. Traditional restoration algorithms based on Zernike polynomials (ZPs) often encounter challenges related to high computational complexity and insufficient capture of high-frequency phase aberration components, so we proposed a Principal-Component-Analysis-based method for representing phase aberrations. This paper discusses the factors influencing the accuracy of restoration, mainly including the sample space size and the sampling interval of D/r₀, on the basis of characterizing phase aberrations by Principal Components (PCs). The experimental results show that a larger D/r₀ sampling interval can ensure the generalization ability and robustness of the principal components in the case of a limited amount of original data, which can help to achieve high-precision deployment of the model in practical applications quickly. In the environment with relatively strong turbulence in the test set of D/r₀= 24, the use of 34 terms of PCs can improve the corrected Strehl ratio (SR) from 0.007 to 0.1585, while the Strehl ratio of the light spot after restoration using 34 terms of ZPs is only 0.0215, demonstrating almost no correction effect. The results indicate that PCs can serve as a better alternative in representing and restoring the characteristics of atmospheric turbulence induced phase aberrations. These findings pave the way to use PCs of phase aberrations with fewer terms than traditional ZPs to achieve data dimensionality reduction, and offer a reference to accelerate and stabilize the model and deep learning based adaptive optics correction.
- phase aberration /
- atmospheric turbulence /
- principal component analysis /
- Zernike polynomials

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Figure 1. Examples of restoration of phase aberration by ZPs vs PCs obtained from different sample space sizes under the same turbulence strength. (a) $D/{r_0} = 8 ,$using the first 8 terms; (b) $D/{r_0} = 16 ,$ using the first 19 terms; (c) $D/{r_0} = 24 ,$using the first 34 terms

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Figure 2. Examples of restoration by 8, 19, and 34 PCs. (a) $D/{r_0} = 8$; (b) $D/{r_0} = 16$; (c) $D/{r_0} = 24$

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Figure 3. Mean SR after phase aberration restoration by ZPs vs PCs obtained from different sizes of sample spaces under different turbulence scenarios

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Figure 4. Comparison of the mean Strehl ratio after phase aberration restoration by PCs obtained from A-5000 and B-5000

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Figure 5. Examples of restoration of phase aberrations by the equivalent terms of ZPs vs PCs obtained from B-5000. (a) $D/{r_0} = 8 ,$ using the first 8 terms; (b) $D/{r_0} = 16 ,$ using the first 19 terms; (c) $D/{r_0} = 24 ,$ using the first 34 terms

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Table 1. Comparison of the mean Strehl ratio after phase restoration by PCs obtained from B-5000 and A-30000 (The first row 4-28 indicates the $D/{r_0}$ of test sets)

Terms	D/r₀
Terms	N	4	8	12	16	20	24	28
8	5000	0.719	0.3563	0.1437	0.0515	0.0177	0.0072	0.0046
8	30000	0.7204	0.3577	0.1439	0.0521	0.0176	0.0073	0.0047
19	5000	0.8496	0.5989	0.368	0.204	0.103	0.0482	0.0235
19	30000	0.8505	0.6011	0.3702	0.2049	0.1041	0.0488	0.024
34	5000	0.9101	0.7412	0.5547	0.3925	0.2582	0.1616	0.0978
34	30000	0.9108	0.7436	0.5582	0.3978	0.2636	0.1644	0.1002

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