基于Walsh函数调制的单帧图像深度学习相位反演技术

刘奇; 杜应磊; 向汝建; 李国会; 张秋实; 向振佼; 吴晶; 岳献; 包安超; 游疆

doi:10.11884/HPLPB202436.240048

基于Walsh函数调制的单帧图像深度学习相位反演技术

doi: 10.11884/HPLPB202436.240048

刘奇^{1, 2,},
杜应磊^1, ,,
向汝建¹,
李国会¹,
张秋实¹,
向振佼¹,
吴晶¹,
岳献¹,
包安超¹,
游疆^{1, 2}

1.
中国工程物理研究院应用电子学研究所，四川绵阳 621900
2.
中国工程物理研究院研究生院，北京 100088

详细信息

作者简介:
刘　奇，liuqi21@gscaep.ac.cn

通讯作者:
杜应磊，boyduyibglei@163.com。

中图分类号: O439
计量
- 文章访问数: 18
- HTML全文浏览量: 10
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2024-02-01
- 修回日期: 2024-03-28
- 录用日期: 2024-03-06
- 网络出版日期: 2024-04-15

Deep learning phase inversion technique for single frame image based on Walsh function modulation

Liu Qi^{1, 2
,},
Du Yinglei^{1
, ,},
Xiang Rujian¹,
Li Guohui¹,
Zhang Qiushi¹,
Xiang Zhenjiao¹,
Wu Jing¹,
Yue Xian¹,
Bao Anchao¹,
You Jiang^{1, 2}

1.
Institute of Applied Electronics, CAEP, Mianyang 621900, China
2.
Graduate School of China Academy of Engineering Physics, Beijing 100088, China

摘要

摘要: 远场波前反演存在简并态，复原波前容易出现多解问题。相较于传统的迭代算法，结合了相位调制与深度学习的相位反演方法不仅显著降低了计算复杂度，还可有效地解决多解问题。这种方法实时性强，结构简洁，显示出其独特的优势。使用不同的沃尔什函数（Walsh）对相位进行调制，采取深度学习的方法训练卷积神经网络从调制后单帧远场强度图中获得4～30阶Zernike系数从而复原出原始波前，解决了相位反演多解问题。对于3～15 cm大气相干长度的湍流像差的残差波前，其RMS与原始波前RMS的比值可达7.8%。深入研究了Zernike阶数、随机噪声、遮挡以及强度图分辨率等多种因素对波前复原精度的影响。研究结果表明，这种基于深度学习的相位反演方法在复杂的环境中展现出了良好的鲁棒性。
- 相位反演 /
- 泽尼克系数 /
- 相位调制 /
- 深度学习 /
- 沃尔什函数
Abstract: The far-field wavefront inversion exhibits degeneracy states, leading to the problem of encountering multiple solutions when recovering the wavefront. In comparison to traditional iterative algorithms, the combination of phase modulation and deep learning in the phase inversion method not only significantly reduces computational complexity but also effectively solves multi-solution problems. This method possesses strong real-time capabilities and a simple structure, showcasing its unique advantages. In this paper, different Walsh functions are used to modulate the phase, and a deep learning approach is taken to train a convolutional neural network to obtain the 4th-30th order Zernike coefficients from the modulated single-frame far-field intensity maps so as to recover the original wavefront, which solves the problem of multiple solutions of phase inversion. For the residual wavefront of the turbulent aberration of 3-15 cm atmospheric coherence length, the ratio of its RMS to the RMS of the original wavefront can reach 7.8%. In addition, this paper also deeply investigates the effects of various factors such as Zernike order, random noise, occlusion, and intensity map resolution on the wavefront recovery accuracy. The results show that this deep learning-based phase inversion method exhibits good robustness in complex environments.
- Phase inversion /
- Zernike coefficient /
- Phase modulation /
- Deep learning /
- Walsh function

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图 1 Walsh 函数的二维极坐标表示

Figure 1. Two-dimensional polar representation of Walsh function

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图 2 正、负离焦像差使用部分Walsh函数调制后的波前和远场光强图

Figure 2. Wavefront and far field intensity plots for positive and negative defocusing aberrations after modulation using partial Walsh functions

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图 3 网络残差单元

Figure 3. NetWork ResNetidual unit

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图 4 实验流程图

Figure 4. Experimental flowchart

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图 5 单帧预测平均耗时

Figure 5. Predicted average time per frame

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图 6 训练损失变化曲线

Figure 6. Train loss curve

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图 7 PV 、RMS、RMS比值散点图

Figure 7. PV 、RMS、RMS ratio scatter plot

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图 8 原始波前复原效果

Figure 8. Original wavefront restoration results

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图 9 旋转180°复共轭波前复原效果

Figure 9. Rotated 180° complex conjugate wavefront restoration results

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图 10 设置遮掩模板例子

Figure 10. Example image of setting a masking template

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图 11 随机噪声样本图

Figure 11. Random noise sample image

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表 1 不同Walsh函数调制样本训练网络测试结果对比

Table 1. Comparison of test results of different Walsh function modulated sample training networks

Walsh function	ResNet18 RMSE/μm	ResNet34 RMSE/μm	ResNet50 RMSE/μm	ResNet101 RMSE/μm
W12	0.0115	0.0105	0.0080	0.0069
W15	0.0111	0.0092	0.0062	0.0067
W3	0.0103	0.0087	0.0055	0.0054

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表 2 不同Zernike阶数波前的RMS比值平均值

Table 2. Average RMS ratio with Zernike order wavefront

different Zernike levels	average RMS ratio/%
Zernike4～10	9.6
Zernike4～15	8.6
Zernike4～20	8.5
Zernike4～25	8.4
Zernike4～30	7.8

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表 3 不同像素远场强度图的RMS比值平均值

Table 3. Average RMS ratio of far-field intensity map with different pixels

intensity image pixels	average RMS ratio/%
256×256	7.8
512×512	10.2
1024×1024	12.9

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表 4 噪声样本在不同模型下的RMS比值平均值

Table 4. Average RMS ratio of noise samples under different models

test data set	samples for training purposes	average RMS ratio of residual wavefront to original wavefront/%
256×256 with random noise samples	350 000 normal sample	invalid
256×256 with random noise samples	350 000 normal sample+ 35 W noise sample	6.5

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