Deep learning phase inversion technique for single frame image based on Walsh function modulation
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摘要: 远场相位反演存在简并态,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第4~30项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。Abstract: The far-field phase 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 environment.
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Key words:
- phase inversion /
- Zernike coefficient /
- phase modulation /
- deep learning /
- Walsh function
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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 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
Zernike levels average RMS ratio/% Zernike 4~10 9.6 Zernike 4~15 8.6 Zernike 4~20 8.5 Zernike 4~25 8.4 Zernike 4~30 7.8 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 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 samples invalid 256×256 with random noise samples 350 000 normal samples+ 350 000 noise samples 6.5 -
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