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To determine the centroid of far-field laser beam spot with high precision and accuracy under intense noise contamination, a positioning algorithm named centroid-PINN is proposed, which is based on physical information neural network. A U-Net neural network is utilized to optimize the centroid estimation error. In order to demonstrate this new method, Gaussian spots polluted by two kinds of noises, i.e. ramp noise and white noise, are generated by simulation to train the neural network. The neural network is tested by two kinds of spots, i.e. Gaussian spot and Sinc-like spot. Both are predicted with high accuracy. Compared with traditional centroid method, the centroid-PINN needs no parameter tuning, especially can cope with ramp noise interference with high accuracy. This work will be conducive to developing the far-field laser beam spot measurement device, and can also serve as a reference for developing the Shack-Hartmann wavefront sensor.
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Keywords:
- measurement /
- centroid computation /
- neural network /
- adaptive optics
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图 1 网络结构
Figure 1. Network architecture.
图 2 训练过程中损失函数变化情况
Figure 2. Loss in training process
图 3 高斯光斑典型结果 (a)典型光斑, 第一行为输入光斑, 第二行为原始的无噪声光斑, 第三行为预测光斑; (b)质心误差
Figure 3. Typical results of gauss spots: (a) Typical spots, first row is input spots, second row is true spot, third row is predicted spot; (b) centroid estimation error.
图 4 类Sinc光斑计算结果 (a)典型光斑, 第一行为输入光斑, 第二行为原始光斑, 第三行为网络输出光斑; (b)质心误差
Figure 4. Typical results of sinc-like spots: (a) Typical spots, first row is input spots, second row is true spot, third row is predicted spot; (b) centroid estimation error.
图 5 不同强度噪声对质心计算的影响 (a)白噪声; (b)斜坡噪声
Figure 5. Influence of noise intensity on centroid computation: (a) White noise; (b) ramp noise.
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[1] Booth M J 2014 Light Sci. Appl. 3 165
Google Scholar
[2] Ji N 2017 Nat. Methods 14 374
Google Scholar
[3] 冯国斌 2014 博士学位论文 (西安: 西安电子科技大学)
Feng G B 2014 Ph. D. Dissertation (Xi’an: Xidian University) (in Chinese)
[4] Andrews L C, Phillips R L 2005 Laser Beam Propagation Through Random Media (Bellingham, Wash: SPIE Press) p4
[5] Ma X, Rao C, Zheng H 2009 Opt. Express 17 8525
Google Scholar
[6] 李自强, 李新阳, 高泽宇, 贾启旺 2021 强激光与粒子束 33 081001
Google Scholar
Li Z Q, Li X Y, Gao Z Y, Jia Q W 2021 High Power Laser Particle Beams 33 081001
Google Scholar
[7] Guo Y, Zhong L, Min L, Wang J, Wu Y, Chen K, Wei K, Rao C 2020 OEA 5 200082
[8] Thomas S, Fusco T, Tokovinin A, Nicolle M, Michau V, Rousset G 2006 Mon. Not. R. Astron. Soc. 371 323
Google Scholar
[9] Lardière O, Conan R, Clare R, Bradley C, Hubin N 2010 Proc. SPIE 7736 773627
Google Scholar
[10] Akondi V, Steven S, Dubra A 2019 Opt. Lett. 44 4167
Google Scholar
[11] Xu L, Wang J, Yao K, Yang L 2021 Opt. Lett. 46 4196
Google Scholar
[12] Gilles L, Ellerbroek B L 2008 Opt. Lett. 33 1159
Google Scholar
[13] Leroux C, Dainty C 2010 Opt. Express 18 1197
Google Scholar
[14] Vyas A, Roopashree M B, Prasad B R 2010 IJCA 1 32
[15] Vargas J, Restrepo R, Estrada J C, Sorzano C O S, Du Y Z, Carazo J M 2012 Appl. Opt. 51 7362
Google Scholar
[16] Ding W, Gong D, Zhang Y, He Y 2014 International Conference on Intelligent Computing and Signal Processing Hangzhou, China, Oct. 19–23, 2014 p774
[17] 李晶, 巩岩, 呼新荣, 李春才 2014 中国激光 41 0316002
Google Scholar
Li J, Gong Y, Hu X R, Li C C 2014 Chin. J. Laser 41 0316002
Google Scholar
[18] 张艳艳, 郝晓龙, 陈洁伟 2015 光学技术 41 59
Google Scholar
Zhang Y Y, Hao X L, Chen J W 2015 Opt. Techn. 41 59
Google Scholar
[19] Kong F, Polo M C, Lambert A 2017 Appl. Opt. 56 6466
Google Scholar
[20] LeCun Y, Bengio Y, Hinton G 2015 Nature 521 436
Google Scholar
[21] Montera D A, Welsh B M, Roggemann M C, Ruck D W 1996 Appl. Opt. 35 5747
Google Scholar
[22] Mello A T, Kanaan A, Guzman D, Guesalaga A 2014 MNRAS 440 2781
Google Scholar
[23] Li Z, Li X 2018 Opt. Express 26 31675
Google Scholar
[24] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686
Google Scholar
[25] Ronneberger O, Fischer P, Brox T 2015 arXiv: 1505.04597
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