Highly robust spatiotemporal wavefront prediction with a mixed graph neural network in adaptive optics

Ju Tang; Ji Wu; Jiawei Zhang; Mengmeng Zhang; Zhenbo Ren; Jianglei Di; Liusen Hu; Guodong Liu; Jianlin Zhao

doi:10.1364/PRJ.497909

Photonics Research, Volume. 11, Issue 11, 1802(2023)

Highly robust spatiotemporal wavefront prediction with a mixed graph neural network in adaptive optics

Ju Tang^1、†, Ji Wu^1、†, Jiawei Zhang¹, Mengmeng Zhang¹, Zhenbo Ren^1,2,5、*, Jianglei Di^1,3,6、*, Liusen Hu⁴, Guodong Liu⁴, and Jianlin Zhao^1,7、*

Author Affiliations

¹Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710129, China

²Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518063, China

³Key Laboratory of Photonic Technology for Integrated Sensing and Communication, Ministry of Education, and Guangdong Provincial Key Laboratory of Information Photonics Technology, Guangdong University of Technology, Guangzhou 510006, China

⁴Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China

⁵e-mail: zbren@nwpu.edu.cn

⁶e-mail: jiangleidi@gdut.edu.cn

⁷e-mail: jlzhao@nwpu.edu.cn

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Figures & Tables(9)

Fig. 1. Flowchart of spatiotemporal wavefront prediction. (a) Training dataset configuration. (b) Graph embedding from the covariance matrix of coefficients. (c) In the testing process, Zernike coefficients of previous 10 frames are inputs, and the predicted coefficients are obtained by the trained MGNN.

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Fig. 2. Network architecture of the MGNN. (a) Overall framework. (b) Details of temporal feature catcher. (c) Details of spatial feature analyzer. (C, W, H) are channel, width, and height, respectively.

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Fig. 3. (a) Optical setup model of the AO system. TGP, turbulence generating pool; WFS, wavefront sensor; DM, deformable mirror. (b) Data flow of conventional AO (gray lines) and predictive AO (blue lines). (c) Simulated atmospheric turbulence measuring process.

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Fig. 4. Comparison of one-frame prediction accuracy by three algorithms. (a), (b) Predicted Zernike coefficients and corresponding wavefronts of future third frame in test set 1 as two samples. MGNN, our proposed method; LSTM, one non-linear algorithm; LMMSE, one linear algorithm; AE, absolute error.

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Fig. 5. Comparison of overall prediction performance in different test sets. (a1) Histograms and normal curves of RMS values in test set 1. N(μ,σ) is the normal distribution with mean μ and standard deviation σ, and S is a magnification factor. (a2) RMS curves of consecutive frames with or without prediction in (a1). (b1) Histograms and normal curves of RMS values in test set 2. (b2) RMS curves of consecutive frames with or without prediction in (b1). MGNN: blue; LSTM: red; LMMSE: orange; conventional AO: gray. Test set 1: the same condition as training; test set 2: windspeed changes. Black arrow: emphasis in comparison.

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Fig. 6. Comparison of overall prediction performance using test sets with changing Fried parameters. Histograms and normal curves of RMS values are counted in test sets 3, 4, 1, 5, respectively. MGNN: blue; LSTM: red; LMMSE: orange; conventional AO: gray. Test sets 3, 4, and 5: Fried parameters change.

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Fig. 7. Robustness to the experimental data. (a1) Histograms and normal curves of RMS values in test set 6. (a2) RMS curves of consecutive frames with or without prediction in (a1). MGNN: blue; LSTM: red; LMMSE: orange; conventional AO: gray. Black arrow: emphasis in comparison. (b) Predicted Zernike coefficients and corresponding wavefronts of future third frame in test set 6. AE, absolute error. (c1) RMS curves of consecutive frames with prediction by the MGNN and MGNN-E. MGNN-E (green): MGNN trained by the experimental data. (c2) Box plots of RMS in (c1).

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Fig. 8. Closed-loop correction wavefront error in experiment. (a) Three stages of the AO system and their corresponding corrected wavefronts. (b) RMS curves of three stages in closed-loop correction. Without AO: black line; conventional AO: gray line; predictive AO with MGNN: blue line. (c) Focal spot and grid imaging of three stages.

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Table 1. Statistical RMS Values of All Test Sets in Simulation and Experiment^a

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Table 1. Statistical RMS Values of All Test Sets in Simulation and Experiment^a

	Test Sets	Parameters	RMS (rad)	Conventional AO	Predictive AO
	Test Sets	Parameters	RMS (rad)	Conventional AO	MGNN	LSTM	LMMSE
Sim.	Set 1	$w = [5, 10, 20] m / s$ $r_{0} = N_{r}$ (15, 2) cm	Mean ( $μ$ )	0.346	0.194	0.209	0.215
	Set 1	$w = [5, 10, 20] m / s$ $r_{0} = N_{r}$ (15, 2) cm	SD ( $σ$ )	0.111	0.061	0.076	0.121
	Set 2	$w = [10, 15, 25] m / s$	Mean ( $μ$ )	1.134	0.739	0.709	0.730
	Set 2	$w = [10, 15, 25] m / s$	SD ( $σ$ )	0.366	0.215	0.241	0.262
	Set 3	$r_{0} = N_{r}$ (5, 2) cm	Mean ( $μ$ )	0.283	0.136	0.339	0.281
	Set 3	$r_{0} = N_{r}$ (5, 2) cm	SD ( $σ$ )	0.078	0.047	0.142	0.200
	Set 4	$r_{0} = N_{r}$ (10, 2) cm	Mean ( $μ$ )	0.370	0.197	0.335	0.272
	Set 4	$r_{0} = N_{r}$ (10, 2) cm	SD ( $σ$ )	0.104	0.050	0.103	0.094
	Set 5	$r_{0} = N_{r}$ (20, 2) cm	Mean ( $μ$ )	0.166	0.076	0.149	0.162
	Set 5	$r_{0} = N_{r}$ (20, 2) cm	SD ( $σ$ )	0.058	0.024	0.115	0.062
Exp.	Set 6	$r_{0} = 15 \pm 0.2 cm$	Mean ( $μ$ )	0.033	0.025	0.092	0.064
Exp.	Set 6	$r_{0} = 15 \pm 0.2 cm$	SD ( $σ$ )	0.012	0.007	0.029	0.025

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Ju Tang, Ji Wu, Jiawei Zhang, Mengmeng Zhang, Zhenbo Ren, Jianglei Di, Liusen Hu, Guodong Liu, Jianlin Zhao. Highly robust spatiotemporal wavefront prediction with a mixed graph neural network in adaptive optics[J]. Photonics Research, 2023, 11(11): 1802

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