Abstract

Convolutional neural networks (CNNs) have been successfully applied to solve optical problems. In this paper, a method is proposed for the reconstruction and analysis of a wavefront with an irregular-shaped aperture based on deep learning, for which a U-type CNN (U-net) was used to reconstruct the wavefront image. The data generated by the simulation contain several types of wavefront images with irregularly shaped apertures for training the U-net. The results indicate that modal wavefront reconstruction of irregular-shaped apertures is feasible based on deep learning; it will be very helpful for the reconstruction and analysis of wavefronts in real time applications, and the method is robust.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (5)

2017 (6)

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
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2016 (4)

2015 (1)

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2014 (4)

2013 (6)

2012 (3)

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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S. Y. Hasan and A. S. Shaker, “Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration,” Appl. Opt. 51(35), 8490–8497 (2012).
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2010 (1)

P. Reardon, F. Liu, and J. Geary, “Schmidt-like corrector plate for cylindrical optics,” Opt. Eng. 49(5), 053002 (2010).
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2008 (1)

2007 (2)

2006 (1)

2004 (1)

G. Miller, E. Moses, and C. Wuest, “The National Ignition Facility,” Opt. Eng. 43(12), 2841 (2004).
[Crossref]

2003 (1)

1998 (1)

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86(11), 2278–2324 (1998).
[Crossref]

1981 (1)

1980 (1)

Asundi, A. K.

Atkinson, C.

L. Feinberg, M. Clampin, R. Keski-Kuha, C. Atkinson, S. Texter, M. Bergeland, and B. Gallagher, James Webb Space Telescope optical telescope element mirror development history and results, SPIE Astronomical Telescopes + Instrumentation (SPIE, 2012), Vol. 8442.

Atry, F.

Azimipour, M.

Barbastathis, G.

Bengio, Y.

I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial networks,” Adv. Neural Inf. Process. Syst. 3, 2672–2680 (2014).

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,” Proc. IEEE 86(11), 2278–2324 (1998).
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Bergeland, M.

L. Feinberg, M. Clampin, R. Keski-Kuha, C. Atkinson, S. Texter, M. Bergeland, and B. Gallagher, James Webb Space Telescope optical telescope element mirror development history and results, SPIE Astronomical Telescopes + Instrumentation (SPIE, 2012), Vol. 8442.

Bottou, L.

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Z. Liao, M. Nostrand, W. Carr, J. Bude, and T. Suratwala, Modeling of laser-induced damage and optic usage at the National Ignition Facility, Pacific Rim Laser Damage 2016: Optical Materials for High Power Lasers (SPIE, 2016), Vol. 9983.

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H. C. Burger, C. J. Schuler, and S. Harmeling, “Image denoising: Can plain neural networks compete with BM3D?” in 2012 IEEE Conference on Computer Vision and Pattern Recognition, 2012), 2392–2399.

Cao, S.-Y.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Carr, W.

Z. Liao, M. Nostrand, W. Carr, J. Bude, and T. Suratwala, Modeling of laser-induced damage and optic usage at the National Ignition Facility, Pacific Rim Laser Damage 2016: Optical Materials for High Power Lasers (SPIE, 2016), Vol. 9983.

Chanan, G.

Chen, H.-Y.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
[Crossref]

Chen, J.

Chen, J.-J.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
[Crossref]

Chen, K.-X.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
[Crossref]

Chen, S.

Chen, X.

Chen, Y.

K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising,” IEEE Trans. on Image Process. 26(7), 3142–3155 (2017).
[Crossref]

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X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, D.-Q.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, F.

W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, J. Su, K. Zheng, X. Yuan, H. Zhou, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, and X. Deng, “Laser performance of the SG-III laser facility,” High Power Laser Sci. Eng. 4, e21 (2016).
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Wang, G.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, G.-M.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, H.

Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, and A. Ozcan, “Deep learning microscopy,” Optica 4(11), 1437–1443 (2017).
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X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, J.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, J.-L.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, L.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Wang, P.

Wang, Q.

Wang, S.

J. Ye, X. Li, Z. Gao, S. Wang, W. Sun, W. Wang, and Q. Yuan, “Modal wavefront reconstruction over general shaped aperture by numerical orthogonal polynomials,” Opt. Eng. 54(3), 034105 (2015).
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J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
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Wang, S.-Q.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, T.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Wang, W.

J. Ye, X. Li, Z. Gao, S. Wang, W. Sun, W. Wang, and Q. Yuan, “Modal wavefront reconstruction over general shaped aperture by numerical orthogonal polynomials,” Opt. Eng. 54(3), 034105 (2015).
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J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
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Q. Wang, D. Cheng, Y. Wang, H. Hua, and G. Jin, “Design, tolerance, and fabrication of an optical see-through head-mounted display with free-form surface elements,” Appl. Opt. 52(7), C88–C99 (2013).
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Wang, Y.-F.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Wang, Y.-N.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, J. Su, K. Zheng, X. Yuan, H. Zhou, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, and X. Deng, “Laser performance of the SG-III laser facility,” High Power Laser Sci. Eng. 4, e21 (2016).
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Xu, D.

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Xu, H.

Xu, L.-Z.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Xu, S.

Xu, X.-Q.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Xu, Y.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Xu, Z.

Yang, D.-H.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Yang, L.

Yang, S.-H.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Yang, Z.

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Ye, H.

Ye, J.

J. Ye, X. Li, Z. Gao, S. Wang, W. Sun, W. Wang, and Q. Yuan, “Modal wavefront reconstruction over general shaped aperture by numerical orthogonal polynomials,” Opt. Eng. 54(3), 034105 (2015).
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J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
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Yoo, D.

Y. Yoon, H. Jeon, D. Yoo, J. Lee, and I. S. Kweon, “Light-Field Image Super-Resolution Using Convolutional Neural Network,” IEEE Signal Process. Lett. 24(6), 848–852 (2017).
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Y. Yoon, H. Jeon, D. Yoo, J. Lee, and I. S. Kweon, “Light-Field Image Super-Resolution Using Convolutional Neural Network,” IEEE Signal Process. Lett. 24(6), 848–852 (2017).
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Yu, S.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Yu, Y.

J. Peng, Y. Yu, and H. Xu, “Compensation of high-order misalignment aberrations in cylindrical interferometry,” Appl. Opt. 53(22), 4947–4956 (2014).
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X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Yuan, H.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Yuan, Q.

J. Ye, X. Li, Z. Gao, S. Wang, W. Sun, W. Wang, and Q. Yuan, “Modal wavefront reconstruction over general shaped aperture by numerical orthogonal polynomials,” Opt. Eng. 54(3), 034105 (2015).
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Yuan, X.

X. Yuan and Y. Pu, “Parallel lensless compressive imaging via deep convolutional neural networks,” Opt. Express 26(2), 1962–1977 (2018).
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Yuan, X.-Y.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Zhai, C.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Zhang, B.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Zhang, F.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Zhang, H.-T.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Zhang, J.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Zhang, K.

K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising,” IEEE Trans. on Image Process. 26(7), 3142–3155 (2017).
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Zhang, L.

K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising,” IEEE Trans. on Image Process. 26(7), 3142–3155 (2017).
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Zhang, L.-P.

X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, G.-P. Li, Q. Li, L.-P. Zhang, H.-J. Su, Z.-Q. Yao, Y.-N. Wang, X.-Z. Xing, X.-N. Li, Y.-T. Zhu, G. Wang, B.-Z. Gu, A. L. Luo, X.-Q. Xu, Z.-C. Zhang, G.-R. Liu, H.-T. Zhang, D.-H. Yang, S.-Y. Cao, H.-Y. Chen, J.-J. Chen, K.-X. Chen, Y. Chen, J.-R. Chu, L. Feng, X.-F. Gong, Y.-H. Hou, H.-Z. Hu, N.-S. Hu, Z.-W. Hu, L. Jia, F.-H. Jiang, X. Jiang, Z.-B. Jiang, G. Jin, A.-H. Li, Y. Li, Y.-P. Li, G.-Q. Liu, Z.-G. Liu, W.-Z. Lu, Y.-D. Mao, L. Men, Y.-J. Qi, Z.-X. Qi, H.-M. Shi, Z.-H. Tang, Q.-S. Tao, D.-Q. Wang, D. Wang, G.-M. Wang, H. Wang, J.-N. Wang, J. Wang, J.-L. Wang, J.-P. Wang, L. Wang, S.-Q. Wang, Y. Wang, Y.-F. Wang, L.-Z. Xu, Y. Xu, S.-H. Yang, Y. Yu, H. Yuan, X.-Y. Yuan, C. Zhai, J. Zhang, Y.-X. Zhang, Y. Zhang, M. Zhao, F. Zhou, G.-H. Zhou, J. Zhu, and S.-C. Zou, “The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST),” Res. Astron. Astrophys. 12(9), 1197–1242 (2012).
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Zhang, Q.

Zhang, X.

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H. Peng, X. M. Zhang, X. Wei, W. Zheng, F. Jing, Z. Sui, D. Fan, and Z. Lin, Status of the SG-III solid state laser project, Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion (SPIE, 1999), Vol. 3492.

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Y. Zhang, C. Wu, Y. Song, K. Si, Y. Zheng, L. Hu, J. Chen, L. Tang, and W. Gong, “Machine learning based adaptive optics for doughnut-shaped beam,” Opt. Express 27(12), 16871–16881 (2019).
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Zhang, Z.-C.

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Zhao, Y.-H.

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Zheng, K.

W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, J. Su, K. Zheng, X. Yuan, H. Zhou, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, and X. Deng, “Laser performance of the SG-III laser facility,” High Power Laser Sci. Eng. 4, e21 (2016).
[Crossref]

Zheng, L.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, Design and fabrication of imaging optical systems with freeform surfaces, SPIE Optical Engineering + Applications (SPIE, 2012), Vol. 8486.

Zheng, W.

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[Crossref]

H. Peng, X. M. Zhang, X. Wei, W. Zheng, F. Jing, Z. Sui, D. Fan, and Z. Lin, Status of the SG-III solid state laser project, Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion (SPIE, 1999), Vol. 3492.

Zheng, Y.

Zhou, F.

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Zhou, G.-H.

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Zhou, H.

W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, J. Su, K. Zheng, X. Yuan, H. Zhou, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, and X. Deng, “Laser performance of the SG-III laser facility,” High Power Laser Sci. Eng. 4, e21 (2016).
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Zhou, W.

W. Zheng, X. Wei, Q. Zhu, F. Jing, D. Hu, J. Su, K. Zheng, X. Yuan, H. Zhou, W. Dai, W. Zhou, F. Wang, D. Xu, X. Xie, B. Feng, Z. Peng, L. Guo, Y. Chen, X. Zhang, L. Liu, D. Lin, Z. Dang, Y. Xiang, and X. Deng, “Laser performance of the SG-III laser facility,” High Power Laser Sci. Eng. 4, e21 (2016).
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Zhou, X.

Zhu, J.

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Zhu, L.

Zhu, Q.

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Zhu, Y.-T.

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Figures (5)

Fig. 1.
Fig. 1. U-net convolutional neural network model architecture. Each blue box corresponds to a multi-channel feature map. The number of channels is on top of the box. The x-y-size is provided at the edge of the box. Red boxes represent copied feature maps. The arrows denote the different operations.
Fig. 2.
Fig. 2. Examples of wavefront images over the irregular-shaped aperture: (a) cross wire; (b) random cutout; (c) hexagonal; (d) optical window; (e) square; (f) oval; (g) triangle; (h) annular.
Fig. 3.
Fig. 3. (a)Training and validation accuracies, and (b) training and validation losses for the 25 epochs.
Fig. 4.
Fig. 4. Some examples to verify the performance of U-net using(a) cross wire, (b) random cutout, (c) hexagonal, (d) square, (e) optical window, (f) oval, and (g) triangle shapes; (h) annular.
Fig. 5.
Fig. 5. Example of reconstructing wavefront image with noise.

Equations (1)

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R M S E = u = 1 W v = 1 H ( y n ( u , v ) y n ( u , v ) ) 2 W H

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