Abstract

Existing wavefront sensorless (WFS-less) adaptive optics (AO) generally require a search algorithm that takes lots of iterations and measurements to get optimal results. So the latency is a serious problem in the current WFS-less AO system, especially in applications to free-space optics communication. To solve this issue, we propose a deep neural network (DNN)–based aberration correction method. The DNN model can detect the wavefront distortion directly from the intensity images, thereby avoiding time-consuming iterative processes. Since the tip-and-tilt mode of Zernike coefficients are considered, the tip-tilt correction system is not necessarily required in the proposed method. From our simulation results, the proposed method can effectively reduce the computation time and has an impressive improvement of root mean square (RMS) in different turbulence conditions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (3)

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

L. Ming, Y. Li, and J. Han, “Gerchberg–Saxton algorithm based phase correction in optical wireless communication,” Phys. Commun. 25, 323–327 (2017).
[Crossref]

Z. Li and X. Zhao, “BP artificial neural network based wave front correction for sensor-less free space optics communication,” Opt. Commun. 385, 219–228 (2017).
[Crossref]

2015 (2)

2014 (1)

2013 (1)

2012 (2)

2011 (1)

2010 (1)

2007 (2)

2006 (2)

2005 (1)

2000 (2)

1999 (1)

1995 (1)

1990 (1)

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1181 (1990).
[Crossref]

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
[Crossref]

Adler, J.

Ao, M.

Bartsch, D. U.

Beaurepaire, E.

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Bonora, S.

Booth, M. J.

Carhart, G. W.

Cauwenberghs, G.

Chang, H.

X. Yin, H. Chang, X. Cui, J. X. Ma, Y. J. Wang, G. H. Wu, L. Zhang, and X. Xin, “Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication,” Appl. Opt. 57(26), 7644–7650 (2018).
[Crossref] [PubMed]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Cohen, M.

Cui, X.

X. Yin, H. Chang, X. Cui, J. X. Ma, Y. J. Wang, G. H. Wu, L. Zhang, and X. Xin, “Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication,” Appl. Opt. 57(26), 7644–7650 (2018).
[Crossref] [PubMed]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Cvijetic, M.

Dai, G.

Débarre, D.

Facomprez, A.

Fainman, Y.

Fraanje, R.

Freeman, W. R.

Glasser, R. T.

Gong, Y.

J. T. Huang, J. Li, and Y. Gong, “An analysis of convolutional neural networks for speech recognition,” in Proceedings of IEEE Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 4989–4993.
[Crossref]

Haber, A.

Han, J.

L. Ming, Y. Li, and J. Han, “Gerchberg–Saxton algorithm based phase correction in optical wireless communication,” Phys. Commun. 25, 323–327 (2017).
[Crossref]

Hinton, G.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Huang, J. T.

J. T. Huang, J. Li, and Y. Gong, “An analysis of convolutional neural networks for speech recognition,” in Proceedings of IEEE Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 4989–4993.
[Crossref]

Jiang, W.

Kroese, H.

LeCun, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Li, J.

J. T. Huang, J. Li, and Y. Gong, “An analysis of convolutional neural networks for speech recognition,” in Proceedings of IEEE Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 4989–4993.
[Crossref]

Li, M.

Li, Y.

L. Ming, Y. Li, and J. Han, “Gerchberg–Saxton algorithm based phase correction in optical wireless communication,” Phys. Commun. 25, 323–327 (2017).
[Crossref]

Li, Z.

Z. Li and X. Zhao, “BP artificial neural network based wave front correction for sensor-less free space optics communication,” Opt. Commun. 385, 219–228 (2017).
[Crossref]

Linhai, H.

Lipson, S. G.

Liu, Y.

Lohani, S.

Ma, J.

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Ma, J. X.

Ming, L.

L. Ming, Y. Li, and J. Han, “Gerchberg–Saxton algorithm based phase correction in optical wireless communication,” Phys. Commun. 25, 323–327 (2017).
[Crossref]

Neil, M. A. A.

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66(3), 207–211 (1976).
[Crossref]

Pereira, S. F.

Poletto, L.

Polo, A.

Rao, C.

Ribak, E. N.

Roddier, N. A.

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1181 (1990).
[Crossref]

Schitter, G.

Smith, C. S.

Song, H.

Sun, P. C.

Takashima, Y.

Tyson, R.

R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).

Urbach, H. P.

Urbach, P.

Vdovin, G.

Verhaegen, M.

Vorontsov, M. A.

Wang, Y. J.

Weyrauch, T.

Wilson, T.

Wu, G.

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Wu, G. H.

Xin, X.

X. Yin, H. Chang, X. Cui, J. X. Ma, Y. J. Wang, G. H. Wu, L. Zhang, and X. Xin, “Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication,” Appl. Opt. 57(26), 7644–7650 (2018).
[Crossref] [PubMed]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Xu, B.

Yang, P.

Yin, X.

X. Yin, H. Chang, X. Cui, J. X. Ma, Y. J. Wang, G. H. Wu, L. Zhang, and X. Xin, “Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication,” Appl. Opt. 57(26), 7644–7650 (2018).
[Crossref] [PubMed]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Yu, Z.

Zhang, L.

X. Yin, H. Chang, X. Cui, J. X. Ma, Y. J. Wang, G. H. Wu, L. Zhang, and X. Xin, “Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication,” Appl. Opt. 57(26), 7644–7650 (2018).
[Crossref] [PubMed]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Zhang, Z.

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Zhao, X.

Z. Li and X. Zhao, “BP artificial neural network based wave front correction for sensor-less free space optics communication,” Opt. Commun. 385, 219–228 (2017).
[Crossref]

Zhu, L.

Zommer, S.

Appl. Opt. (5)

J. Opt. Soc. Am. A (3)

Nature (1)

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref] [PubMed]

Opt. Commun. (2)

Z. Li and X. Zhao, “BP artificial neural network based wave front correction for sensor-less free space optics communication,” Opt. Commun. 385, 219–228 (2017).
[Crossref]

H. Chang, X. Yin, X. Cui, Z. Zhang, J. Ma, G. Wu, L. Zhang, and X. Xin, “Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg–Saxton-based phase retrieval algorithm,” Opt. Commun. 405, 271–275 (2017).
[Crossref]

Opt. Eng. (1)

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1181 (1990).
[Crossref]

Opt. Express (7)

Opt. Lett. (4)

Phys. Commun. (1)

L. Ming, Y. Li, and J. Han, “Gerchberg–Saxton algorithm based phase correction in optical wireless communication,” Phys. Commun. 25, 323–327 (2017).
[Crossref]

Other (2)

R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).

J. T. Huang, J. Li, and Y. Gong, “An analysis of convolutional neural networks for speech recognition,” in Proceedings of IEEE Conference on Acoustics, Speech and Signal Processing (IEEE, 2015), pp. 4989–4993.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Conceptual scheme of proposed sensor-less AO system model.
Fig. 2
Fig. 2 Simulation demonstration for atmospheric turbulence using Zernike polynomials with D / r 0 valued respectively in (a) 1, (b) 3, (c) 5, (d) 7, (e) 9, (f) 11, (g) 13, (h) 15.
Fig. 3
Fig. 3 Original Gaussian beam (a) and Far-field intensity patterns of the distorted Gaussian beam with D / r 0 valued respectively in (b) 1, (c) 3, (d) 5, (e) 7, (f) 9, (g) 11, (h) 13, (i) 15.
Fig. 4
Fig. 4 Changes of L2 loss on the test set with MLP (a), CNN3 (b), CNN5 (c), CNN7 (d), CNN9(e), CNN11(f).
Fig. 5
Fig. 5 Model structure of CNN7.
Fig. 6
Fig. 6 Intensity image and corresponding phase distortion before (a) and after (b) compensation ( D / r 0 = 7 ).
Fig. 7
Fig. 7 The changes of the RMS under different degree of distortion before and after correction.
Fig. 8
Fig. 8 The latency of proposed method compared with the SPGD under different degree of distortion ( D / r 0 = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 ).

Equations (8)

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I ( x , y ) = | U 0 ( x 0 , y 0 ) * F ( P ( x ' , y ' ) ) | 2
P ( x ' , y ' ) = A ( x ' , y ' ) e i k Φ ( x ' , y ' )
Φ ( x ' , y ' ) = j a j Z j
Z eveni = n + 1 R n m ( r ) 2 cos ( m θ ) , m 0 , Z oddi = n + 1 R n m ( r ) 2 sin ( m θ ) , m 0 , z i = n + 1 R n 0 ( r ) , m = 0 ,
R n m ( r ) = s = 0 ( n m ) / 2 ( 1 ) s ( n s ) ! s ! [ ( n + m ) / 2 s ] ! [ ( n m ) / 2 s ] ! r n 2 s
f : I a
L 2 L o s s = i ( y p r e d i c t y t r u e ) 2
R M S = 1 π 0 2 π 0 1 [ Φ ( r , θ ) Φ ¯ ] 2 r d r d θ

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