Abstract

This paper proposes a method used to calculate centroid for Shack-Hartmann wavefront sensor (SHWFS) in adaptive optics (AO) systems that suffer from strong environmental light and noise pollutions. In these extreme situations, traditional centroid calculation methods are invalid. The proposed method is based on the artificial neural networks that are designed for SHWFS, which is named SHWFS-Neural Network (SHNN). By transforming spot detection problem into a classification problem, SHNNs first find out the spot center, and then calculate centroid. In extreme low signal-noise ratio (SNR) situations with peak SNR (SNRp) of 3, False Rate of SHNN-50 (SHNN with 50 hidden layer neurons) is 6%, and that of SHNN-900 (SHNN with 900 hidden layer neurons) is 0%, while traditional methods’ best result is 26 percent. With the increase of environmental light interference’s power, the False Rate of SHNN-900 remains around 0%, while traditional methods’ performance decreases dramatically. In addition, experiment results of the wavefront reconstruction are presented. The proposed SHNNs achieve significantly improved performance, compared with the traditional method, the Root Mean Square (RMS) of residual decreases from 0.5349 um to 0.0383 um. This method can improve SHWFS’s robustness.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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2018 (1)

2017 (2)

F. Kong, M. C. Polo, and A. Lambert, “Centroid estimation for a Shack-Hartmann wavefront sensor based on stream processing,” Appl. Opt. 56(23), 6466–6475 (2017).
[Crossref] [PubMed]

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

2015 (1)

X. Li, X. Li, and C. Wang, “Optimum threshold selection method of centroid computation for Gaussian spot,” Proc. SPIE 9675, 967517 (2015).
[Crossref]

2014 (1)

2012 (1)

2010 (3)

2009 (1)

2008 (1)

S. J. Weddell and R. Y. Webb, “Reservoir computing for prediction of the spatially-variant point spread function,” IEEE J. Sel. Top. Signal Process. 2(5), 624–634 (2008).
[Crossref]

2006 (2)

H. Guo, N. Korablinova, Q. Ren, and J. Bille, “Wavefront reconstruction with artificial neural networks,” Opt. Express 14(14), 6456–6462 (2006).
[Crossref] [PubMed]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

2004 (1)

2003 (1)

2002 (2)

C. Rao, W. Jiang, and N. Ling, “Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence,” Opt. Eng. 41(2), 534–541 (2002).
[Crossref]

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779(1), 148–160 (2002).
[Crossref]

2000 (1)

1997 (3)

1996 (1)

1994 (1)

1993 (2)

T. K. Barrett and D. G. Sandler, “Artificial neural network for the determination of Hubble Space Telescope aberration from stellar images,” Appl. Opt. 32(10), 1720–1727 (1993).
[Crossref] [PubMed]

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

1991 (1)

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Netw. 4(2), 251–257 (1991).
[Crossref]

1989 (1)

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control Signal Syst. 2(4), 303–314 (1989).
[Crossref]

Acton, D. S.

Ares, J.

Bará, S.

Barrett, T. K.

Belenguer, T.

Bille, J.

Bradley, C.

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

Browne, S.

Cao, Z.

Carazo, J. M.

Chen, X.

Clare, R.

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

Conan, R.

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

Copland, J.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779(1), 148–160 (2002).
[Crossref]

Cybenko, G.

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control Signal Syst. 2(4), 303–314 (1989).
[Crossref]

Dainty, C.

Dayton, D.

Du, Y. Z.

Duncan, A. L.

Ellerbroek, B. L.

Estrada, J. C.

Fusco, T.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29(23), 2743–2745 (2004).
[Crossref] [PubMed]

Girshick, R.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

Gonglewski, J.

González-Fernandez, L.

Guo, H.

He, K.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

Hornik, K.

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Netw. 4(2), 251–257 (1991).
[Crossref]

Hubin, N.

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

Jiang, W.

C. Rao, W. Jiang, and N. Ling, “Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence,” Opt. Eng. 41(2), 534–541 (2002).
[Crossref]

Kendrick, R. L.

Kong, F.

Korablinova, N.

Lambert, A.

Lardiere, O.

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

Leroux, C.

Leshno, M.

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

Li, X.

X. Li, X. Li, and C. Wang, “Optimum threshold selection method of centroid computation for Gaussian spot,” Proc. SPIE 9675, 967517 (2015).
[Crossref]

X. Li, X. Li, and C. Wang, “Optimum threshold selection method of centroid computation for Gaussian spot,” Proc. SPIE 9675, 967517 (2015).
[Crossref]

Lin, V. Y.

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

Ling, N.

C. Rao, W. Jiang, and N. Ling, “Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence,” Opt. Eng. 41(2), 534–541 (2002).
[Crossref]

Liu, C.

Lloyd-Hart, M.

M. Lloyd-Hart and P. McGuire, “Spatio-temporal prediction for adaptive optics wavefront reconstructors,” in Proc. European Southern Observatory Conf. on Adaptive Optics, pp. 95–102 (1995).

Ma, X.

Mancebo, T.

McDermott, S.

McGuire, P.

M. Lloyd-Hart and P. McGuire, “Spatio-temporal prediction for adaptive optics wavefront reconstructors,” in Proc. European Southern Observatory Conf. on Adaptive Optics, pp. 95–102 (1995).

Michau, V.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29(23), 2743–2745 (2004).
[Crossref] [PubMed]

Montera, D. A.

Mu, Q.

Neal, D.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779(1), 148–160 (2002).
[Crossref]

Neal, D. R.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779(1), 148–160 (2002).
[Crossref]

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29(23), 2743–2745 (2004).
[Crossref] [PubMed]

Northcott, M. J.

Pinkus, A.

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

Polo, M. C.

Poyneer, L. A.

Quiroga, J. A.

Rao, C.

X. Ma, C. Rao, and H. Zheng, “Error analysis of CCD-based point source centroid computation under the background light,” Opt. Express 17(10), 8525–8541 (2009).
[Crossref] [PubMed]

C. Rao, W. Jiang, and N. Ling, “Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence,” Opt. Eng. 41(2), 534–541 (2002).
[Crossref]

Ren, Q.

Ren, S.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

Restrepo, R.

Rigaut, F.

Rogers, S.

Roggemann, M. C.

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29(23), 2743–2745 (2004).
[Crossref] [PubMed]

Ruck, D. W.

Sandler, D. G.

Sandven, S.

Schocken, S.

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

Sorzano, C. O. S.

Sun, J.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Vargas, J.

Wang, C.

X. Li, X. Li, and C. Wang, “Optimum threshold selection method of centroid computation for Gaussian spot,” Proc. SPIE 9675, 967517 (2015).
[Crossref]

Wang, Y.

Webb, R. Y.

S. J. Weddell and R. Y. Webb, “Reservoir computing for prediction of the spatially-variant point spread function,” IEEE J. Sel. Top. Signal Process. 2(5), 624–634 (2008).
[Crossref]

Weddell, S. J.

S. J. Weddell and R. Y. Webb, “Reservoir computing for prediction of the spatially-variant point spread function,” IEEE J. Sel. Top. Signal Process. 2(5), 624–634 (2008).
[Crossref]

Welsh, B. M.

Zhang, X.

Zheng, H.

Appl. Opt. (10)

T. K. Barrett and D. G. Sandler, “Artificial neural network for the determination of Hubble Space Telescope aberration from stellar images,” Appl. Opt. 32(10), 1720–1727 (1993).
[Crossref] [PubMed]

R. L. Kendrick, D. S. Acton, and A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33(27), 6533–6546 (1994).
[Crossref]

D. A. Montera, B. M. Welsh, M. C. Roggemann, and D. W. Ruck, “Prediction of wave-front sensor slope measurements with artificial neural networks,” Appl. Opt. 36(3), 675–681 (1997).
[Crossref] [PubMed]

J. Ares, T. Mancebo, and S. Bará, “Position and displacement sensing with Shack-Hartmann wave-front sensors,” Appl. Opt. 39(10), 1511–1520 (2000).
[Crossref] [PubMed]

D. A. Montera, B. M. Welsh, M. C. Roggemann, and D. W. Ruck, “Processing wave-front-sensor slope measurements using artificial neural networks,” Appl. Opt. 35(21), 4238–4251 (1996).
[Crossref] [PubMed]

F. Rigaut, B. L. Ellerbroek, and M. J. Northcott, “Comparison of curvature-based and Shack-Hartmann-based adaptive optics for the Gemini telescope,” Appl. Opt. 36(13), 2856–2868 (1997).
[Crossref] [PubMed]

L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42(29), 5807–5815 (2003).
[Crossref] [PubMed]

J. Vargas, L. González-Fernandez, J. A. Quiroga, and T. Belenguer, “Shack–Hartmann centroid detection method based on high dynamic range imaging and normalization techniques,” Appl. Opt. 49(13), 2409–2416 (2010).
[Crossref]

J. Vargas, R. Restrepo, J. C. Estrada, C. O. S. Sorzano, Y. Z. Du, and J. M. Carazo, “Shack-Hartmann centroid detection using the spiral phase transform,” Appl. Opt. 51(30), 7362–7367 (2012).
[Crossref] [PubMed]

F. Kong, M. C. Polo, and A. Lambert, “Centroid estimation for a Shack-Hartmann wavefront sensor based on stream processing,” Appl. Opt. 56(23), 6466–6475 (2017).
[Crossref] [PubMed]

IEEE J. Sel. Top. Signal Process. (1)

S. J. Weddell and R. Y. Webb, “Reservoir computing for prediction of the spatially-variant point spread function,” IEEE J. Sel. Top. Signal Process. 2(5), 624–634 (2008).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017).
[Crossref] [PubMed]

Math. Control Signal Syst. (1)

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control Signal Syst. 2(4), 303–314 (1989).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371(1), 323–336 (2006).
[Crossref]

Neural Netw. (2)

K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Netw. 4(2), 251–257 (1991).
[Crossref]

M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Netw. 6(6), 861–867 (1993).
[Crossref]

Opt. Eng. (1)

C. Rao, W. Jiang, and N. Ling, “Atmospheric characterization with Shack-Hartmann wavefront sensors for non-Kolmogorov turbulence,” Opt. Eng. 41(2), 534–541 (2002).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Proc. SPIE (3)

X. Li, X. Li, and C. Wang, “Optimum threshold selection method of centroid computation for Gaussian spot,” Proc. SPIE 9675, 967517 (2015).
[Crossref]

O. Lardiere, R. Conan, R. Clare, C. Bradley, and N. Hubin, “Compared performance of different centroiding algorithms for high–pass filtered laser guide star Shack–Hartmann wavefront sensors,” Proc. SPIE 7736, 773672 (2010).

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779(1), 148–160 (2002).
[Crossref]

Other (4)

C. Szegedy, A. Toshev, and D. Erhan, “Deep neural networks for object detection,” in Proceedings of Advances in Neural Information Processing Systems (NIPS, 2013), pp. 2553-2561.

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Figures (15)

Fig. 1
Fig. 1 (a) Simulated data with Gaussian distribution noise and ramp interference. (b) Simulated data with Gaussian distribution noise and vertical/horizontal Gaussian interference.
Fig. 2
Fig. 2 (a) ANNs with one hidden layer and one output. (b) The basic operation and function of a neuron. The bias (or threshold) b is very important, but we will no longer note that in following Figs. just for convenience.
Fig. 3
Fig. 3 CoG algorithm expressed by ANN. (a) Computation graph of coordinate X. (b) Computation graph of coordinate Y.
Fig. 4
Fig. 4 CoG algorithm expressed by ANN.
Fig. 5
Fig. 5 A classification network similar to CoG method for spot detection.
Fig. 6
Fig. 6 An architecture with 900 hidden layer neurons.
Fig. 7
Fig. 7 (a) The original image. (b) Network output. (c) The spot center algorithm found.
Fig. 8
Fig. 8 Accuracy and Loss in training process.
Fig. 9
Fig. 9 Low SNR subaperture images.
Fig. 10
Fig. 10 CEE of different methods in low SNR situations.
Fig. 11
Fig. 11 False Rate of different methods in low SNR situations.
Fig. 12
Fig. 12 False Rate with different power of ramp interference.
Fig. 13
Fig. 13 False Rate with different power of vertical/horizontal interference.
Fig. 14
Fig. 14 (a) Real data with different level of environment light interference. (b) Subaperture images with calculated centroids. The cross stands for SHNN-50 result, and the triangle stands for TCoG result.
Fig. 15
Fig. 15 (a) Original wavefront. (b) Reconstructed wavefront in interfered situation by using SHNN-50. (c) Reconstructed wavefront in interfered situation by using SHNN-900. (d) Reconstructed wavefront in interfered situation by using TCoG. (e) Residual wavefront by using SHNN-50. (f) Residual wavefront by using SHNN-900. (g) Residual wavefront by using TCoG.

Tables (2)

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Table 1 False Rate of different methods in low SNR situations.

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Table 2 Experiments of TCoG, SHNN-50 and SHNN-900.

Equations (23)

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I( x,y )= N ph 2π σ spot 2 exp[ ( x x 0 ) 2 + ( y y 0 ) 2 2 σ spot 2 ]
N S = A S ( r x x+ r y y )
N v = A v exp[ ( x x v ) 2 2 σ nv 2 ]
N h = A h exp[ ( y y h ) 2 2 σ nh 2 ]
SN R p = I p σ total
Power= E N E S
CEE= ( x c x 0 ) 2 + ( y c y 0 ) 2
{ x i = m=1 M n=1 N x nm I nm m=1 M n=1 N I nm y i = m=1 M n=1 N y nm I nm m=1 M n=1 N I nm
T m = μ n +( I m μ n ) m 100
m= 368.5 SN R p
{ x i = m=1 M n=1 N W nm x nm I nm m=1 M n=1 N W nm I nm y i = m=1 M n=1 N W nm y nm I nm m=1 M n=1 N W nm I nm
Y=δ( x j w j +b )
w 1,1 [1] ... w 25,1 [1] =1 w 26,2 [1] ... w 50,2 [1] =2 ... w n,m [1] =m w 601,25 [1] ... w 625,25 [1] =25
z= m=1 25 n=1 25 x nm I nm
y= z m=1 25 n=1 25 I nm
w 1,1 [1] ... w 25,1 [1] =1,2,...,25 w 26,2 [1] ... w 50,2 [1] =1,2,...,25 ... w n,m [1] =n w 601,25 [1] ... w 625,25 [1] =1,2,...,25
n =span{ δ( wx+b ):w R n ,bR }
ReLu( t )=max( 0,t )={ tast>0 0ast<0
z=X W 1 + b 1
a=max( z,0 )
Y=a W 2 + b 2
Y predict, i =g( Y i )= e Y i j=1 n e Y j
Loss=J( Y label , Y predict )= Y label log Y predict +λ w 2

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