Abstract

The pistons of sparse aperture systems need to be controlled within a fraction of a wavelength for the system’s optimal imaging performance. In this paper, we demonstrate that deep learning is capable of performing piston sensing with a single wide-band image after appropriate training. Taking the sensing issue as a fitting task, the deep learning-based method utilizes a deep convolutional neural network to learn complex input-output mapping relations between the broadband intensity distributions and corresponding piston values. Given a trained network and one broadband focal intensity image as the input, the piston can be obtained directly and the capture range achieving the coherence length of the broadband light is available. Simulations and experiments demonstrate the validity of the proposed method. Using only in-focused broadband images as the inputs without defocus division and wavelength dispersion, obviously relaxes the optics complexity. In view of the efficiency and superiority, it’s expected that the method proposed in this paper may be widely applied in multi-aperture imaging.

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

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References

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Cuneo, P.

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D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
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Farley, J.

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Froustey, E.

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Khosla, A.

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Lauraitis, K.

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R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

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Lorell, K.

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F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

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R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

Marcotto, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
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Matosian, K.

Mauclert, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

McCann, M. T.

M. T. McCann, E. Froustey, M. Unser, and K. H. Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

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Meilland, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

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Michaels, S.

Miller, D. W.

S.-J. Chung, D. W. Miller, and O. L. de Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156–2167 (2004).
[Crossref]

Mourard, D.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
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Nelson, J.

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Nishizaki, Y.

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Ohara, C. M.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Olga, R. K.

R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

Paine, S. W.

Palmer, A.

Patru, F.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Paxman, R.

Paxman, R. G.

Petrone, P.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Pinna, E.

Puglisi, A.

Redding, D. C.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Rodríguez-Ramos, J. M.

Roseman, D.

Russell, S.

Saito, M.

Sandler, D.

J. R. P. Angel, P. Wizinowich, M. Lloyd-Hart, and D. Sandler, “Adaptive optics for array telescopes using neural-network techniques,” Nature 348(6298), 221–224 (1990).
[Crossref]

Satheesh, S.

R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

Schweiger, P.

Shi, F.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

Sigler, R.

Smith, J.

Stefanini, P.

Stone, R.

Stubbs, D.

Su, H.

R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

Swietek, G.

Tanida, J.

Tarmoul, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Thatcher, J.

Tischhauser, C.

Tozzi, A.

Troy, M.

Trujillo-Sevilla, J.

Unser, M.

M. T. McCann, E. Froustey, M. Unser, and K. H. Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

Valdivia, M.

van Dam, M. A.

Vera, E.

Wang, J.

H. Yi, Y. Li, C. Fan, and J. Wang, “A New Method of Phase Diversity Wave-front Sensing Based on SOFM NN,” Guangzi Xuebao 7(5), 352–354 (2008).

Wizinowich, P.

J. R. P. Angel, P. Wizinowich, M. Lloyd-Hart, and D. Sandler, “Adaptive optics for array telescopes using neural-network techniques,” Nature 348(6298), 221–224 (1990).
[Crossref]

Wong, H.

Yi, H.

H. Yi, Y. Li, C. Fan, and J. Wang, “A New Method of Phase Diversity Wave-front Sensing Based on SOFM NN,” Guangzi Xuebao 7(5), 352–354 (2008).

Zarifis, V.

Appl. Opt. (6)

Guangzi Xuebao (1)

H. Yi, Y. Li, C. Fan, and J. Wang, “A New Method of Phase Diversity Wave-front Sensing Based on SOFM NN,” Guangzi Xuebao 7(5), 352–354 (2008).

IEEE Trans. Image Process. (1)

M. T. McCann, E. Froustey, M. Unser, and K. H. Jin, “Deep convolutional neural network for inverse problems in imaging,” IEEE Trans. Image Process. 26(9), 4509–4522 (2017).
[Crossref] [PubMed]

Int. J. Comput. Vis. (1)

R. K. Olga, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Khosla, K. Aditya, M. Bernstein, A. C. Berg, and F. Li, “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis. 115(3), 211–252 (2014).

J. Opt. Soc. Am. A (1)

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

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Nature (1)

J. R. P. Angel, P. Wizinowich, M. Lloyd-Hart, and D. Sandler, “Adaptive optics for array telescopes using neural-network techniques,” Nature 348(6298), 221–224 (1990).
[Crossref]

Opt. Eng. (1)

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Opt. Express (1)

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Proc. SPIE (1)

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, and S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiment on NGST’s wavefront control testbed,” Proc. SPIE 4850, 318–328 (2003).
[Crossref]

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P. L. Wizinowich, M. Lloydhart, B. A. Mcleod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multiple-mirror telescope,” Proc. SPIE 1542, (1991).

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” Int. Conf. on Learn. Represent. (ICLR) (2015).

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Figures (14)

Fig. 1
Fig. 1 The training PSF images generated by (a-d) the two-aperture imaging system and (e-h) the four-aperture imaging system.
Fig. 2
Fig. 2 The framework of DCNN.
Fig. 3
Fig. 3 Training procedure.
Fig. 4
Fig. 4 Output feature examples from convolution kernels, pooling layers, and non-linear mapping layers.
Fig. 5
Fig. 5 The two-aperture configuration.
Fig. 6
Fig. 6 The residual RMS errors of 500 images randomly selected from the testing set for the two-aperture system.
Fig. 7
Fig. 7 Distribution of residual RMS errors on the training set and the testing set for the two-aperture imaging system.
Fig. 8
Fig. 8 The four-aperture configuration.
Fig. 9
Fig. 9 Distribution of the residual RMS errors on the training set and the testing set for the four-aperture imaging system.
Fig. 10
Fig. 10 Experimental setup of the two-aperture system.
Fig. 11
Fig. 11 Loss function curve through training on real images.
Fig. 12
Fig. 12 The residual RMS errors of the testing set on real images.
Fig. 13
Fig. 13 Distribution of the residual RMS errors of the testing set on real images.
Fig. 14
Fig. 14 The images without (a) and with (b) piston correction.

Tables (1)

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Table 1 comparison of average RMS errors over testing sets on different systems

Equations (4)

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I(x,y)=o(x,y)PSF(x,y)+n(x,y)
PSF( x,y )= | FT{ P( u,v ) } | 2
P(u,v)=p(u u 1 ,v v 1 )+ n=2 N p(u u n ,v v n ) exp( 2πi λ OP D n )
PSF( x,y )= λ 1 λ M c( λ )PSF( x,y,λ ) dλ

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