Abstract

Recurrent neural networks are usually used for processing sequential data. They have been employed in this paper to deal with the sequence of diffraction subimages created by every intersection from a segmented mirror. Every subimage is first processed by a convolutional neural network that extracts a set of features from each of them. It was attained superior prediction accuracy with the recurrent approach than with convolution layers alone. Furthermore, a consistency test was added to detect wrong predictions before computing the global piston values. The final system predicts global piston values with rms = 7.34 nm, high reliability, and capture range of [ − 21λ, 21λ]. Atmospheric seeing, polishing and tip-tilt residual errors were also added in the simulations.

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

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2019 (2)

2018 (1)

2013 (1)

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

2009 (1)

2008 (1)

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

2006 (2)

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

A. Schumacher and N. Devaney, “Phasing segmented mirrors using defocused images at visible wavelengths,” Mon. Not. R. Astron. Soc. 366(2), 537–546 (2006).
[Crossref]

2005 (1)

2001 (1)

M. G. Lofdahl and H. Eriksson, “Algorithm for resolving 2pi ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40(6), 984–991 (2001).
[Crossref]

2000 (1)

1998 (1)

1997 (1)

M. Schuster and K. K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

1966 (1)

Ba, J.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Baudoz, P.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

Bengio, Y.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Boccaletti, A.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

Cavarroc, C.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

Chanan, G.

Cho, K.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Chueca, S.

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

Chung, J.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Cuevas, S.

V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, and L. J. Sanchez, “Co-phasing of segmented mirror telescopes with curvature sensing,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, vol. 4004 (International Society for Optics and Photonics, 2000), pp. 540–552.

Dekens, F.

Derie, F.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Devaney, N.

A. Schumacher and N. Devaney, “Phasing segmented mirrors using defocused images at visible wavelengths,” Mon. Not. R. Astron. Soc. 366(2), 537–546 (2006).
[Crossref]

Díaz-García, L.

Dohlen, K.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Eriksson, H.

M. G. Lofdahl and H. Eriksson, “Algorithm for resolving 2pi ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40(6), 984–991 (2001).
[Crossref]

Esposito, S.

S. Esposito, E. Pinna, A. Puglisi, A. Tozzi, and P. Stefanini, “Pyramid sensor for segmented mirror alignment,” Opt. Lett. 30(19), 2572–2574 (2005).
[Crossref]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Fernández-Valdivia, J. J.

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

Fried, D. L.

Fuensalida, J. J.

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” in Optical Telescopes of Today and Tomorrow, vol. 2871 (International Society for Optics and Photonics, 1997), pp. 613–617.

Fusco, T.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

Garfias, F.

V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, and L. J. Sanchez, “Co-phasing of segmented mirror telescopes with curvature sensing,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, vol. 4004 (International Society for Optics and Photonics, 2000), pp. 540–552.

Gil, J. S.

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

Gonte, F.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Graves, A.

A. Graves, “Supervised sequence labelling,” in Supervised sequence labelling with recurrent neural networks, (Springer, 2012), pp. 5–13.

Guerra-Ramos, D.

Gulcehre, C.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Hinton, G. E.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, (2012), pp. 1097–1105.

Karban, R.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Kasper, M.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

Kingma, D. P.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Kirkman, D.

Krizhevsky, A.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, (2012), pp. 1097–1105.

Langlois, M.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Li, D.

Liu, Y.

Lloyd-Hart, M.

P. C. McGuire, D. G. Sandler, M. Lloyd-Hart, and T. A. Rhoadarmer, “Adaptive optics: Neural network wavefront sensing, reconstruction, and prediction,” in Scientific Applications of Neural Nets, (Springer, 1999), pp. 97–138.

Lofdahl, M. G.

M. G. Lofdahl and H. Eriksson, “Algorithm for resolving 2pi ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40(6), 984–991 (2001).
[Crossref]

Ma, H.

Ma, X.

Martinez, P.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

Mast, T.

McGuire, P. C.

P. C. McGuire, D. G. Sandler, M. Lloyd-Hart, and T. A. Rhoadarmer, “Adaptive optics: Neural network wavefront sensing, reconstruction, and prediction,” in Scientific Applications of Neural Nets, (Springer, 1999), pp. 97–138.

Michaels, S.

Montoya, L.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Nelson, J.

Noethe, L.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Ohara, C.

Orlov, V. G.

V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, and L. J. Sanchez, “Co-phasing of segmented mirror telescopes with curvature sensing,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, vol. 4004 (International Society for Optics and Photonics, 2000), pp. 540–552.

Paliwal, K. K.

M. Schuster and K. K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

Pinna, E.

S. Esposito, E. Pinna, A. Puglisi, A. Tozzi, and P. Stefanini, “Pyramid sensor for segmented mirror alignment,” Opt. Lett. 30(19), 2572–2574 (2005).
[Crossref]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Puglisi, A.

Ren, G.

Reyes, M.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Rhoadarmer, T. A.

P. C. McGuire, D. G. Sandler, M. Lloyd-Hart, and T. A. Rhoadarmer, “Adaptive optics: Neural network wavefront sensing, reconstruction, and prediction,” in Scientific Applications of Neural Nets, (Springer, 1999), pp. 97–138.

Ridriguez-Ramos, J. M.

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

Rodriguez-Ramos, J. M.

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” in Optical Telescopes of Today and Tomorrow, vol. 2871 (International Society for Optics and Photonics, 1997), pp. 613–617.

Rodríguez-Ramos, J. M.

Rouan, D.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

Sanchez, L. J.

V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, and L. J. Sanchez, “Co-phasing of segmented mirror telescopes with curvature sensing,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, vol. 4004 (International Society for Optics and Photonics, 2000), pp. 540–552.

Sandler, D. G.

P. C. McGuire, D. G. Sandler, M. Lloyd-Hart, and T. A. Rhoadarmer, “Adaptive optics: Neural network wavefront sensing, reconstruction, and prediction,” in Scientific Applications of Neural Nets, (Springer, 1999), pp. 97–138.

Schumacher, A.

A. Schumacher and N. Devaney, “Phasing segmented mirrors using defocused images at visible wavelengths,” Mon. Not. R. Astron. Soc. 366(2), 537–546 (2006).
[Crossref]

Schuster, M.

M. Schuster and K. K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

Sedano, A. L.

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

Stefanini, P.

Surdej, I.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Sutskever, I.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, (2012), pp. 1097–1105.

Terrett, D.

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Tozzi, A.

Troy, M.

Trujillo-Sevilla, J.

Vérinaud, C.

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

Voitsekhovich, V. V.

V. G. Orlov, S. Cuevas, F. Garfias, V. V. Voitsekhovich, and L. J. Sanchez, “Co-phasing of segmented mirror telescopes with curvature sensing,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, vol. 4004 (International Society for Optics and Photonics, 2000), pp. 540–552.

Wang, D.

Xie, Z.

Xu, S.

Xu, Y.

Yaitskova, N.

N. Yaitskova, “Adaptive optics correction of segment aberration,” J. Opt. Soc. Am. A 26(1), 59–71 (2009).
[Crossref]

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

N. Yaitskova, F. Gonte, F. Derie, L. Noethe, I. Surdej, R. Karban, K. Dohlen, M. Langlois, S. Esposito, E. Pinna, M. Reyes, L. Montoya, and D. Terrett, “The active phasing experiment: Part i. concept and objectives,” in Ground-based and Airborne Telescopes, vol. 6267 (International Society for Optics and Photonics, 2006), p. 62672Z.

Yan, D.

Appl. Opt. (2)

Astron. Astrophys. (2)

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on earth-like planet detection with extremely large telescopes,” Astron. Astrophys. 447(1), 397–403 (2006).
[Crossref]

P. Martinez, A. Boccaletti, M. Kasper, C. Cavarroc, N. Yaitskova, T. Fusco, and C. Vérinaud, “Comparison of coronagraphs for high-contrast imaging in the context of extremely large telescopes,” Astron. Astrophys. 492(1), 289–300 (2008).
[Crossref]

IEEE Trans. Signal Process. (1)

M. Schuster and K. K. Paliwal, “Bidirectional recurrent neural networks,” IEEE Trans. Signal Process. 45(11), 2673–2681 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

A. Schumacher and N. Devaney, “Phasing segmented mirrors using defocused images at visible wavelengths,” Mon. Not. R. Astron. Soc. 366(2), 537–546 (2006).
[Crossref]

Opt. Eng. (2)

J. J. Fernández-Valdivia, A. L. Sedano, S. Chueca, J. S. Gil, and J. M. Ridriguez-Ramos, “Tip-tilt restoration of a segmented optical mirror using a geometric sensor,” Opt. Eng. 52(5), 056601 (2013).
[Crossref]

M. G. Lofdahl and H. Eriksson, “Algorithm for resolving 2pi ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40(6), 984–991 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Other (8)

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Figures (7)

Fig. 1.
Fig. 1. Diffraction image from the simulations. Junction of three segments showed in dash line.
Fig. 2.
Fig. 2. Piston step value decomposition into numerical and categorical values.
Fig. 3.
Fig. 3. Schematic representation of the network architecture.
Fig. 4.
Fig. 4. Regression loss during training.
Fig. 5.
Fig. 5. Classification accuracy during training.
Fig. 6.
Fig. 6. Number of global piston values that can be resolved during training.
Fig. 7.
Fig. 7. Global piston error over training in logarithmic scale.

Tables (1)

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Table 1. Simulation parameters

Equations (1)

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| Δ ϕ 1 + Δ ϕ 3 + Δ ϕ 3 | K .

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