Abstract

In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N = 9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N + 5 = 14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N + 4 = 13 intensity measurements.

© 2010 Optical Society of America

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  1. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and D. G. Voelz, "Adaptive imaging system for phase-distorted extended source and multiple-distance objects," Appl. Opt. 36(15), 3319-3328 (1997).
    [CrossRef] [PubMed]
  2. G. Vdovin, "Optimization-based operation of micromachined deformable mirrors," Proc. SPIE 3353, 902-909 (1998).
    [CrossRef]
  3. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, "Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration," J. Opt. Soc. Am. A 17(8), 1440-1453 (2000).
    [CrossRef]
  4. W. Lubeigt, G. Valentine, J. M. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10(13), 550-555 (2002).
    [PubMed]
  5. U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
    [CrossRef]
  6. M. de Boer, K. Hinnen, M. Verhaegen, R. Fraanje, G. Vdovin, and N. Doelman, "Control of a thermal deformable mirror: correction of a static disturbance with limited sensor information," in Proceedings of the 4th International Workshop on Adaptive Optics for Industry and Medicine, pages 61-71, Münster, Germany, 2003.
  7. R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, "Adaptive beam profile control using a simulated annealing algorithm," Opt. Express 13(16), 6085-6091 (2005).
    [CrossRef] [PubMed]
  8. A. A. Aleksandrov, A. V. Kudryashov, A. L. Rukosuev, T. Yu. Cherezova, and Yu. V. Sheldakova, "An adaptive optical system for controlling laser radiation," J. Opt. Technol. 74(8), 550-554 (2007).
    [CrossRef]
  9. P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
    [CrossRef]
  10. W. Lubeigt, S. P. Poland, G. J. Valentine, A. J. Wright, J. M. Girkin, and D. Burns, "Search-based active optic systems for aberration correction in time-independent applications," Appl. Opt. 49(3), 307-314 (2010).
    [CrossRef] [PubMed]
  11. O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25(1), 52-54 (2000).
    [CrossRef]
  12. L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
    [CrossRef] [PubMed]
  13. M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788-5792 (2002).
    [CrossRef]
  14. P. Marsh, D. Burns, and J. M. Girkin, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express 11(10), 1123-1130 (2003).
    [CrossRef] [PubMed]
  15. A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Tech. 67(1), 36-44 (2005).
    [CrossRef] [PubMed]
  16. S. P. Poland, A. J. Wright, and J. M. Girkin, "Evaluation of fitness parameters used in an iterative approach to aberration correction in optical sectioning microscopy," Appl. Opt. 47(6), 731-736 (2008).
    [CrossRef] [PubMed]
  17. D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, "Adaptive optics for structured illumination microscopy," Opt. Express 16(13), 9290-9305 (2008).
    [CrossRef] [PubMed]
  18. D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, "Image-based adaptive optics for two-photon microscopy," Opt. Lett. 34(16), 2495-2497 (2009).
    [CrossRef] [PubMed]
  19. F. Roddier, Adaptive Optics in Astronomy, (Cambridge University Press, Cambridge, UK, 1999).
    [CrossRef]
  20. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, New York, USA, 1998).
  21. M. J. Booth, "Wave front sensor-less adaptive optics: a model-based approach using sphere packings," Opt. Express 14(4), 1339-1352 (2006).
    [CrossRef] [PubMed]
  22. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, USA, 1996).
  23. H. Song, G. Vdovin, R. Fraanje, G. Schitter, and M. Verhaegen, "Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system," Opt. Lett. 34(1), 61-63 (2009).
    [CrossRef]
  24. M. Verhaegen, and V. Verdult, Filtering and System Identification: A Least Squares Approach, (Cambridge University Press, Cambridge, USA, 2007).
    [CrossRef]
  25. J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
    [CrossRef]
  26. M. Schwertner, M. J. Booth, and T. Wilson, "Characterizing specimen induced aberrations for high NA adaptive optical microscopy," Opt. Express 12(26), 6540-6552 (2004).
    [CrossRef] [PubMed]
  27. G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, "Correction of low order aberrations using continuous deformable mirrors," Opt. Express 16(5), 2859-2866 (2008).
    [CrossRef] [PubMed]
  28. S. Y. Kung, Digital Neural Networks, (Prentice-Hall, Upper Saddle River, NJ, USA, 1993).
  29. S. Haykin, Neural Networks: a Comprehensive Foundation, (Macmillan, New York, USA, 1994).
  30. M. Brown, and C. Harris, Neurofuzzy Adaptive Modeling and Control, (Prentice-Hall, New York, USA, 1994).
  31. H. Demuth, M. Beale, and M. Hagan, Neural Network Toolbox 5 User’s Guide, (The MathWorks, Inc., 2007).
    [PubMed]
  32. M. Born, and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).
  33. W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C; the Art of Scientific Computing, 2nd ed. (Cambridge University Press, New York, USA, 1992).
  34. M. Loktev, D. Monteiroa, and G. Vdovin, "Comparison study of the performance of piston, thin plate and membrane mirrors for correction of turbulence-induced phase distortions," Opt. Commun. 192, 91-99 (2001).
    [CrossRef]

2010 (1)

2009 (2)

2008 (3)

2007 (2)

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

A. A. Aleksandrov, A. V. Kudryashov, A. L. Rukosuev, T. Yu. Cherezova, and Yu. V. Sheldakova, "An adaptive optical system for controlling laser radiation," J. Opt. Technol. 74(8), 550-554 (2007).
[CrossRef]

2006 (1)

2005 (2)

R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, "Adaptive beam profile control using a simulated annealing algorithm," Opt. Express 13(16), 6085-6091 (2005).
[CrossRef] [PubMed]

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Tech. 67(1), 36-44 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

P. Marsh, D. Burns, and J. M. Girkin, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express 11(10), 1123-1130 (2003).
[CrossRef] [PubMed]

U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
[CrossRef]

2002 (3)

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788-5792 (2002).
[CrossRef]

W. Lubeigt, G. Valentine, J. M. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10(13), 550-555 (2002).
[PubMed]

2001 (1)

M. Loktev, D. Monteiroa, and G. Vdovin, "Comparison study of the performance of piston, thin plate and membrane mirrors for correction of turbulence-induced phase distortions," Opt. Commun. 192, 91-99 (2001).
[CrossRef]

2000 (2)

1998 (1)

G. Vdovin, "Optimization-based operation of micromachined deformable mirrors," Proc. SPIE 3353, 902-909 (1998).
[CrossRef]

1997 (1)

1995 (1)

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Albert, O.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25(1), 52-54 (2000).
[CrossRef]

Aleksandrov, A. A.

Ao, M. W.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Bente, E.

Benveniste, A.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Booth, M. J.

Botcherby, E. J.

Bulte, H.

Burns, D.

Buske, I.

U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
[CrossRef]

Carhart, G. W.

Cauwenberghs, G.

Cherezova, T. Yu.

Cohen, M.

Débarre, D.

Delyon, B.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

El-Agmy, R.

Fraanje, R.

Girkin, J. M.

Glorennec, P.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Greenaway, A. H.

Heuck, H. M.

U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
[CrossRef]

Hjalmarsson, H.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Hu, S. J.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Jiang, W. H.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Juditsky, A.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788-5792 (2002).
[CrossRef]

Kudryashov, A. V.

Liu, Y.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Ljung, L.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Loktev, M.

G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, "Correction of low order aberrations using continuous deformable mirrors," Opt. Express 16(5), 2859-2866 (2008).
[CrossRef] [PubMed]

M. Loktev, D. Monteiroa, and G. Vdovin, "Comparison study of the performance of piston, thin plate and membrane mirrors for correction of turbulence-induced phase distortions," Opt. Commun. 192, 91-99 (2001).
[CrossRef]

Lubeigt, W.

Marsh, P.

Monteiroa, D.

M. Loktev, D. Monteiroa, and G. Vdovin, "Comparison study of the performance of piston, thin plate and membrane mirrors for correction of turbulence-induced phase distortions," Opt. Commun. 192, 91-99 (2001).
[CrossRef]

Mourou, G.

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788-5792 (2002).
[CrossRef]

Norris, T. B.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25(1), 52-54 (2000).
[CrossRef]

Patterson, B. A.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Tech. 67(1), 36-44 (2005).
[CrossRef] [PubMed]

Poland, S. P.

Pruidze, D. V.

Reid, D.

Ricklin, J. C.

Rukosuev, A. L.

Samokhin, A.

Schitter, G.

Schwertner, M.

Sheldakova, Yu. V.

Sherman, L.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25(1), 52-54 (2000).
[CrossRef]

Sjöberg, J.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Soloviev, O.

Song, H.

Srinivas, S.

Valentine, G.

Valentine, G. J.

W. Lubeigt, S. P. Poland, G. J. Valentine, A. J. Wright, J. M. Girkin, and D. Burns, "Search-based active optic systems for aberration correction in time-independent applications," Appl. Opt. 49(3), 307-314 (2010).
[CrossRef] [PubMed]

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Tech. 67(1), 36-44 (2005).
[CrossRef] [PubMed]

Vdovin, G.

Verhaegen, M.

Voelz, D. G.

Vorontsov, M. A.

Watanabe, T.

Wilson, T.

Wittrock, U.

U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
[CrossRef]

Wright, A. J.

Xu, B.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Yang, P.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Yang, W.

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

Ye, J. Y.

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

Zhang, Q.

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

Appl. Opt. (3)

Automatica (1)

J. Sjöberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky, "Nonlinear black-box modeling in system identification: a unified overview," Automatica 31(12), 1691-1724 (1995).
[CrossRef]

J. Microsc. (1)

L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, "Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror," J. Microsc. 206(1), 65-71 (2002).
[CrossRef] [PubMed]

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

J. Opt. Technol. (1)

Microsc. Res. Tech. (1)

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, "Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy," Microsc. Res. Tech. 67(1), 36-44 (2005).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, "Adaptive mode optimization of a continuous-wave solid-state laser using an intracavity piezoelectric deformable mirror," Opt. Commun. 278(2), 377-381 (2007).
[CrossRef]

M. Loktev, D. Monteiroa, and G. Vdovin, "Comparison study of the performance of piston, thin plate and membrane mirrors for correction of turbulence-induced phase distortions," Opt. Commun. 192, 91-99 (2001).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. U.S.A. (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788-5792 (2002).
[CrossRef]

Proc. SPIE (2)

G. Vdovin, "Optimization-based operation of micromachined deformable mirrors," Proc. SPIE 3353, 902-909 (1998).
[CrossRef]

U. Wittrock, I. Buske, and H. M. Heuck, "Adaptive aberration control in laser amplifiers and laser resonators," Proc. SPIE 4969, 122-136 (2003).
[CrossRef]

Other (11)

M. de Boer, K. Hinnen, M. Verhaegen, R. Fraanje, G. Vdovin, and N. Doelman, "Control of a thermal deformable mirror: correction of a static disturbance with limited sensor information," in Proceedings of the 4th International Workshop on Adaptive Optics for Industry and Medicine, pages 61-71, Münster, Germany, 2003.

F. Roddier, Adaptive Optics in Astronomy, (Cambridge University Press, Cambridge, UK, 1999).
[CrossRef]

J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, New York, USA, 1998).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, USA, 1996).

M. Verhaegen, and V. Verdult, Filtering and System Identification: A Least Squares Approach, (Cambridge University Press, Cambridge, USA, 2007).
[CrossRef]

S. Y. Kung, Digital Neural Networks, (Prentice-Hall, Upper Saddle River, NJ, USA, 1993).

S. Haykin, Neural Networks: a Comprehensive Foundation, (Macmillan, New York, USA, 1994).

M. Brown, and C. Harris, Neurofuzzy Adaptive Modeling and Control, (Prentice-Hall, New York, USA, 1994).

H. Demuth, M. Beale, and M. Hagan, Neural Network Toolbox 5 User’s Guide, (The MathWorks, Inc., 2007).
[PubMed]

M. Born, and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C; the Art of Scientific Computing, 2nd ed. (Cambridge University Press, New York, USA, 1992).

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Figures (7)

Fig. 1
Fig. 1

Schematic of a common closed-loop WFSless AO system. The incident light beam is disturbed in front of the entrance pupil. The control system adapts the control signal u(k) to maximize the intensity measurement y(k).

Fig. 2
Fig. 2

Cost function J() depends on the number of data points for solving the NLLS problem in Eq. (14). For clarity of explanation, the intensity variation a is not considered. In (a), the nonlinearity is represented as y = f ( x + u ) = ( 2 J 1 ( x + u ) x + u ) 2 to simulate the intensity distribution in the Airy disk [32], with J1 the Bessel function of the first kind. The aberration shift the original system y = f (u) horizontally by x = −1.25. The model uncertainty is neglected, i.e., = f. With single data point P1, the cost function J() has two minima at = −1.25 and = 3.25 as plotted in (b). With points P1 and P2, J() has one unique global minimum at = −1.25 but there is a local minimum at = 2.5. This local minimum vanishes when P3 is added and the domain of convex is increased.

Fig. 3
Fig. 3

Block diagram of the closed-loop WFSless AO system. The physical WFSless AO system has voltage V(k) as input, but conceptually u(k) can be considered as its input because of the hysteresis compensator and the modal transform.

Fig. 4
Fig. 4

Accuracy of the neural network model for different number of neurons NQ. VAF increases with NQ in both identification and validation sets for NQ ≤ 20. The difference in VAF is negligible for NQ > 20. Hence 20 neurons are used.

Fig. 5
Fig. 5

Time line of the WFSless AO system with the MBAC algorithm, including initialization and aberration correction. The initial sampling interval is ts = 20 ms. The computational time tc,1 for the first aberration estimation takes about 40 ms, while the estimation time tc,2 afterwards takes about 20 ms because a better initial guess is provided for the solving the NLLS problem.

Fig. 6
Fig. 6

Aberration correction with the MBAC+Simplex algorithm and with the simplex algorithm alone, for one static aberration. The MBAC algorithm consists of the initialization and the aberration correction. The initial intensity is 0.17. With the MBAC algorithm, the intensity converges to 0.86 at the 14th time sample, which it takes 30 time samples for the simplex algorithm alone to reach 0.8. The simplex algorithm after MBAC also shows faster convergence than the simplex algorithm alone.

Fig. 7
Fig. 7

Correction of 20 static aberrations. The initial intensity is 0.49 in average. With the MBAC algorithm, the intensity increases to 0.82 at the 12th time sample and to 0.87 at the 13th time sample. The intensity converges to 0.89 by the MBAC at the 15th time sample, while Simplex 2 needs 45 time samples to reach the same level. The standard deviation of (k) is also reduced with the MBAC algorithm, indicating that MBAC can give a more deterministic intensity improvement than simplex.

Equations (17)

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max u ( k ) y ( k ) ,
y ( k ) = Σ 2 | Σ 1 a i ( ξ , η , k ) exp [ j 2 π λ ( ϕ x ( ξ , η , k ) + ϕ m ( ξ , η , k ) ) ] exp [ j 2 π λ d ( α ξ + β η ) ] d ξ d η | 2 d α d β + w ( k ) .
a i ( ξ , η , k ) = a i ,
ϕ x ( ξ , η , k ) = ϕ x ( ξ , η ) ,
ϕ m ( ξ , η , k ) = D ( ξ , η ) u ( k )
y ( k ) = Σ 2 | Σ 1 a i exp [ j 2 π λ ( ϕ x ( ξ , η ) + D ( ξ , η ) u ( k ) ) ] exp [ j 2 π λ d ( α ξ + β η ) ] d ξ d η | 2 d α d β + w ( k ) .
y ( k ) = g ( ϕ x ( ξ , η ) + D ( ξ , η ) u ( k ) ) + w ( k ) ,
ϕ x ( ξ , η ) = D ( ξ , η ) x ϕ 1 ( ξ , η ) + Δ ϕ x ( ξ , η ) .
ϕ x ( ξ , η ) D ( ξ , η ) x .
y ( k ) g ( D ( ξ , η ) ( x + u ( k ) ) ) + w ( k ) .
y ( k ) f ( x + u ( k ) ) + w ( k ) .
y ^ ( k ) = f ^ ( u ( k ) ) = W 1 tanh ( W 2 u ( k ) + s 1 ) + s 2 .
{ y ( 1 ) = a f ^ ( x + u ( 1 ) ) y ( 2 ) = a f ^ ( x + u ( 2 ) ) y ( K ) = a f ^ ( x + u ( K ) )
( a ^ , x ^ ) = argmin a ^ , x ^ || Y [ 1 , K ] Y ^ [ 1 , K ] || 2 2 J ( a ^ , x ^ ) ,
Y [ 1 , K ] = [ y ( 1 ) y ( 2 ) y ( K ) ] , Y ^ [ 1 , K ] = [ y ^ ( 1 ) y ^ ( 2 ) y ^ ( K ) ] = [ a ^ f ^ ( x ^ + u ( 1 ) ) a ^ f ^ ( x ^ + u ( 2 ) ) a ^ f ^ ( x ^ + u ( K ) ) ] .
( W 1 , W 2 , s 1 , s 2 ) = arg min ( W 1 * , W 2 * , s 1 * , s 2 * ) 1 N t Σ k = 1 N t ( y ( k ) y ^ ( k ) ) 2 .
VAF ( y ^ , y ) = ( 1 var ( y ^ y ) var ( y ) ) × 100 % .

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