Abstract

To achieve high-resolution imaging the standard control algorithm used for classical adaptive optics (AO) is the simple but efficient proportional–integral (PI) controller. The goal is to minimize the rms error of the residual wave front. However, using the PI controller, it is not possible to do this. One possible way to minimize the rms error is to use linear quadratic Gaussian (LQG) control. In practice, however, this control algorithm still encounters an unexpected problem that leads to the divergence of control in AO. This paper proposes a modified LQG (MLQG) to solve this issue. The controller is analyzed explicitly. Laboratory tests shows strong stability and high precision compared to the classical control.

© 2014 Optical Society of America

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  3. C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
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  7. C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).
  8. C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).
  9. C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
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  30. T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
    [CrossRef]
  31. T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
    [CrossRef]
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    [CrossRef]
  34. P. Kim, J. An, and K. You, “A fuzzy adaptive fading Kalman filter approach for accuracy improvement of a laser interferometer,” in Computer Applications for Security, Control and System Engineering (Springer, 2012), pp. 245–253.
  35. C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
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    [CrossRef]

2011

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

D. P. Looze, “Structure of LQG controllers based on a hybrid adaptive optics system model,” Eur. J. Control 17, 237–248 (2011).
[CrossRef]

2010

2009

2008

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

L. A. Poyneer and J.-P. Véran, “Predictive wavefront control for adaptive optics with arbitrary control loop delays,” J. Opt. Soc. Am. A 25, 1486–1496 (2008).
[CrossRef]

2007

P. Piatrou and M. C. Roggemann, “Performance study of Kalman filter controller for multiconjugate adaptive optics,” J. Opt. A 46, 1446–1455 (2007).
[CrossRef]

2006

2005

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

2004

2003

C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low-cost INS/GPS,” J. Navigat. 56, 143–152 (2003).
[CrossRef]

2002

D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890–901 (2002).
[CrossRef]

1998

1995

1994

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

E. Gendron and P. Lena, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

E. Gendron and P. Lena, “Astronomical adaptive optics II. Experimental results of an optimized modal control,” Astron. Astrophys. 111, 153–167 (1994).

1993

R. N. Paschall and D. J. Anderson, “Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” J. Opt. A 32, 6347–6358 (1993).
[CrossRef]

1976

An, J.

P. Kim, J. An, and K. You, “A fuzzy adaptive fading Kalman filter approach for accuracy improvement of a laser interferometer,” in Computer Applications for Security, Control and System Engineering (Springer, 2012), pp. 245–253.

Anderson, D. J.

R. N. Paschall and D. J. Anderson, “Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” J. Opt. A 32, 6347–6358 (1993).
[CrossRef]

Baudoz, P.

Beuzit, J.-L.

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

Charton, J.

Chemla, F.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Conan, J.-M.

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

Conan, R.

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

Correia, C.

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

C. Correia, J.-P. Véran, and L. Poyneer, “Gemini planet imager minimum-variance tip-tilt controllers,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Dessenne, C.

Doelman, N.

R. Fraanje, J. Rice, M. Verhaegen, and N. Doelman, “Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering,” J. Opt. Soc. Am. A 27, A235–A245 (2010).
[CrossRef]

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

Dohlen, K.

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

Ellerbroek, B.

L. Gilles and B. Ellerbroek, “Computationally efficient, practical implementation of tomographic minimum variance wavefront control using laser and natural guide stars for MCAO and MOAO,” Proceedings of European Control Conference, Budapest, Hungary (2009).

Fraanje, R.

Fusco, T.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, A122–A132 (2010).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

Gavel, D.

D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890–901 (2002).
[CrossRef]

Gendron, E.

E. Gendron and P. Lena, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

E. Gendron and P. Lena, “Astronomical adaptive optics II. Experimental results of an optimized modal control,” Astron. Astrophys. 111, 153–167 (1994).

Gilles, L.

L. Gilles and B. Ellerbroek, “Computationally efficient, practical implementation of tomographic minimum variance wavefront control using laser and natural guide stars for MCAO and MOAO,” Proceedings of European Control Conference, Budapest, Hungary (2009).

Guesalaga, A.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Guzman, D.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

Hide, C.

C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low-cost INS/GPS,” J. Navigat. 56, 143–152 (2003).
[CrossRef]

Hinnen, K.

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

Kasper, M.

Kim, P.

P. Kim, J. An, and K. You, “A fuzzy adaptive fading Kalman filter approach for accuracy improvement of a laser interferometer,” in Computer Applications for Security, Control and System Engineering (Springer, 2012), pp. 245–253.

Kulcsár, C.

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
[CrossRef]

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, A122–A132 (2010).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

Le Roux, B.

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

Lena, P.

E. Gendron and P. Lena, “Astronomical adaptive optics II. Experimental results of an optimized modal control,” Astron. Astrophys. 111, 153–167 (1994).

E. Gendron and P. Lena, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

Looze, D. P.

Macintosh, B. A.

Madec, P.-Y.

Meimon, S.

Montagnier, G.

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

Montri, J.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

Moore, T.

C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low-cost INS/GPS,” J. Navigat. 56, 143–152 (2003).
[CrossRef]

Mouillet, D.

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

Mugnier, L. M.

Neichel, B.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Nicolle, M.

Noll, R. J.

Paschall, R. N.

R. N. Paschall and D. J. Anderson, “Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” J. Opt. A 32, 6347–6358 (1993).
[CrossRef]

Petit, C.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, A122–A132 (2010).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

Piatrou, P.

P. Piatrou and M. C. Roggemann, “Performance study of Kalman filter controller for multiconjugate adaptive optics,” J. Opt. A 46, 1446–1455 (2007).
[CrossRef]

Poyneer, L.

C. Correia, J.-P. Véran, and L. Poyneer, “Gemini planet imager minimum-variance tip-tilt controllers,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Poyneer, L. A.

Puget, P.

Rabaud, D.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

Rao, M.

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

Raynaud, H.-F.

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

Rice, J.

Rigaut, F.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Rodriguez, I.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

Roggemann, M. C.

P. Piatrou and M. C. Roggemann, “Performance study of Kalman filter controller for multiconjugate adaptive optics,” J. Opt. A 46, 1446–1455 (2007).
[CrossRef]

Rousset, G.

T. Fusco, G. Rousset, J.-F. Sauvage, C. Petit, J.-L. Beuzit, K. Dohlen, D. Mouillet, J. Charton, M. Nicolle, M. Kasper, P. Baudoz, and P. Puget, “High-order adaptive optics requirements for direct detection of extrasolar planets: application to the SPHERE instrument,” Opt. Express 14, 7515–7534 (2006).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

C. Dessenne, P.-Y. Madec, and G. Rousset, “Optimization of a predictive controller for closed-loop adaptive optics,” Appl. Opt. 37, 4623–4633 (1998).
[CrossRef]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

Sauvage, J.-F.

Shen, X.

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

Smith, M.

C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low-cost INS/GPS,” J. Navigat. 56, 143–152 (2003).
[CrossRef]

Véran, J.-P.

Verhaegen, M.

R. Fraanje, J. Rice, M. Verhaegen, and N. Doelman, “Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering,” J. Opt. Soc. Am. A 27, A235–A245 (2010).
[CrossRef]

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

Viaris de Lesegno, P.

Wiberg, D.

D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890–901 (2002).
[CrossRef]

Xia, Q.

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

Ying, Y.

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

You, K.

P. Kim, J. An, and K. You, “A fuzzy adaptive fading Kalman filter approach for accuracy improvement of a laser interferometer,” in Computer Applications for Security, Control and System Engineering (Springer, 2012), pp. 245–253.

Appl. Opt.

Astron. Astrophys.

E. Gendron and P. Lena, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

E. Gendron and P. Lena, “Astronomical adaptive optics II. Experimental results of an optimized modal control,” Astron. Astrophys. 111, 153–167 (1994).

Automatica

Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica 30, 1333–1338 (1994).
[CrossRef]

Comptes Rendus Physique

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Optimal control for multi-conjugate adaptive optics,” Comptes Rendus Physique 6, 1059–1069 (2005).
[CrossRef]

Eur. J. Control

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for astronomical adaptive optics with resonant deformable mirrors,” Eur. J. Control 17, 222–236 (2011).
[CrossRef]

D. P. Looze, “Structure of LQG controllers based on a hybrid adaptive optics system model,” Eur. J. Control 17, 237–248 (2011).
[CrossRef]

IEEE Trans. Control Syst. Technol.

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2-optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

J. Navigat.

C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low-cost INS/GPS,” J. Navigat. 56, 143–152 (2003).
[CrossRef]

J. Opt. A

R. N. Paschall and D. J. Anderson, “Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” J. Opt. A 32, 6347–6358 (1993).
[CrossRef]

P. Piatrou and M. C. Roggemann, “Performance study of Kalman filter controller for multiconjugate adaptive optics,” J. Opt. A 46, 1446–1455 (2007).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

L. A. Poyneer and B. A. Macintosh, “Spatially filtered wavefront sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810–819 (2004).
[CrossRef]

L. A. Poyneer and J.-P. Véran, “Predictive wavefront control for adaptive optics with arbitrary control loop delays,” J. Opt. Soc. Am. A 25, 1486–1496 (2008).
[CrossRef]

L. A. Poyneer and J.-P. Véran, “Kalman filtering to suppress spurious signals in adaptive optics control,” J. Opt. Soc. Am. A 27, A223–A234 (2010).
[CrossRef]

T. Fusco, C. Petit, G. Rousset, J.-M. Conan, and J.-L. Beuzit, “Closed-loop experimental validation of the spatially filtered Shack–Hartmann concept,” J. Opt. Soc. Am. A 30, 1255–1257(2005).

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, A122–A132 (2010).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

D. P. Looze, “Minimum variance control structure for adaptive optics systems,” J. Opt. Soc. Am. A 23, 603–612 (2006).
[CrossRef]

D. P. Looze, “Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model,” J. Opt. Soc. Am. A 26, 1–9 (2009).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Minimum-variance control for woofer–tweeter systems in adaptive optics,” J. Opt. Soc. Am. A 27, A133–A144 (2010).
[CrossRef]

R. Fraanje, J. Rice, M. Verhaegen, and N. Doelman, “Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering,” J. Opt. Soc. Am. A 27, A235–A245 (2010).
[CrossRef]

Opt. Express

Proc. SPIE

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, and G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE 5903, 59030K (2005).
[CrossRef]

D. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890–901 (2002).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “Globally optimal minimum-variance control in adaptive optical systems with mirror dynamics,” Proc. SPIE 7015, 70151F (2008).

Other

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

L. Gilles and B. Ellerbroek, “Computationally efficient, practical implementation of tomographic minimum variance wavefront control using laser and natural guide stars for MCAO and MOAO,” Proceedings of European Control Conference, Budapest, Hungary (2009).

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” Proceedings of Adaptive Optics for Extremely Large Telescopes (AO4ELT), Paris, France (2010).

C. Correia, J.-P. Véran, and L. Poyneer, “Gemini planet imager minimum-variance tip-tilt controllers,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and B. Le Roux, “Optimality, observers and controllers in adaptive optics,” Adaptive Optics: Methods, Analysis and Applications, Charlotte, North Carolina, (2005).

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” Adaptive Optics: Methods, Analysis and Applications, Toronto, Canada (2011).

P. Kim, J. An, and K. You, “A fuzzy adaptive fading Kalman filter approach for accuracy improvement of a laser interferometer,” in Computer Applications for Security, Control and System Engineering (Springer, 2012), pp. 245–253.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the closed-loop model of AO.

Fig. 2.
Fig. 2.

Statistical turbulence of the PS. (a) PSD of angle of arrival under the wind speed 1°/s. (b) Variance of Zernike coefficients of wavefront. The triangle line represents the theoretical values.

Fig. 3.
Fig. 3.

Parameters variation in the closed loop on 5°/s of the PS. (a)  λ variation with the time. (b) Gain L k variation with the time. The black crosses in the circle are the filtered states when the abrupt noise happens.

Fig. 4.
Fig. 4.

Residual errors’ rms compares to that of an open loop when the distorted wavefront is corrected by different methods, including MLQG, LQG, and PI at 1°/s of rotation speed of PS.

Fig. 5.
Fig. 5.

Closed-loop PSD with different algorithms. Open loop is on the blue line. Closed loop with PI algorithm is on the red-long-dash line. Closed loop with MLQG algorithm is on the black-short-dash line. (a) PSD of the 1ed Zernike mode (tip). (b) third Zernike mode (defocusing). (c) fifth Zernike mode. (d) 52nd (the last mode) Zernike mode.

Fig. 6.
Fig. 6.

Closed-loop PSF after correction with LQG controlling method at the different wind speeds (1°/s, 3°/s, 5°/s). The intensity is normalized for all images.

Fig. 7.
Fig. 7.

Power spectrum comparison of open loop and closed loop with PI and LQG methods at the rotation speed at 1°/s. (a) The power spectrums of open loop and closed loop with LQG and PI methods. (b) The rejection function of PI control and LQG control.

Fig. 8.
Fig. 8.

Long exposure PSF images. The first three maps are 200 × 200 pixels. The last one is 400 × 400 pixels (a) open loop without PS. (b) Closed loop with LQG method when PS speed is at 1°/s. (c) Closed loop with PI method when PS speed is at 1°/s. (d) Open loop when PS is at 1°/s.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

x k + 1 = A x k + B u k + v k
z k = H x k + w k .
φ k + 1 = A s φ k + v k ,
x k = ( φ k u k ) .
u k + 1 = u k + G S k ,
u k + 1 = P ϕ k + 1 / k .
P = ( N T N ) 1 N T ,
x k + 1 / k = A x k / k 1 + B u k + A L ( y k H k y ¯ k ) .
L = C k H k T ( H k C k H k T + C w ) 1 ,
C ν = C x A T C x A ,
C k + 1 / k = A C k / k 1 A T + C ν A C k / k 1 H k T ( H k C k H k T + C w ) 1 H k C k A T .
u k = P ϕ k + 1 / k tur ,
J = lim n + 1 n ( k = 1 n 1 T ( k 1 ) T k T | ϕ ϕ k | 2 d s ) + lim n + 1 n k = 1 n | ϕ k N u k | 2 = J r , 1 + J r , 2 .
C k / k 1 = λ k A k / k 1 C k 1 A k / k 1 T + Q k 1 ,
C k = ( I L k H k ) C k / k 1 ,
d k = Z k H k X k / k 1 ,
E [ d k , d k T ] = H k C k / k 1 H k T + R k .
| d k ( i ) | W H k C k / k 1 H k T + R k ( i , i ) ,
V j ( k ) = E [ d k , d k 1 T ] 0 , ( j 0 ) .
V j ( k ) = H k + j A k + j 1 ( I L k + j 1 H k + j 1 ) A k + 1 ( I L k + 1 H k + 1 ) A k [ C k / k 1 H k T L k V 0 ( k ) ] , ( j 0 ) ,
C k / k 1 H k T L k V 0 ( k ) = 0 .
λ k = max { 1 , 1 n tr [ N k M k 1 ] } ,
λ k = max { 1 , α tr [ N k ] / tr [ M k ] } .
L = C k / k 1 H T [ H C k / k 1 H T + R ] 1 ,
C k / k 1 = λ k A C k / k 1 A T + Q ,
C k = [ I L k H ] C k / k 1 .

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