Mitigation of vibrations in adaptive optics by minimization of closed-loop residuals |
Optics Express, Vol. 21, Issue 9, pp. 10676-10696 (2013)
http://dx.doi.org/10.1364/OE.21.010676
Acrobat PDF (1119 KB)
Abstract
We describe a new technique to reduce tip and tilt vibrations via the design of adaptive optics controllers in a frequency framework. The method synthesizes controllers by minimizing an H_{2} norm of the tip and tilt residuals. In this approach, open loop slopes (pseudo-open-loop) are reconstructed from on-sky data and input into off-line simulations of the adaptive optics system. The proposed procedure executes a sequence of off-line closed-loop runs with increasing controller complexity and searches for the controller that minimizes the variance of residuals. Although the method avoids any identification of the vibration and turbulence models during the controller synthesis, the actual models are indirectly constructed as a by-product of the H_{2} norm minimization. The technique has been implemented on and tested with two operational instruments, namely Paranal’s NACO and Gemini-South’s GeMS, showing an effective rejection of the main vibrations in the loop and also improving the overall performance of the system over varying turbulence conditions. It is shown that a superior performance is obtained when compared to the standard integrator controller.
© 2013 OSA
1. Introduction
1. C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics Systems III, 84471C (2012).
3. C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26(6), 1307–1325 (2009). [CrossRef] [PubMed]
4. C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II , 62721T (2006). [CrossRef]
6. G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control 17(3), 316–326 (2011). [CrossRef]
8. E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract. 17(1), 122–135 (2009). [CrossRef]
9. B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A 21(7), 1261–1276 (2004). [CrossRef]
10. 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(17), 7464–7476 (2006). [CrossRef] [PubMed]
11. A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51(19), 4520–4535 (2012). [CrossRef] [PubMed]
- i) Advanced controllers (LQG & H_{∞}) perform similarly. This is not surprising since both techniques use models for vibrations and turbulence and the design of the controllers is based on the minimization of the closed-loop residuals
- ii) Although frequency based approaches (H_{∞} / H_{2}) and LQG solutions are equivalent provided that dynamics of the mirror and resonances can be introduced in the problem formulation, the main difference between these two approaches lies in the way these dynamical modes are introduced in the modeling. In [12] a method of including mirror dynamics has been proposed, but its implementation in an unsupervised procedure like the one presented in this article is not clear.
12. C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27(2), 333–349 (2010). [CrossRef] [PubMed]
- iii) Compared to the standard integrator, substantial reductions (20 to 30% for the cited work) in the variance seems plausible using advanced controllers such as LQG or H_{∞}, but only if they are correctly matched to the actual disturbances
- iv) When large model errors are present in these techniques, the gains in performance provided by the advanced controllers are lost, showing no clear difference with the classical integrator. Hence, a regular updating of the controller is mandatory
- (i) In spite of identifying the disturbance models correctly, very often the power spectral density (PSD) of the AO loop residuals differs from the expected flat response of LQG, H_{2} or H_{∞} methods. This is due not only to the varying characteristics of the disturbance, but also to unmodeled dynamics or non-linearities in the AO components.
- (ii) According to Bode’s theorem and H_{2}/H_{∞} theory, imbalances in the closed-loop residual spectrum will drive the performance away from the optimum. For instance, over-rejected frequencies worsen the performance in other parts of the spectrum.
9. B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A 21(7), 1261–1276 (2004). [CrossRef]
10. 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(17), 7464–7476 (2006). [CrossRef] [PubMed]
13. C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A 29(3), 185–194 (2012). [CrossRef] [PubMed]
15. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef]
2. Controller theory
2.1. Integrator
2.2. H_{2} control
15. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef]
15. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef]
11. A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51(19), 4520–4535 (2012). [CrossRef] [PubMed]
- - H_{2} is intuitive since it minimizes a quadratic norm containing the variance of residuals
- - H_{∞} seeks to flatten a mixed norm of residuals and noise when this may be difficult to achieve due to the mirror’s limited bandwidth.
- - H_{2} is more efficient in terms of computation since it does not require a search for the optimum as required in the H_{∞} case [15]. Our first approximation to this method was carried out using the H_{∞} synthesis, but it proved inadequate due to the excessive processing time required. The H_{∞} approach involves a binary search with unknown convergence speed, which translates into an unpredictable (and usually high) number of Riccati solution calculations.
15. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef]
15. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef]
3. C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26(6), 1307–1325 (2009). [CrossRef] [PubMed]
3. Astronomical adaptive optics systems used
3.1. GeMS
17. B. L. Ellerbroek and F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18(10), 2539–2547 (2001). [CrossRef] [PubMed]
18. B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE 8447, Adaptive Optics Systems III , 84474Q (2012).
3.2. NACO
19. G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE . 4839, Adaptive Optical System Technologies II, 140 (2003).
4. Procedure to tune the tip-tilt loop
4.1 The cost function: variance of residuals
8. E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract. 17(1), 122–135 (2009). [CrossRef]
20. 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(11), A122–A132 (2010). [CrossRef] [PubMed]
8. E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract. 17(1), 122–135 (2009). [CrossRef]
11. A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51(19), 4520–4535 (2012). [CrossRef] [PubMed]
4.2 Loop delay and mirror dynamics
12. C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27(2), 333–349 (2010). [CrossRef] [PubMed]
4.3 The tuning sequence
21. 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(7), 1559–1570 (1995). [CrossRef]
4.3.1 Step 1: the fixed gain integrator
4.3.2 Step 2: the optimal integrator
4.3.3 Step 3: the first order model or leaky integrator
23. J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965). [CrossRef]
4.3.4 Step 4: first order plus 1 notch
8. E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract. 17(1), 122–135 (2009). [CrossRef]
4.4. Step 5: first order plus 2 notches
4. C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II , 62721T (2006). [CrossRef]
13. C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A 29(3), 185–194 (2012). [CrossRef] [PubMed]
- a) Estimate function W_{y} based on the temporal PSD of the tip or tilt at higher frequencies
- b) Define a parameterized function W_{e} formed by the first order function in Eq. (23) with an initial value for C_{0} and C_{1} (unity for instance).
- c) Construct the state space model of P(s) as in Eq. (4). This model contains the dynamics of W_{e} and W_{y} defined above.
- e) Repeat steps b), c) and d) for different values of C_{0} and C_{1} till the variance estimated by Eq. (21) reaches a minimum. This can be done with any standard minimum search techniques. Register the optimal parameters C_{0}* and C_{1}*
- f) Define a new W_{y} function as the product of the first order function found in e) with a notch filter as defined in Eq. (24)
- g) Construct the state space model of the new P(s) as in Eq. (4).
- i) Using gradient search techniques, find the optimal parameters η_{1} and η_{2} with ω_{o}* fixed
- j) Repeat steps f) thru i) with increasing number of notch filters until the reduction in the variance of residual reaches a value below a threshold defined by the user
- k) Perform a final minimization, this time for all the parameters and starting from the values found in the previous step. This will speed up convergence.
4.5 Validation of the method with NACO
5. On-line implementation at GeMS
5.1. Results from calibration source
5.2. On-sky implementation
6. Implementation issues
11. A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51(19), 4520–4535 (2012). [CrossRef] [PubMed]
7. Conclusion
Acknowledgments
References
1. | C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics Systems III, 84471C (2012). |
2. | J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III , 844711 (2010). |
3. | C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26(6), 1307–1325 (2009). [CrossRef] [PubMed] |
4. | C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II , 62721T (2006). [CrossRef] |
5. | B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011). |
6. | G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control 17(3), 316–326 (2011). [CrossRef] |
7. | J. M. Conan, H. F. Raynaud, C. Kulcsár, and S. Meimon, “Are integral controllers adapted to the new era of ELT adaptive optics?” Proc. of the 2nd AO4ELT Conference (2011). |
8. | E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract. 17(1), 122–135 (2009). [CrossRef] |
9. | B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A 21(7), 1261–1276 (2004). [CrossRef] |
10. | 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(17), 7464–7476 (2006). [CrossRef] [PubMed] |
11. | A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51(19), 4520–4535 (2012). [CrossRef] [PubMed] |
12. | C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27(2), 333–349 (2010). [CrossRef] [PubMed] |
13. | C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A 29(3), 185–194 (2012). [CrossRef] [PubMed] |
14. | J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998). |
15. | J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H_{∞} control problems,” IEEE Trans. Automat. Contr. 34(8), 831–847 (1989). [CrossRef] |
16. | A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE . 8447, Adaptive Optics Systems III , 844711 (2012). |
17. | B. L. Ellerbroek and F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18(10), 2539–2547 (2001). [CrossRef] [PubMed] |
18. | B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE 8447, Adaptive Optics Systems III , 84474Q (2012). |
19. | G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE . 4839, Adaptive Optical System Technologies II, 140 (2003). |
20. | 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(11), A122–A132 (2010). [CrossRef] [PubMed] |
21. | 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(7), 1559–1570 (1995). [CrossRef] |
22. | E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys. 291, 337 (1994). |
23. | J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965). [CrossRef] |
OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(350.1260) Other areas of optics : Astronomical optics
(010.1285) Atmospheric and oceanic optics : Atmospheric correction
ToC Category:
Adaptive Optics
History
Original Manuscript: January 25, 2013
Revised Manuscript: April 15, 2013
Manuscript Accepted: April 20, 2013
Published: April 24, 2013
Citation
Andres Guesalaga, Benoit Neichel, Jared O’Neal, and Dani Guzman, "Mitigation of vibrations in adaptive optics by minimization of closed-loop residuals," Opt. Express 21, 10676-10696 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10676
Sort: Year | Journal | Reset
References
- C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).
- J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III,844711 (2010).
- C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009). [CrossRef] [PubMed]
- C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006). [CrossRef]
- B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).
- G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011). [CrossRef]
- J. M. Conan, H. F. Raynaud, C. Kulcsár, and S. Meimon, “Are integral controllers adapted to the new era of ELT adaptive optics?” Proc. of the 2nd AO4ELT Conference (2011).
- E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract.17(1), 122–135 (2009). [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 adaptative optics,” J. Opt. Soc. Am. A21(7), 1261–1276 (2004). [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. Express14(17), 7464–7476 (2006). [CrossRef] [PubMed]
- A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012). [CrossRef] [PubMed]
- C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010). [CrossRef] [PubMed]
- C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A29(3), 185–194 (2012). [CrossRef] [PubMed]
- J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).
- J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989). [CrossRef]
- A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).
- B. L. Ellerbroek and F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A18(10), 2539–2547 (2001). [CrossRef] [PubMed]
- B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).
- G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).
- 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. A27(11), A122–A132 (2010). [CrossRef] [PubMed]
- J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995). [CrossRef]
- E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).
- J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965). [CrossRef]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
Figures
Fig. 1 | Fig. 2 | Fig. 3 |
Fig. 4 | Fig. 5 | Fig. 6 |
Fig. 7 | Fig. 8 | Fig. 9 |
Fig. 10 | Fig. 11 | Fig. 12 |
Fig. 13 | Fig. 14 | Fig. 15 |
Fig. 16 | Fig. 17 | |
« Previous Article | Next Article »
OSA is a member of CrossRef.