Vibration suppression in astronomical adaptive optics (AO) systems has gathered great attention in the context of next-generation instrumentation for current telescopes and future Extremely Large Telescopes. Laser tomographic AO systems require natural guide stars to measure the low-order modes such as tip–tilt (TT) and TT-anisoplanatism. To increase the sky coverage, the guide stars are often faint, thus requiring lower temporal sampling frequencies to work on a more favorable signal-to-noise regime. Such sampling frequencies can be of the order of, or even lower than, the range of frequencies where vibrations are likely to appear. Ideally, vibrations affecting the low-order modes could be corrected at the higher laser loop frame rate using an upsampling procedure. This paper compares the most relevant solutions proposed hitherto to a novel multirate algorithm using the linear-quadratic-Gaussian (LQG) approach capable of upsampling the correction to further reduce the impact of vibrations. Results from numerical Monte Carlo simulations span a large range of parameters from pure sinusoids to relatively broad peak vibrations, covering the likely-to-be signals in a realistic AO system. The improvement is shown at sampling frequencies from 20 to 800 Hz, including below the vibration itself, in the example of 29.5 Hz on a Thirty Meter Telescope-like scenario. The multirate LQG ensures the least residual for both faint and bright stars for all the peak widths considered based on telemetry from the Keck Observatory.

© 2012 Optical Society of America

1. F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
2. J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford, 1998).
3. Y. Clenet, M. E. Kasper, N. Ageorges, C. Lidman, T. Fusco, O. Marco, M. Hartung, D. Mouillet, B. Koehler, G. Rousset, and N. N. Hubin, “NACO performance: status after 2 years of operation,” Proc. SPIE 5490, 107–117 (2004). [CrossRef]
4. J.-P. Veran and L. Poyneer, “Characterization of the T/T conditions at Gemini using adaptive optics telemetry data,” in Proceedings of 1st AO4ELT Conference—Adaptative Optics for Extremely Large Telescopes, T. F. Y. Clénet, J.-M. Conan, and G. Rousset, eds. (EDP Sciences, 2009), paper 05002.
5. M. Hess, C. E. Nance, J. W. Vause, M. Hrynevych, M. R. Swain, and M. Colavita, “Strategy for identifying and mitigating facility vibrations to improve optical performance at the W. M. Keck Observatory,” Proc. SPIE 4837, 342–351 (2003). [CrossRef]
6. J. Borelli, J. Trowitzsch, M. Brix, M. Kürster, W. Gässler, T. Bertram, and F. Briegel, “The LBT real-time based control software to mitigate and compensate vibrations,” Proc. SPIE 7740, 774005 (2010). [CrossRef]
7. S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “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]
8. 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]
9. L. Wang, B. Ellerbroek, and J. P. Veran, “High fidelity sky coverage analysis via time domain adaptive optics simulations,” Appl. Opt. 48, 5076–5087 (2009). [CrossRef]
10. N. D. Lieto, P. Haguenauer, J. Sahlmann, and G. Vasisht, “Adaptive vibration cancellation on large telescopes for stellar interferometry,” Proc. SPIE 7013, 70130H (2008). [CrossRef]
11. J. Véran, C. Irving, A. Beauvillier, and G. Herriot, “Implementation of type-II tip-tilt control in NFIRAOS with woofer-tweeter and vibration cancellation,” Proc. SPIE 7736, 77364I (2010). [CrossRef]
12. H. F. Raynaud, C. Kulcsár, C. Correia da Silva, and J.-M. Conan, “Multirate LQG AO control,” Proc. SPIE 7015, 701538 (2008). [CrossRef]
13. B. D. O. Anderson and J. B. Moore, Optimal Filtering (Dover, 1995).
14. C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirroir dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010). [CrossRef]
15. 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]
16. A. V. Oppenheim and A. S. Willsky, Signals & Systems, 2nd ed. (Prentice-Hall, 1997).
17. H.-F. Raynaud, C. Correia, C. Kulcsár, and J.-M. Conan, “Minimum-variance control of astronomical adaptive optics systems with actuator dynamics under synchronous and asynchronous sampling,” Int. J. Robust Nonlinear Control 21, 768–789 (2011). [CrossRef]
18. T. Söderström, Discrete-Time Stochastic Systems, Advanced Textbooks in Control and Signal Processing (Springer-Verlag, 2002).
19. B. Ellerbroek, S. Adkins, D. Andersen, J. Atwood, S. Browne, C. Boyer, P. Byrnes, K. Caputa, R. Conan, R. Cousty, D. Erikson, J. Fitzsimmons, F. Gamache, L. Gilles, G. Herriot, P. Hickson, O. Lardier, P. Morin, J. Pazder, T. Pfrommer, D. Quinn, V. Reshetov, S. Roberts, J.-C. Sinquin, M. Schoeck, M. Smith, G. Tyler, J. Vaughn, J.-P. Veran, C. Vogel, L. Wang, and I. Wevers, “First light adaptive optics systems and components for the thirty meter telescope,” Proc. SPIE 7736, 773604 (2010). [CrossRef]
20. G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, “NFIRAOS: TMT’s facility adaptive optics system,” Proc. SPIE 7736, 77360B (2010). [CrossRef]
21. S. D’Odorico, S. Ramsay, N. Hubin, J. C. Gonzales, and F. M. Zerbi, “An introduction to the E-ELT instrumentation and post-focal adaptive optics module studies,” Messenger 140, 17 (2010).
22. W. Skidmore, T. Travouillon, R. Riddle, K. Kinoshita, R. Johnston, P. Murg, H. Thompson, R. Matsuda, M. Colavita, G. Tolleth, R. Goodrich, E. Chock, H. Lewis, and S. Panteleev, “Experiments at the W. M. Keck Observatory to support the Thirty Meter Telescope design work,” Proc. SPIE 7733773350 (2010). [CrossRef]

Appl. Opt.

• L. Wang, B. Ellerbroek, and J. P. Veran, “High fidelity sky coverage analysis via time domain adaptive optics simulations,” Appl. Opt. 48, 5076–5087 (2009). [CrossRef]

Int. J. Robust Nonlinear Control

• H.-F. Raynaud, C. Correia, C. Kulcsár, and J.-M. Conan, “Minimum-variance control of astronomical adaptive optics systems with actuator dynamics under synchronous and asynchronous sampling,” Int. J. Robust Nonlinear Control 21, 768–789 (2011). [CrossRef]

J. Opt. Soc. Am. A

• C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirroir dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010). [CrossRef]
• S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “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]
• 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]

Messenger

• S. D’Odorico, S. Ramsay, N. Hubin, J. C. Gonzales, and F. M. Zerbi, “An introduction to the E-ELT instrumentation and post-focal adaptive optics module studies,” Messenger 140, 17 (2010).

Opt. Express

• 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]

Proc. SPIE

• N. D. Lieto, P. Haguenauer, J. Sahlmann, and G. Vasisht, “Adaptive vibration cancellation on large telescopes for stellar interferometry,” Proc. SPIE 7013, 70130H (2008). [CrossRef]
• J. Véran, C. Irving, A. Beauvillier, and G. Herriot, “Implementation of type-II tip-tilt control in NFIRAOS with woofer-tweeter and vibration cancellation,” Proc. SPIE 7736, 77364I (2010). [CrossRef]
• H. F. Raynaud, C. Kulcsár, C. Correia da Silva, and J.-M. Conan, “Multirate LQG AO control,” Proc. SPIE 7015, 701538 (2008). [CrossRef]
• M. Hess, C. E. Nance, J. W. Vause, M. Hrynevych, M. R. Swain, and M. Colavita, “Strategy for identifying and mitigating facility vibrations to improve optical performance at the W. M. Keck Observatory,” Proc. SPIE 4837, 342–351 (2003). [CrossRef]
• Y. Clenet, M. E. Kasper, N. Ageorges, C. Lidman, T. Fusco, O. Marco, M. Hartung, D. Mouillet, B. Koehler, G. Rousset, and N. N. Hubin, “NACO performance: status after 2 years of operation,” Proc. SPIE 5490, 107–117 (2004). [CrossRef]
• W. Skidmore, T. Travouillon, R. Riddle, K. Kinoshita, R. Johnston, P. Murg, H. Thompson, R. Matsuda, M. Colavita, G. Tolleth, R. Goodrich, E. Chock, H. Lewis, and S. Panteleev, “Experiments at the W. M. Keck Observatory to support the Thirty Meter Telescope design work,” Proc. SPIE 7733773350 (2010). [CrossRef]
• B. Ellerbroek, S. Adkins, D. Andersen, J. Atwood, S. Browne, C. Boyer, P. Byrnes, K. Caputa, R. Conan, R. Cousty, D. Erikson, J. Fitzsimmons, F. Gamache, L. Gilles, G. Herriot, P. Hickson, O. Lardier, P. Morin, J. Pazder, T. Pfrommer, D. Quinn, V. Reshetov, S. Roberts, J.-C. Sinquin, M. Schoeck, M. Smith, G. Tyler, J. Vaughn, J.-P. Veran, C. Vogel, L. Wang, and I. Wevers, “First light adaptive optics systems and components for the thirty meter telescope,” Proc. SPIE 7736, 773604 (2010). [CrossRef]
• G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, “NFIRAOS: TMT’s facility adaptive optics system,” Proc. SPIE 7736, 77360B (2010). [CrossRef]

Other

• J.-P. Veran and L. Poyneer, “Characterization of the T/T conditions at Gemini using adaptive optics telemetry data,” in Proceedings of 1st AO4ELT Conference—Adaptative Optics for Extremely Large Telescopes, T. F. Y. Clénet, J.-M. Conan, and G. Rousset, eds. (EDP Sciences, 2009), paper 05002.
• F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
• J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford, 1998).
• J. Borelli, J. Trowitzsch, M. Brix, M. Kürster, W. Gässler, T. Bertram, and F. Briegel, “The LBT real-time based control software to mitigate and compensate vibrations,” Proc. SPIE 7740, 774005 (2010). [CrossRef]
• B. D. O. Anderson and J. B. Moore, Optimal Filtering (Dover, 1995).
• A. V. Oppenheim and A. S. Willsky, Signals & Systems, 2nd ed. (Prentice-Hall, 1997).
• T. Söderström, Discrete-Time Stochastic Systems, Advanced Textbooks in Control and Signal Processing (Springer-Verlag, 2002).

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