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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 17 — Aug. 21, 2006
  • pp: 7464–7476

Optimal control, observers and integrators in adaptive optics

Caroline Kulcsár, Henri-François Raynaud, Cyril Petit, Jean-Marc Conan, and Patrick Viaris de Lesegno  »View Author Affiliations


Optics Express, Vol. 14, Issue 17, pp. 7464-7476 (2006)
http://dx.doi.org/10.1364/OE.14.007464


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Abstract

The fundamental issue of residual phase variance minimization in adaptive optics (AO) loops is addressed here from a control engineering perspective. This problem, when suitably modeled using a state-space approach, can be broken down into an optimal deterministic control problem and an optimal estimation problem, the solution of which are a linear quadratic (LQ) control and a Kalman filter. This approach provides a convenient framework for analyzing existing AO controllers, which are shown to contain an implicit phase turbulent model. In particular, standard integrator-based AO controllers assume a constant turbulent phase, which renders them prone to the notorious wind-up effect.

© 2006 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

ToC Category:
Focus Issue: Adaptive Optics

History
Original Manuscript: April 3, 2006
Revised Manuscript: June 23, 2006
Manuscript Accepted: August 10, 2006
Published: August 21, 2006

Citation
Caroline Kulcsár, Henri-François Raynaud, Cyril Petit, Jean-Marc Conan, and Patrick Viaris de Lesegno, "Optimal control, observers and integrators in adaptive optics," Opt. Express 14, 7464-7476 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7464


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References

  1. F. Roddier (Ed.), Adaptive Optics in Astronomy, (Cambridge University Press, 1999). [CrossRef]
  2. T. Fusco, G. Rousset, J.-L. Beuzit, D. Mouillet, K. Dohlen, R. Conan, C. Petit, G. Montagnier, “Conceptual design of an extreme AO dedicated to extra-solar planet detection by the VLT-planet finder instrument,” Proc. SPIE, 5903, (2005). [CrossRef]
  3. R.H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605–615 (1975).
  4. D.C. Johnson, B.M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]
  5. Comptes Rendus de l’Académie des Sciences, Adaptive Optics in Astronomy, (Elsevier, France, Comptes Rendus Physique, 2005) Vol. 6, Num. 10.
  6. G. Rousset, F. Lacombe, et al. “NAOS, the first AO system of the VLT: on sky performance,” Proc. SPIE 4839, 140–149 (2002). [CrossRef]
  7. B. Le Roux, J.-M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004). [CrossRef]
  8. C. Mohtadi, “Bode’s integral theorem for discrete-time systems,” Proc. IEE 137, 57–66 (1990).
  9. J.G. Proakis, D.G. Manolakis, Digital Signal Processing - Principles, algorithms and applications, (Prentice Hall, Upper Saddle River, New Jersey, 3rd ed., 1996).
  10. L. Guikhman, A. Skorokhod, The theory of stochastic processes, (Springer Verlag Ed., Berlin, 1979).
  11. E. Gendron, P. Lena, “Astronomical Adaptive optics I. modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).
  12. D.M. Wiberg, C.E. Max, D.T. Gavel, “A special non-dynamic LQG controller: part I, application to adaptive optics,” Proceedings of the 43th IEEE Conference on Decision and Control 3, 3333–3338 (2004).
  13. C. Dessenne, P.-Y. Madec, G. Rousset, “Optimization of a predictive controller for the closed loop adaptive optics,” Appl. Opt. 37, 4623 (1998). [CrossRef]
  14. A. Wirth, J. Navetta, D. Looze, S. Hippler, A. Glindemann, D. Hamilton, “Real-time modal control implementation for adaptive optics,” Appl. Opt. 37, 4586–4597 (1998). [CrossRef]
  15. J.S. Gibson, B.L. Ellerbroek, “Adaptive optics wave-front correction by use of adaptive filtering and control,” Appl. Opt. 39, 2525–2538 (2000). [CrossRef]
  16. H. W. Sorenson, “Least-square estimation: from Gauss to Kalman,” IEEE Spectrum 7, 63–68 (1970). [CrossRef]
  17. P.D. Joseph, J.T. Tou, “On linear control theory,” AIEE Trans. Applications in Industry, pgs. 193–196 (1961).
  18. R. N. Patchell, Jacobs, “Separability, neutrality and certainty equivalence,” Int. J. Control 13, (1971). [CrossRef]
  19. Y. Bar-Shalom, E. Tse, “Dual effect, certainty equivalence and separation in stochastic control,” IEEE Trans. Automat. Contr. 19, 494–500 (1974). [CrossRef]
  20. R.N. Paschall, D.J. Anderson, “Linear Quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements,” Appl. Opt. 32, 6347–6358 (1993). [CrossRef] [PubMed]
  21. M.W. Oppenheimer, M. Pachter, “Adaptive optics for airbone platforms—part 2: controller design,” Opt. Laser Technol. 34, 159–176 (2002). [CrossRef]
  22. A.H. Jazwinski, Stochastic Processes and Filtering Theory, (Academic Press, 1970).
  23. B.D.O Anderson, J.B. Moore, Optimal Control, Linear Quadratic Methods, (Prentice Hall, London, 1990).
  24. B. Le Roux, J.-M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” Proc. SPIE, 4839, (2003). [CrossRef]
  25. J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995). [CrossRef]
  26. C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, G. Rousset, “Kalman Filter based control loop for Adaptive Optics,” Proc. SPIE, 5490, (2004). [CrossRef]
  27. C. Petit, J.-M. Conan, C. Kulcsár, H. F. Raynaud, T. Fusco, J. Montri, D. Rabaud. “Optimal control for Multi-Conjugate Adaptive Optics,” Elsevier, Comptes Rendus Physique 6, 1059–1069 (2005). [CrossRef]

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