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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 11 — Nov. 1, 2010
  • pp: A145–A156

Closed-loop control of a woofer–tweeter adaptive optics system using wavelet-based phase reconstruction

Peter J. Hampton, Pan Agathoklis, Rodolphe Conan, and Colin Bradley  »View Author Affiliations


JOSA A, Vol. 27, Issue 11, pp. A145-A156 (2010)
http://dx.doi.org/10.1364/JOSAA.27.00A145


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Abstract

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer–tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O ( N ) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O ( N ) reconstruction techniques. The controller configuration is based on the woofer–tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer–tweeter controller leads to very good results with respect to speed and accuracy.

© 2010 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.0100) Image processing : Image processing
(100.7410) Image processing : Wavelets

History
Original Manuscript: December 2, 2009
Revised Manuscript: August 11, 2010
Manuscript Accepted: August 11, 2010
Published: September 20, 2010

Citation
Peter J. Hampton, Pan Agathoklis, Rodolphe Conan, and Colin Bradley, "Closed-loop control of a woofer–tweeter adaptive optics system using wavelet-based phase reconstruction," J. Opt. Soc. Am. A 27, A145-A156 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-11-A145


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References

  1. F. Roddier, Imaging through the Atmosphere (Cambridge University Press, 1999).
  2. J. J. Widiker, S. R. Harris, and B. D. Duncan, “High speed Shack–Hartmann wavefront sensor design with commercial off-the-shelf optics,” Appl. Opt. 45, 383–395 (2006). [CrossRef] [PubMed]
  3. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  4. J. Herrmann, “Least-squaress wavefront errors of minimum norm,” J. Opt. Soc. Am. 67, 28–35 (1980). [CrossRef]
  5. C. R. Vogel and Q. Yang, “Multigrid algorithm for least-squares wavefront reconstruction,” Appl. Opt. 45, 705–715 (2006). [CrossRef] [PubMed]
  6. S. A. Cornelissen, P. A. Bierden, and T. G. Bifano, “Development of a 4096 element deformable mirror for high contrast astronomical imaging,” Proc. SPIE 6306, 630606 (2006). [CrossRef]
  7. B. L. Ellerbroek, “Efficient computation of minimum-variance wavefront reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002). [CrossRef]
  8. L. Gilles, B. Ellerbroek, and C. Vogel, “multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002). [CrossRef]
  9. L. Gilles, “Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics,” Opt. Lett. 28, 1927–1929 (2003). [CrossRef] [PubMed]
  10. K. Freischlad and C. Koliopoulos, “Modal estimation of a wave-front from difference measurements using the discrete Fourier transform,” J. Opt. Soc. Am. A 3, 1852–1861 (1986). [CrossRef]
  11. L. A. Poyneer, D. T. Gavel, and J. M. Brase, “Fast wavefront reconstruction in large adaptive optics systems with the Fourier transform,” J. Opt. Soc. Am. A 18, 2100–2111 (2002). [CrossRef]
  12. L. Lessard, M. West, D. MacMynowski, and S. Lall, “Warm-started wavefront reconstruction for adaptive optics,” J. Opt. Soc. Am. A 25, 1147–1155 (2008). [CrossRef]
  13. D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001). [CrossRef]
  14. P. J. Hampton, P. Agathoklis, and C. Bradley, “A new wave-front reconstruction method for adaptive optics systems using wavelets,” IEEE J. Sel. Top. Signal Process. 2, 781–792 (2008). [CrossRef]
  15. R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 10, pp. 439–451 (1988). [CrossRef]
  16. L. A. Poyneer and J.-P. Véran, “Optimal modal Fourier transform wave-front control,” J. Opt. Soc. Am. A 22, 1515–1526 (2005). [CrossRef]
  17. L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier-transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24, 2645–2660 (2007). [CrossRef]
  18. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995), Chap. 6.
  19. R. G. Dekany, M. C. Britton, D. T. Gavel, B. L. Ellerbroek, G. Herriot, C. E. Max, and J.-P. Véran, “Adaptive optics requirements for TMT,” Proc. SPIE 5490879–890 (2004). [CrossRef]
  20. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  21. J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. 19, 926–945 (2002). [CrossRef]
  22. P. J. Hampton, R. Conan, C. Bradley, and P. Agathoklis, “Control of a woofer tweeter system of deformable mirrors,” Proc. SPIE 6274, 62741Z (2006). [CrossRef]
  23. R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46, 4329–4340 (2007). [CrossRef] [PubMed]
  24. J.-F. Lavigne, J.-P. Véran, and L. Poyneer, “Woofer–tweeter control algorithm for the Gemini planet imager,” in Adaptive Optics: Analysis and Methods; Computational Optical Sensing and Imaging; Digital Holography and Three-Dimensional Imaging; and Signal Recovery and Synthesis (Optical Society of America, 2007), paper AWB5. [PubMed]
  25. J.-F. Lavigne and J.-P. Véran, “woofer-tweeter control in an adaptive optics system using a Fourier reconstructor,” J. Opt. Soc. Am. A 25, 2271–2279 (2008). [CrossRef]
  26. R. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  27. J.-P. Véran and G. Herriot, “Centroid gain compensation in Shack–Hartmann adaptive optics systems with natural or laser guide star,” J. Opt. Soc. Am. A 17, 1430–1439 (2000). [CrossRef]
  28. M. A. van Dam, D. Le Mignant, and B. A. Macintosh, “Performance of the Keck observatory adaptive-optics system,” Appl. Opt. 43, 5458–5467 (2004). [CrossRef] [PubMed]
  29. P. J. Hampton, R. Conan, O. Keskin, C. Bradley, and P. Agathoklis, “Self characterization of linear and non-linear adaptive optics systems,” Appl. Opt. 47, 126–134 (2008). [CrossRef] [PubMed]
  30. P. J. Hampton, P. Agathoklis, and C. Bradley, “wavefront reconstruction over a circular aperture using gradient data extrapolated via the mirror equations,” Appl. Opt. 48, 4018–4030 (2009). [CrossRef] [PubMed]
  31. D. S. Watkins, Fundamentals of Matrix Computations (Wiley, 2002). [CrossRef]
  32. R. W. Hockney, “A fast direct solution of Poisson’s equation using Fourier analysis,” J. Assoc. Comput. Mach. 12, 95–113 (1965). [CrossRef]
  33. T. Nakajima, “Signal-to-noise ratio of the bispectral analysis of speckle interferometry,” J. Opt. Soc. Am. A 5, 1477–1491 (1988). [CrossRef]
  34. F. Rigaut, B. L. Ellerbroek, and M. J. Northcott, “Comparison of curvature-based and Shack-Hartmann based adaptive optics for the Gemini telescope,” Appl. Opt. 36, 2856–2868 (1997). [CrossRef] [PubMed]
  35. F. Martin and R. Conan, “Optical parameters relevant for high angular resolution at Paranal from GSM instrument and surface layer contribution,” Astrophys. Suppl. Ser. 144, 39–44 (2000). [CrossRef]
  36. B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics testbench,” Opt. Express 14, 10132–10138 (2006). [CrossRef] [PubMed]

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