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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

  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1084–1093

Local, hierarchic, and iterative reconstructors for adaptive optics

Douglas G. MacMartin  »View Author Affiliations


JOSA A, Vol. 20, Issue 6, pp. 1084-1093 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001084


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Abstract

Adaptive optics systems for future large optical telescopes may require thousands of sensors and actuators. Optimal reconstruction of phase errors using relative measurements requires feedback from every sensor to each actuator, resulting in computational scaling for n actuators of n2. The optimum local reconstructor is investigated, wherein each actuator command depends only on sensor information in a neighboring region. The resulting performance degradation on “global” modes is quantified analytically, and two approaches are considered for recovering global performance. Combining local and global estimators in a two-layer hierarchic architecture yields computations scaling with n4/3; extending this approach to multiple layers yields linear scaling. An alternative approach that maintains a local structure is to allow actuator commands to depend on both local sensors and prior local estimates. This iterative approach is equivalent to a temporal low-pass filter on global information and gives a scaling of n3/2. The algorithms are simulated by using data from the Palomar Observatory adaptive optics system. The analysis is general enough to also be applicable to active optics or other systems with many sensors and actuators.

© 2003 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(350.1260) Other areas of optics : Astronomical optics

History
Original Manuscript: September 6, 2002
Revised Manuscript: January 31, 2003
Manuscript Accepted: January 31, 2003
Published: June 1, 2003

Citation
Douglas G. MacMartin, "Local, hierarchic, and iterative reconstructors for adaptive optics," J. Opt. Soc. Am. A 20, 1084-1093 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-6-1084


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References

  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford Series on Optical and Imaging Sciences 16 (Oxford U. Press, New York, 1998).
  2. R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000). [CrossRef]
  3. J. Nelson, T. Mast, eds., “Conceptual design for a 30-meter telescope,” (University of California and California Institute of Technology, Berkeley, Calif., 2002).
  4. R. H. Hudgin, “Optimal wave-front estimation,” J. Opt. Soc. Am. 67, 378–382 (1977). [CrossRef]
  5. K. Freischlad, C. Zeiss, “Wavefront integration from difference data,” in Interferometry: Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, G. T. Reid, eds., Proc. SPIE1755, 212–218 (1992). [CrossRef]
  6. L. A. Poyneer, D. T. Gavel, J. M. Brase, “Fast wavefront reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002). [CrossRef]
  7. B. L. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002). [CrossRef]
  8. L. Gilles, C. R. Vogel, B. L. Ellerbroek, “Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002). [CrossRef]
  9. W. J. Wild, E. J. Kibblewhite, R. Vuilleumier, “Sparse matrix wave-front estimators for adaptive-optics systems for large ground-based telescopes,” Opt. Lett. 20, 955–957 (1995). [CrossRef] [PubMed]
  10. T. P. Murphy, R. G. Lyon, J. E. Dorband, J. M. Hollis, “Sparse matrix approximation method for an active optical control system,” Appl. Opt. 40, 6505–6514 (2001). [CrossRef]
  11. K. Li, E. B. Kosmatopoulos, P. A. Ioannou, H. Ryaciotaki-Boussalis, “Large segmented telescopes: centralized, decentralized and overlapping control designs,” IEEE Control Syst. Mag., October2000, 59–72.
  12. R. D’Andrea, C. Langbort, R. Chandra, “A state space approach to control of interconnected systems,” in Mathematical Systems Theory in Biology, Communication, Computation and Finance, IMA Vol. 134 in Mathematics and Its Application, J. Rosenthal, D. S. Gillian, eds. (Springer-Verlag, New York, 2003), pp. 157–182.
  13. D. M. Young, Iterative Solution of Large Linear Systems (Academic, New York, 1971).
  14. F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 1035–1044 (2002). [CrossRef]
  15. M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000). [CrossRef]
  16. J.-P. Gaffard, G. Ledanois, “Adaptive optics transfer function modeling,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 34–45 (1991). [CrossRef]
  17. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  18. T. Truong, G. Brack, T. Trinh, M. Troy, F. Shi, R. G. Dekany, “Real-time wavefront processors for the next generation of adaptive optics systems: a design and analysis,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 911–922 (2002). [CrossRef]

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