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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 17 — Aug. 21, 2006
  • pp: 7487–7498

Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm

Curtis R. Vogel and Qiang Yang  »View Author Affiliations

Optics Express, Vol. 14, Issue 17, pp. 7487-7498 (2006)

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We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

© 2006 Optical Society of America

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

ToC Category:
Focus Issue: Adaptive Optics

Original Manuscript: March 13, 2006
Revised Manuscript: May 10, 2006
Manuscript Accepted: June 2, 2006
Published: August 21, 2006

Curtis R. Vogel and Qiang Yang, "Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm," Opt. Express 14, 7487-7498 (2006)

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  1. J. M. Beckers, "Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics," in Proceedings of European Southern Observatory Conference and Workshop on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed., Vol. 30 of ESO Conference andWorkshop Proceedings (European Southern Observatory, Garching, Germany, 1988), pp. 693-703.
  2. D. C. Johnston and B. M. Welsh, "Analysis of multi-conjugate adaptive optics," J. Opt. Soc. Am. A 11, 394-408 (1994). [CrossRef]
  3. T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, and V. Michau, "Optimal wave-front reconstruction strategies for multi-conjugate adaptive optics," J. Opt. Soc. Am. A 18, 2527-2538 (2001). [CrossRef]
  4. R. G. Dekany, M. C. Britton, D. T. Gavel, B. L. Ellerbroek, G. Herriot, C. E. Max, J-P. Veran, "Adaptive optics requirements definition for TMT," Advancements in Adaptive Optics, edited by D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, Proc. SPIE 5490, 879-890 (2004). [CrossRef]
  5. 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]
  6. G. Golub and C. VanLoan, Matrix Computations, 2nd Edition, Johns Hopkins University Press, 1989.
  7. L. Gilles, C. R. Vogel, and B. L. Ellerbroek, "Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction," J. Opt. Soc. Am. A,  19, 1817-1822 (2002). [CrossRef]
  8. L. Gilles, B. L. Ellerbroek, and, C. R. Vogel, "Preconditioned conjugate gradient wave-front reconstructors for multi-conjugate adaptive optics," Appl. Opt. 42, 5233-5250 (2003). [CrossRef] [PubMed]
  9. B. L. Ellerbroek, L. Gilles, and C. R. Vogel, "Numerical simulations of multi-conjugate adaptive optics wavefront reconstruction on giant telescopes," Appl. Opt. 42, 4811-4818 (2003). [CrossRef] [PubMed]
  10. Q. Yang, C.R. Vogel, and B.L. Ellerbroek, "Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography," Appl. Opt. 45, 5281-5293 (2006). [CrossRef] [PubMed]
  11. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford University Press, 1998.
  12. D. Fried, "Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67,370-375 (1977). [CrossRef]

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