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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. 30, Iss. 8 — Aug. 1, 2013
  • pp: 1680–1686

Kaczmarz algorithm for multiconjugated adaptive optics with laser guide stars

Matthias Rosensteiner and Ronny Ramlau  »View Author Affiliations


JOSA A, Vol. 30, Issue 8, pp. 1680-1686 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001680


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Abstract

We recently introduced the Kaczmarz algorithm for solving the atmospheric tomography problem in multiconjugate adaptive optics (MCAO). This iterative method solves the problem significantly faster than the standard matrix vector multiplication. We present the algorithm as well as an extension, which includes the effects of laser guide stars, such as the cone effect, tip/tilt indetermination, and spot elongation. We show that we can successfully cope with these effects and that the algorithm is suited for an MCAO system for the future generation of extremely large telescopes.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(350.1260) Other areas of optics : Astronomical optics
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Imaging Systems

History
Original Manuscript: May 8, 2013
Revised Manuscript: June 20, 2013
Manuscript Accepted: June 21, 2013
Published: July 24, 2013

Citation
Matthias Rosensteiner and Ronny Ramlau, "Kaczmarz algorithm for multiconjugated adaptive optics with laser guide stars," J. Opt. Soc. Am. A 30, 1680-1686 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-8-1680


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References

  1. F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
  2. F. Rigaut, B. Ellerbroek, and R. Flicker, “Priciples, limitations and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022–1031 (2000). [CrossRef]
  3. B. Ellerbroek, L. Gilles, and C. Vogel, “A computationally efficient wavefront reconstructor for simulation or multi-conjugate adaptive optics on giant telescopes,” Proc. SPIE 4839, 989–1000 (2002). [CrossRef]
  4. L. Gilles, B. Ellerbroek, and C. Vogel, “Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics,” Proc. SPIE 4839, 1011–1022 (2002). [CrossRef]
  5. B. Ellerbroek, L. Gilles, and C. Vogel, “Numerical simulations of multiconjugate adaptive optics wavefront reconstuction on giant telescopes,” Appl. Opt. 42, 4811–4818 (2003). [CrossRef]
  6. B. Ellerbroek and C. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” Proc. SPIE 5169, 206–217 (2003). [CrossRef]
  7. L. Gilles, B. Ellebroek, and C. Vogel, “Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics,” Appl. Opt. 42, 5233–5250 (2003). [CrossRef]
  8. L. Gilles, B. Ellerbroek, and C. Vogel, “A comparison of multigrid V-cycle versus fourier domain preconditioning for laser guide star atmospheric tomography,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007).
  9. L. Gilles and B. Ellerbroek, “Split atmospheric tomography using laser and natural guide stars,” J. Opt. Soc. Am. 25, 2427–2435 (2008). [CrossRef]
  10. C. Vogel and Q. Yang, “Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm,” Opt. Express 14, 7487–7498 (2006).
  11. Q. Yang, C. Vogel, and B. Ellerbroek, “Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography,” Appl. Opt. 45, 5281–5293 (2006). [CrossRef]
  12. T. Fusco, J. Conan, G. Rousset, L. Mugnier, and V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001). [CrossRef]
  13. D. Gavel, “Tomography for multiconjugate adaptive optics systems using laser guide stars,” Proc. SPIE 5490, 1356–1373 (2004).
  14. R. Ramlau and M. Rosensteiner, “An efficient solution to the atmospheric turbulence tomography problem using Kaczmarz iteration,” Inverse Probl. 28, 095004 (2012). [CrossRef]
  15. M. Rosensteiner, “Wavefront reconstruction for extremely large telescopes via CuRe with domain decomposition,” J. Opt. Soc. Am. A 29, 2328–2336 (2012). [CrossRef]
  16. S. Kaczmarz, “Angenäherte auflösung von systemen linearer gleichungen,” Bulletin International de l’Académie Polonaise des Sciences et des Lettres. Classe des Sciences Mathématiques et Naturelles. Série A, Sciences Mathématiques 35, 355–357 (1937).
  17. N. Ageorges and C. Dainty, eds., Laser Guide Star Adaptive Optics for Astronomy, NATO Asi Series. Series C, Mathematical and Physical Science (Springer, 2000).
  18. M. Zhariy, A. Neubauer, M. Rosensteiner, and R. Ramlau, “Cumulative wavefront reconstructor for the Shack–Hartman sensor,” Inverse Problems and Imaging 5, 893–913 (2011). [CrossRef]
  19. M. Rosensteiner, “Cumulative reconstructor: fast wavefront reconstruction algorithm for extremely large telescopes,” J. Opt. Soc. Am. A 28, 2132–2138 (2011). [CrossRef]
  20. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
  21. F. Natterer, The Mathematics of Computerized Tomography (Teubner, 1986).
  22. R. Kowar and O. Scherzer, “Convergence analysis of a Landweber–Kaczmarz method for solving nonlinear ill-posed equations,” in Ill-Posed and Inverse Problems (book series), Vol. 23, pp. 69–90 (2002).
  23. M. Haltmeier, A. Leitao, and O. Scherzer, “Kaczmarz methods for regularizing nonlinear ill-posed equations i: Convergence analysis,” Inverse Problems and Imaging 1, 289–298 (2007).
  24. J. Baumeister, B. Kaltenbacher, and A. Leitäo, “On Levenberg-Marquardt Kaczmarz methods for regularizing systems of nonlinear ill-posed equations,” Inverse Problems and Imaging 4, 335–350 (2010).
  25. A. De Cezaro, M. Haltmeier, A. Leito, and O. Scherzer, “On steepest-descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations,” Appl. Math. Comput 202, 596–607 (2008). [CrossRef]
  26. M. C. Roggemann and B. Welsh, Imaging Through Turbulence, CRC Press Laser and Optical Science and Technology Series (CRC Press, 1996).
  27. R. M. Clare, M. L. Louarn, and C. Béchet, “Optimal noise-weighted reconstruction with elongated Shack–Hartmann wavefront sensor images for laser tomography adaptive optics,” Appl. Opt. 49, G27–G36 (2010). [CrossRef]
  28. M. Le Louarn, C. Verinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006). [CrossRef]

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