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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 550–560

Finite element-wavelet hybrid algorithm for atmospheric tomography

Mykhaylo Yudytskiy, Tapio Helin, and Ronny Ramlau  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 550-560 (2014)

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Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl. 29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE 7736, 77360X (2010)] in terms of quality.

© 2014 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:
Atmospheric and Oceanic Optics

Original Manuscript: October 15, 2013
Revised Manuscript: December 5, 2013
Manuscript Accepted: December 5, 2013
Published: February 14, 2014

Mykhaylo Yudytskiy, Tapio Helin, and Ronny Ramlau, "Finite element-wavelet hybrid algorithm for atmospheric tomography," J. Opt. Soc. Am. A 31, 550-560 (2014)

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