A1 Journal article (refereed), original research

Finite element-wavelet hybrid algorithm for atmospheric tomography

LUT Authors / Editors

Publication Details
Authors: Yudytskiy Mykhaylo, Helin Tapio, Ramlau Ronny
Publisher: Optical Society of America
Publication year: 2014
Language: English
Related Journal or Series Information: Journal of the Optical Society of America A
Journal name in source: Journal of the Optical Society of America A: Optics and Image Science, and Vision
Volume number: 31
Issue number: 3
Start page: 550
End page: 560
Number of pages: 11
ISSN: 1084-7529
JUFO-Level of this publication: 2
Open Access: Not an Open Access publication


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)" role="presentation">��(��),
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.

Last updated on 2021-09-04 at 10:50