ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Günter Auzinger
S. 286 - 309 doi:10.1553/etna_vol48s286 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol48s286
Abstract: In wide-field applications of adaptive optics systems, the problem of atmospheric tomography has to be solved. Commonly used methods for this purpose operate on a set of two-dimensional reconstruction layers. Due to run-time restrictions and demands on stability, in general the usable number of such reconstruction layers is less than the number of atmospheric turbulence layers. Hence, model reduction has to be applied to the profile of atmosphere layers in order to achieve a smaller number of the most relevant reconstruction layers. In continuation of earlier published and purely heuristic experiments, we concentrate on the question how the choice of the heights of these reconstruction layers influences the performance of the tomographic solver, aiming for a more rigorous analysis. We derive a function representing an approximate expected value for the best-case residual error, i.e., a limitation (in a statistical sense) for what any tomographic solver is able to reach. We provide a method for the minimization of this function, which consequently yields an algorithm for the (approximately) optimal choice of the reconstruction layer heights for a given input atmosphere model, i.e., given the turbulence strength depending on the altitude. Our implementation of the optimization algorithm has acceptable run-time, and first tests of the resulting layer profiles show that the obtained quality is significantly better than for other choices of the reconstruction layer profiles. Keywords: model reduction, adaptive optics, atmospheric tomography, layer compression, optimization Published Online: 2018/08/27 09:46:00 Object Identifier: 0xc1aa5572 0x0039c821 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |