Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


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.

Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
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https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at

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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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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: bestellung.verlag@oeaw.ac.at
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doi:10.1553/etna_vol48s286



doi:10.1553/etna_vol48s286



Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Günter Auzinger
PDF Icon  Model reduction in atmospheric tomography by optimal grouping of turbulent layers ()
S.  286 - 309
doi:10.1553/etna_vol48s286

Open access

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
  2018/08/27 09:46:00
Object Identifier:  0xc1aa5572 0x0039c821
.

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.



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