Issue |
A&A
Volume 681, January 2024
|
|
---|---|---|
Article Number | A102 | |
Number of page(s) | 11 | |
Section | Astronomical instrumentation | |
DOI | https://doi.org/10.1051/0004-6361/202346902 | |
Published online | 23 January 2024 |
Eigenbases for a force-constrained position control of adaptive shell mirrors
1
ESO Headquarters Karl-Schwarzschild-Str. 2,
85748
Garching bei München,
Germany
e-mail: cverinau@eso.org
2
Space ODT – Optical Deblurring Technologies Ltd,
Porto,
Portugal
Received:
15
May
2023
Accepted:
3
August
2023
Context. The deployment of meter-scale (hitherto pre-focal) adaptive deformable mirrors finds some prominent examples in the leading ground-based visible to near-infrared facilities (e.g. the Very Large Telescope (VLT), the Large Binocular Telescope (LBT), or the Magellan Telescope) and is being adopted by several others (e.g. the Multiple Mirror Telescope (MMT) or Subaru). Furthermore, two out of the three giant segmented-mirror telescopes now under design will feature them. In all these cases, the proprietary technology is based on voice-coils and is limited in force, stroke, and velocity.
Aims. Because of the nature of their purpose, that is, adaptive wave-front correction, any kind of optimality relies on the control of a subset of principal wave-front components or eigenmodes, for short, a basis of functions in a mathematical sense. Here we provide algorithmic procedures for generating such eigenbases, also called Karhunen–Loève (KL) modes, that integrate force limitations in their definitions whilst maintaining standard orthonormality, statistical independence, and deformable mirror span.
Methods. The double-diagonalisation method was revisited to build KL modes ranked by the force applied on the actuators.
Results. We analysed this new KL basis for von Kármán turbulence statistics and present the fitting error and the distribution of positions and forces. We further illustrate their use in the case of the quaternary mirror control for the European Extremely Large Telescope, and we include the outer actuator minioning and force policy constraints.
Key words: instrumentation: adaptive optics / telescopes / methods: analytical
© The Authors 2024
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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