Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

On the optimal reconstruction and control of adaptive optical systems with mirror dynamics

Not Accessible

Your library or personal account may give you access

Abstract

In adaptive optics (AO) the deformable mirror (DM) dynamics are usually neglected because, in general, the DM can be considered infinitely fast. Such assumption may no longer apply for the upcoming Extremely Large Telescopes (ELTs) with DM that are several meters in diameter with slow and/or resonant responses. For such systems an important challenge is to design an optimal regulator minimizing the variance of the residual phase. In this contribution, the general optimal minimum-variance (MV) solution to the full dynamical reconstruction and control problem of AO systems (AOSs) is established. It can be looked upon as the parent solution from which simpler (used hitherto) suboptimal solutions can be derived as special cases. These include either partial DM-dynamics-free solutions or solutions derived from the static minimum-variance reconstruction (where both atmospheric disturbance and DM dynamics are neglected altogether). Based on a continuous stochastic model of the disturbance, a state-space approach is developed that yields a fully optimal MV solution in the form of a discrete-time linear-quadratic-Gaussian (LQG) regulator design. From this LQG standpoint, the control-oriented state-space model allows one to (1) derive the optimal state-feedback linear regulator and (2) evaluate the performance of both the optimal and the sub-optimal solutions. Performance results are given for weakly damped second-order oscillatory DMs with large-amplitude resonant responses, in conditions representative of an ELT AO system. The highly energetic optical disturbance caused on the tip/tilt (TT) modes by the wind buffeting is considered. Results show that resonant responses are correctly handled with the MV regulator developed here. The use of sub-optimal regulators results in prohibitive performance losses in terms of residual variance; in addition, the closed-loop system may become unstable for resonant frequencies in the range of interest.

© 2010 Optical Society of America

Full Article  |  PDF Article
More Like This
Minimum-variance control for woofer–tweeter systems in adaptive optics

Carlos Correia, Henri-François Raynaud, Caroline Kulcsár, and Jean-Marc Conan
J. Opt. Soc. Am. A 27(11) A133-A144 (2010)

Fractional loop delays in adaptive optics modeling and control

Lucas Marquis, Henri-François Raynaud, Nicolas Galland, Jose Marco de la Rosa, Icíar Montilla, Óscar Tubío Araújo, Marcos Reyes García-Talavera, and Caroline Kulcsár
J. Opt. Soc. Am. A 41(1) 111-126 (2024)

Wide field adaptive optics laboratory demonstration with closed-loop tomographic control

Anne Costille, Cyril Petit, Jean-Marc Conan, Caroline Kulcsár, Henri-François Raynaud, and Thierry Fusco
J. Opt. Soc. Am. A 27(3) 469-483 (2010)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (14)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (103)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved