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

被引:57
作者
Correia, Carlos [1 ,2 ]
Raynaud, Henri-Francois [2 ]
Kulcsar, Caroline [2 ]
Conan, Jean-Marc [1 ]
机构
[1] Off Natl Etud & Rech Aerosp, F-92322 Chatillon, France
[2] Univ Paris 13, Lab Traitement & Transport Informat, F-93430 Villetaneuse, France
关键词
CONTROL LAW; TURBULENCE; MODEL;
D O I
10.1364/JOSAA.27.000333
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
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. (C) 2010 Optical Society of America
引用
收藏
页码:333 / 349
页数:17
相关论文
共 27 条
[1]  
Anderson B.D.O., 1995, Optimal Filtering
[2]  
ANDERSON BDO, 1995, OPTIMAL CONTROL LINE
[3]  
[Anonymous], P 30 IEEE C DEC CONT
[4]  
ARSENAULT R, 2006, P SPIE, V6272
[5]   DUAL EFFECT, CERTAINTY EQUIVALENCE, AND SEPARATION IN STOCHASTIC CONTROL [J].
BARSHALOM, Y ;
TSE, E .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1974, AC19 (05) :494-500
[6]   Stochastic realization approach to the efficient simulation of phase screens [J].
Beghi, Alessandro ;
Cenedese, Angelo ;
Masiero, Andrea .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2008, 25 (02) :515-525
[7]   WAVE-FRONT TEMPORAL SPECTRA IN HIGH-RESOLUTION IMAGING THROUGH TURBULENCE [J].
CONAN, JM ;
ROUSSET, G ;
MADEC, PY .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1995, 12 (07) :1559-1570
[8]  
CORREIA C, 2008, P SPIE, V7015
[9]  
GASMI R, 2008, P SPIE, V7017
[10]  
GENDRON E, 1994, ASTRON ASTROPHYS, V291, P337