کنترل خطی گاوسی معادله درجه دوم کاربردی برای سیستم فیلد گسترده اپتیک تطبیقی: شبیه سازی و نتایج تجربی

Adaptive optics (AO) is a proven technique to correct turbulence on ground-based astronomical telescopes. The corrected Field of View (FoV) is however limited by the anisoplanatism effect. To extend the FoV, new Wide Field AO (WFAO) concepts have been recently developed. They aim at providing a wide FoV correction through the use of multi-guide-star WaveFront Sensors (WFSs) and several Deformable Mirrors (DMs). Such WFAO systems require a tomographic reconstruction of the atmospheric turbulence, leading to a multivariable problem of much higher complexity than in classic AO. They also raise new questions in terms of calibration and control. The Linear Quadratic Gaussian (LQG) control formalism is a natural way to cope with this issue. It enables both tomographic reconstruction and distinction between controlled output and measurements. In this paper, LQG control is presented and applied to WFAO systems. Performance is evaluated thanks to simulations based on theoretical studies, but also through laboratory experiments. We present the first results of the implementation of LQG control on a WFAO system, the HOMER bench, that has been developed recently at ONERA and which is devoted to WFAO laboratory research.

This paper is focused on the use ofLQGcontrol forWFAO systems. LQG control is particularly well-adapted to these concepts as it incorporates tomographic reconstruction and temporal prediction of the turbulent volume.We have presented numerical simulation results of the performance of LQG control on the HOMER bench, devoted to WFAO concepts. In MCAO, results have been compared with least-square + integral action control, and confirm that a major advantage of LQG control is the ability to specify the field of interest in which the correction will be optimized. This is essential for future WFAO instruments currently under study for very large and extremely large telescopes.TheHOMERnumerical simulations confirm that significant performance improvements with respect to standard AO control can be achieved in spite of model errors. We have good and homogeneous correction of the turbulence in the FoV with high levels of SR inMCAO.We also show how to optimize the performance of LQG control. These numerical simulation tests also illustrate the inherent flexibility of theLQGcontroller, where the minimum variance prediction of the turbulence can be projected in any direction of interest. This enables to optimize performance in specified direction(s) of interest which are different from the directions of analysis, in other words controlled variables and measurements are clearly distinct. A state-space approach also allows to choose the space where the phase is to be represented. This may have a strong influence on performance. We have also presented here the first experimental demonstration of closed-loop NTAO thanks to the implementation of LQG control on the HOMER bench. A study of robustness in performance of LQG control is now necessary for future use on real telescope AO systems: identification of critical parameters and sensitivity of performance to their variation. In this line, calibration and identification strategies have to be established to limit component model errors.The results obtained here represent a first step in the framework of the study of very and extremely large telescopes instruments and particularly for tomographic control laws in closed-loop. Developments of theHOMER bench are thus ongoing to experimentally simulate even more realistic WFAO systems. Also, thanks to the flexibility of the HOMER bench configuration, future work shall include comparison with sub-optimal control strategies in WFAO [2, 16, 33]. Different turbulent conditions shall also be explored particularly in presence of high order effects. To realize such conditions, a turbulence generator is planned to be used. It will be more representative of spatial and temporal characteristics of the turbulence, leading to more realistic and rich perturbations. Their impact on performance for different control laws should hence lead to interesting results.