Turbulence modeling and Kalman prediction for the control of large AO systems

Measurements of large ground telescopes are affected by the presence of the terrestrial atmospheric turbulence: local changes of the atmospheric refraction index (e.g. due to wind and temperature variations) cause a non flat surface of the wavefront of light beams incoming on the telescope, thus degrading the quality of the observed images. Adaptive Optics (AO) systems are of fundamental importance to reduce such atmospheric influence on ground telescopes and thus to obtain high resolution observations. The goal of the AO system is that of estimating and compensating the atmospheric turbulence effect by properly commanding a set of deformable mirrors. Because of delays in the closed loop system, the Kalman filter plays an important role in ensuring an effective control performance by providing good atmosphere predictions. However, the need of periodically updating the Kalman filter gain because of changes in the atmosphere characteristics, the increase of telescopes and sensors resolutions and the high sampling rate impose quite strict restrictions to the computational load for computing the Kalman gain. Motivated by the above considerations, some strategies have been recently considered in the system theory and astronomical communities for the efficient computation of the Kalman gain for large AO systems. Specifically, this paper presents some changes to a recently proposed procedure: the proposed approach, which exploits some results in the control theory of distributed systems, computes an approximation of the optimal gain in the frequency domain exploiting the spatial homogeneity of the system. Then, the control strategy takes advantage of some information on the turbulent phase dynamic, that is estimated from the turbulence measurements. Performances of the proposed method are investigated in some simulations.