A comparison of Kalman filter based algorithms for turbulent phase control in an adaptive optics system

Telescope resolution is theoretically limited by the diffraction effect, and hence it is inversely proportional to the lens diameter. However, the real resolution of images acquired by large ground telescopes is reduced by the atmospheric turbulence effect. For this reason, telescopes are provided with an adaptive optics (AO) system which aims at compensating the turbulence effect. In this paper we consider a control algorithm for the AO system based on a turbulence prediction method. We propose two linear models, both based on a principal component analysis (PCA) spatial representation, to fit the turbulence temporal dynamic and provide its temporal prediction. We assume that some information about the turbulence has already been estimated, and we exploit it in the computation of the model parameters. The first proposed model yields the best performance but at a quite high computational cost, whereas the second model is best suited in the case of high sampling rates. Furthermore, our simulations show that the PCA spatial representation is robust to errors in the parameter estimation.