Adaptive optics is a technique that uses the measurements of a wave front sensor to flatten distorted wave fronts with a deformable mirror in a feedback loop in order to provide diffraction-limited performance with ground-based telescopes. In order to achieve the highest possible Strehl, a measure of performance, the measurement and the control of the most important disturbances (tip and tilt) have to be optimized. These modes, in spite of being the first modes to be controlled, have the biggest impact on the final performance of the system. This paper concentrates on the estimation and control of the atmospheric tip/tilt leaving out for the moment other sources of error that originate inside the telescope in form of vibrations. It will be shown that the proposed control strategy can reduce the residual variance of the controlled modes by a factor 2 and that, if applied to all modes, can achieve a significantly better Strehl.
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