Frequency-based design of adaptive optics systems

The problem of reducing the effects of wavefront distortion and structural vibrations in ground-based telescopes is addressed within a modal-control framework. The proposed approach aims at optimizing the parameters of a given modal stabilizing controller with respect to a performance criterion which reflects the residual phase variance and is defined on a sampled frequency domain. This framework makes it possible to account for turbulence and vibration profiles of arbitrary complexity (even empirical power spectral densities from data), while the controller order can be kept at a desired value. Moreover it is possible to take into account additional requirements, as robustness in the presence of disturbances whose intensity and frequency profile vary with time. The proposed design procedure results in solving a minmax problem and can be converted into a linear programming problem with quadratic constraints, for which there exist several standard optimization techniques. The optimization starts from a given stabilizing controller which can be either a non-model-based controller (in this case no identification effort is required), or a model-based controller synthesized by means of turbulence and vibration models of limited complexity. In this sense the approach can be viewed not only as alternative, but also as cooperative with other control design approaches. The results obtained by means of an End-to-End simulator are shown to emphasize the power of the proposed method.