In adaptive optical systems that compensate for random wave-front disturbances, a wave front is measured and corrections are made to bring it to the desired shape. For most systems of this type, the local wave-front slope is first measured, the wave front is next reconstructed from the slope, and a correction is then fitted to the reconstructed wave front. Here a more realistic model of the wave-front measurements is used than in the previous literature, and wave-front estimation and correction are analyzed as a unified process rather than being treated as separate and independent processes. The optimum control law is derived for an arbitrary array of slope sensors and an arbitrary array of correctors. Application of this law is shown to produce improved results with noisy measurements. The residual error is shown to depend directly on the density of the slope measurements, but the sensitivity to the precise location of the measurements that was indicated in the earlier literature is not observed.
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