In a compensated imaging (CI) system the wave-front distortion is changing randomly in time and the data processing must follow the changes and even, to some extent, predict them. Furthermore, the system is not infinitely fast; it has time delays and bandwidth limitations which can be quite significant. Couple to this the substantial photon noise in the wave-front measurements, and it becomes desirable to find the optimal data processing to use for system control. This paper derives the optimal linear control algorithm assuming the aberration and noise statistics are known for a compensated imaging system, and discusses the properties of this algorithm.
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