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11 July 2008 Multirate LQG AO control
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All thing being equal, increasing the sampling rate of a computer-controlled feedback loop extends its effective bandwidth, and thus the achievable performance in terms of disturbance rejection. This applies to AO systems, where deformable mirror's (DM) control voltages are computed from wavefront sensor's (WFS) measurements. However, faster sampling, i.e. shorter exposure time for the WFS's CCD, results (especially for low-flux astronomical applications) in higher measurement noise, thereby degrading overall performance. A way to circumvent this limitation is to increase only the DM's control rate. However, standard integral AO control is inherently ill-suited for such multirate mode, because integrators require an uninterrupted measurement stream to maintain closed-loop stability. On the other hand, Linear Quadratic Gaussian (LQG) AO control, where DM controls are computed from explicit predictions of future values of the turbulent phase provided by a Kalman filter, can be easily adapted to multirate configurations where the WFS sampling period is a multiple of the DM's one, provided that a stochastic model of the turbulent phase at the fast (DM) rate is available. The Kalman filter, between two successive measurements, operates in (observer) open-loop mode, with predictions updated by extrapolating current trends in the turbulent phase's trajectory. Thus, while simple vector-valued AR(1) turbulence models are sufficient for single-rate LQG AO loops, more complex stochastic models are likely to be needed to achieve good performance in multirate configurations.
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H. F. Raynaud, C. Kulcsár, C. Correia da Silva, and J. M. Conan "Multirate LQG AO control", Proc. SPIE 7015, Adaptive Optics Systems, 701538 (11 July 2008); doi: 10.1117/12.789231;

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