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.