Many adaptive optics applications require wavefront corrections with a high stroke, and at a high bandwidth. Often, these two requirements cannot be met by a single wavefront corrector, and, instead, the combination of a low-bandwidth, high-stroke woofer and a high-bandwidth low-stroke tweeter is used in a so-called woofer–tweeter architecture. The optimal (minimum residual phase variance) way to split the correction between the woofer and the tweeter in the context of a linear–quadratic–Gaussian (LQG) controller has been addressed previously. However, the necessity to fold the temporal characteristics of the woofer and tweeter into the LQG controller significantly increases its complexity. In this Letter, this optimal strategy is compared to a simpler, ad hoc approach, which consists in optimizing the LQG controller as if it were controlling a high-bandwidth, high-stroke corrector and splitting the correction using first-order high- and low-pass temporal filters. In the case of tilt correction for NFIRAOS on the Thirty Meter Telescope, it is found that the ad hoc approach, which is already used or planned for several systems, holds the same overall correction performance compared to the optimal strategy.
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