Extension of the matched-filter algorithm to multiple guide star Shack-Hartmann wavefront sensor

The adaptive optics (AO) systems with multiple laser guide stars (LGSs) may significantly benefit in terms of hardware simplification from merging several LGS optical channels into one with a single wavefront sensor. As Shack-Hartmann sensors typically suffer from incomplete filling of the camera area, there exists an opportunity to overlay several Hartmann spot patterns densely within a compact composite one, resulting in very frugal use of the camera pixels. We show that such a pattern with only slight spot overlap can be composed even in the quite extreme case of the Giant Magellan Telescope laser tomography AO system employing six highly elongated side-launched laser beacons. The problem of disentangling the overlapped spots is efficiently solvable by a generalization of the matched-filter (MF) algorithm, which is the main focus of this work. Dynamic calibration by star dithering in the case of extended MF is still possible, albeit more complicated. Computational complexity increase and performance degradation in comparison to classical MF can be minimized to acceptable values by careful system parameter tuning.