Last week, when I wrote about Guide Stars, I presented roughly, how a Shack Hartmann sensor is utilized to obtain information on the perturbation of the wavefront taht should be plane in the ideal case. To determine the actuator commands for the deformable mirror, a linear system of equations has to be solved.
The common approach until, in all modesty, the Austrian Adaptive Optics team entered the play, was the so-called matrix vector method (MVM), which has, a computational effort of the order n^2, when n is the number of actuators. The influence matrix was inverted once and then applyed to the sensor signals.
CuRe (the cumulative reconstructor), which has beeen developed in Linz, takes into account the special form of the Shack Hartmann operations and succeeds to obtain a performance of order n. While the MVM took 20 milliseconds on an 8 CPU realisation, CuRe did the same job in 130 microseconds on a single CPU. A speed-up of almost 1000.
The actuator commands then look as indicated by the following image (which I like to call "psychedelic donut").
More details can be found in CuRe - A new wavefront reconstruction by Andreas Obereder, Ronny Ramlau, Matthias Rosensteiner and Mariya Zhariy.