We present a novel type of nonlinear reconstructor for all Fourier-type wavefront sensors like the Pyramid Wavefront Sensor. Different to interaction matrix approaches which critically degrade image quality due to approximation errors in nonlinear regimes, the new wavefront estimation algorithm has been designed to be robust in such frameworks. It works by employing an iterative technique to circumvent the major drawbacks associated with linear methods. A significant advantage to this approach is that the developed nonlinear algorithm is a generalised wavefront reconstruction method meaning that the reconstructor is directly applicable to any Fourier-type WFS.
Modern ground-based telescopes rely on adaptive optics (AO) systems for the compensation of image degradation caused by atmospheric turbulences. Within an AO system, measurements of incoming light from guide stars are used to adjust deformable mirror(s) in real time that correct for atmospheric distortions. The incoming wavefront has to be derived from sensor measurements, and this intermediate result is then translated into the shape(s) of the deformable mirror(s). Rapid changes of the atmosphere lead to the need for fast wavefront reconstruction algorithms. We review a fast matrix-free algorithm that was developed by Neubauer to reconstruct the incoming wavefront from Shack–Hartmann measurements based on a finite element discretization of the telescope aperture. The method is enhanced by a domain decomposition ansatz. We show that this algorithm reaches the quality of standard approaches in end-to-end simulation while at the same time maintaining the speed of recently introduced solvers with linear order speed.
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