A Gradient Based Method for Atmospheric Tomography

Daniela Saxenhuber* and Ronny Ramlau

Large ground-based telescopes rely on adaptive optics systems to remove the effects of atmospheric distortions in order to achieve a good image quality. Adaptive optics systems physically correct atmospheric turbulences via deformable mirrors in real-time. The optimal shape of the deformable mirrors is determined from wavefront measurements of natural guide stars as well as laser guide stars. Problem related effects such as tip/tilt indetermination, spot elongation as well as the statistics of the atmosphere will be included in model. The calculation of the optimal mirror deformations from incoming wavefronts is an ill-posed inverse problem. In order to achieve a reconstruction within the required time frame, numerically cheap iterative solvers are needed. In this talk, we propose a gradient based method for the atmospheric reconstruction. The operator describing the available measurements is derived and a numerical scheme yielding a highly accurate reconstruction of the atmosphere will be presented. Numerical results will be demonstrated for the European Extremely Large Telescope (E-ELT).

Mathematics Subject Classification: 65R32 45Q05

Keywords: Inverse Problems; Atmospheric tomography;

Minisymposion: Iterative Methods for Ill-Posed Problems