# American Institute of Mathematical Sciences

August  2016, 10(3): 781-805. doi: 10.3934/ipi.2016021

## A gradient-based method for atmospheric tomography

 1 Altenbergerstrasse 69, Linz, 4040, Austria, Austria

Received  February 2015 Revised  January 2016 Published  August 2016

In Adaptive Optics (AO) systems for ground-based telescopes, one aims at mechanically correcting for atmospheric aberrations by means of quickly moving deformable mirrors. In complex AO systems, which are using several light sources and aim at a good reconstruction in a large field of view, the derivation of optimal mirror commands from measured light typically includes the problem of atmospheric tomography. As the computational effort for such a limited-angle tomography problem is strongly increasing for growing telescope sizes, fast algorithms are needed. We present a novel algorithm for atmospheric tomography that takes real-life effects such as tip/tilt indetermination, cone effect and spot elongation into account. Furthermore, we discuss two models for the tip and tilt components of an incoming wavefront and incorporate them into the reconstruction. We find a fast step size choice for our Gradient-based iteration and compare it with different existing step size choices. Numerical results are demonstrated for two different AO systems on a 42 m telescope, using the European Southern Observatory's end-to-end simulation tool, OCTOPUS.
Citation: Daniela Saxenhuber, Ronny Ramlau. A gradient-based method for atmospheric tomography. Inverse Problems & Imaging, 2016, 10 (3) : 781-805. doi: 10.3934/ipi.2016021
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