A gradient-based method for atmospheric tomography

Daniela  Saxenhuber; Ronny  Ramlau

doi:10.3934/ipi.2016021

Article Contents

2016, Volume 10, Issue 3: 781-805. Doi: 10.3934/ipi.2016021

This issue Previous Article Reconstruction of penetrable obstacles in the anisotropic acoustic scattering Next Article Image segmentation based on the hybrid total variation model and the K-means clustering strategy

A gradient-based method for atmospheric tomography

Daniela Saxenhuber^1, and
Ronny Ramlau^1,

1.
Altenbergerstrasse 69, Linz, 4040

Received: February 2015

Revised: January 2016

Published: August 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 65F22, 65F20; Secondary: 65Y20, 85A04.

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