The method of the approximate inverse for atmospheric tomography

Author： Gerth Daniel Hahn Bernadette N Ramlau Ronny

E-ISSN： 1361-6420|31|6|65002-65027

ISSN： 0266-5611

Source： Inverse Problems, Vol.31, Iss.6, 2015-06, pp. : 65002-65027

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Abstract

In this paper, we propose a new approach for the atmospheric tomography based on the method of the approximate inverse. The image quality of Earth-bound telescopes is severely degraded by turbulences of the atmosphere of the Earth. In order to receive sharp images, the incoming light is corrected for these distortions using deformable mirrors. In atmospheric tomography, the turbulence profile is reconstructed so that the shape of the mirrors can be adjusted in an optimal way. We perform this reconstruction step by applying the method of the approximate inverse, a non-iterative regularization method which requires the solution of an adjoint problem, to Multi-Conjugate Adaptive Optics. We show that the approximate inverse leads to efficient algorithms and give numerical examples. The adjoint problem, which can be precomputed, is solved with an iterative Kaczmarz-type algorithm. In this first study of the new algorithm, tip/tilt effects and spot elongation are not included.