Atmospheric turbulence profiling with unknown power spectral density

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Helin , T , Kindermann , S , Lehtonen , J & Ramlau , R 2018 , ' Atmospheric turbulence profiling with unknown power spectral density ' , Inverse Problems , vol. 34 , no. 4 , 044002 .

Title: Atmospheric turbulence profiling with unknown power spectral density
Author: Helin, Tapio; Kindermann, Stefan; Lehtonen, Jonatan; Ramlau, Ronny
Contributor organization: Department of Mathematics and Statistics
Inverse Problems
Date: 2018-03-08
Language: eng
Number of pages: 32
Belongs to series: Inverse Problems
ISSN: 0266-5611
Abstract: Adaptive optics (AO) is a technology in modern ground-based optical telescopes to compensate for the wavefront distortions caused by atmospheric turbulence. One method that allows to retrieve information about the atmosphere from telescope data is so-called SLODAR, where the atmospheric turbulence profile is estimated based on correlation data of Shack-Hartmann wavefront measurements. This approach relies on a layered Kolmogorov turbulence model. In this article, we propose a novel extension of the SLODAR concept by including a general non-Kolmogorov turbulence layer close to the ground with an unknown power spectral density. We prove that the joint estimation problem of the turbulence profile above ground simultaneously with the unknown power spectral density at the ground is ill-posed and propose three numerical reconstruction methods. We demonstrate by numerical simulations that our methods lead to substantial improvements in the turbulence profile reconstruction compared to the standard SLODAR-type approach. Also, our methods can accurately locate local perturbations in non-Kolmogorov power spectral densities.
Subject: inverse problem
integral equation
adaptive optics
turbulence profiling
111 Mathematics
Peer reviewed: Yes
Rights: unspecified
Usage restriction: openAccess
Self-archived version: acceptedVersion

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