Atmospheric Turbulence Profile Estimation from Fluctuation Analysis of Extended Object Images

Description

Atmospheric turbulence is responsible of spatio-temporal fluctuations of astronomical object images obtained by means of ground-based telescopes. The image motion is due to the angle formed by the pupil plane with the wave-front slope all over the pupil. This defines an averaged angle of arrival which may be also considered at each point of the wave-front. Fried [Ref. 1] has established an expression that links between the turbulence "optical strength" Cn2(h) along an optical path and the spatial structure function d() of object image fluctuations. The aim of this work is to propose an optical method to estimate the atmospheric turbulence profile. This is based on the inversion of Fried's integral equation which leads to the estimation of vertical turbulence profile from the observed structure function. The inverse problem is linear in Cn2 but ill-conditioned as it is showed by the singular value decomposition. In order to get stable solution, we use the Marquardt-Levenberg method. Applications on synthetic data show the efficiency and the stability of the developed method. We applied then this method to estimate the optical turbulence profile from the analysis of solar images

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