Atmospheric turbulence profiles C2n(h) deduced from solar limb observations

Atmospheric turbulence is responsible of the spatio-temporal fluctuations in astronomical object images obtained by means of ground-based telescopes. They are due to wave-front degradations present at the entrance of the instrument pupil plane. We first establish in this paper the formulation of the angle-of-arrival angular structure function $d(\theta)$ of image fluctuations which is linked to the turbulence "optical strength" $C_n^2(h)$. We use this property to propose an optical method to estimate atmospheric turbulence profiles. This is based on the inversion of the $d(\theta)$ integral equation using the Marquardt-Levenberg method. Application to synthetic data shows the efficiency and the stability of the developed method. We applied then this method to estimate optical turbulence profiles from the analysis of solar limb images.