Estimation of the Atmospheric Turbulence Parameters Using the Angle-of-Arrival Covariance Function

Abstract

The Fried’s length r₀, the outer scale L₀, the isoplanatism θ₀, the coherence time τ₀, and the profile of the optical turbulence energy \(C_{n}^{2}(h)\) are parameters of the wavefront spatiotemporal coherence. Numerous optical methods are used to determine the images quality through the estimation of the parameters r₀, L₀, θ₀, and τ₀, where numerical simulations of the transversal and longitudinal covariance (as a function of the angle-of-arrival (AA)) play a significant role. In this work, we, first, perform the statistical analysis of the fluctuations of angle-of-arrival using theoretical models of the atmospheric turbulence, and second, the statistical analysis of the AA fluctuations in solar limb images. This analysis plays a significant role in the optimization of techniques, such as adaptive optics (OA) and in interferometry, in astronomical observations with high angular resolution.