Online estimation of the wavefront outer scale profile from adaptive optics telemetry

Abstract

We describe an online method to estimate the wavefront outer scale profile,L0(h), for very large and future extremely large telescopes. The stratified information on this parameter impacts the estimation of the main turbulence parameters [turbulence strength, Cn2(h); Fried’s parameter, r0; isoplanatic angle, θ 0; and coherence time, τ 0) and determines the performance of wide-field adaptive optics (AO) systems. This technique estimates L0(h) using data from the AO loop available at the facility instruments by constructing the cross-correlation functions of the slopes between two or more wavefront sensors, which are later fitted to a linear combination of the simulated theoretical layers having different altitudes and outer scale values. We analysesome limitations found in the estimation process: (i) its insensitivity to large values of L0(h) as the telescope becomes blind to outer scales larger than its diameter; (ii) the maximum number of observable layers given the limited number of independent inputs that the cross-correlation functions provide and (iii) the minimum length of data required for a satisfactory convergence of the turbulence parameters without breaking the assumption of statistical stationarity of the turbulence. The method is applied to the Gemini South multiconjugate AO system that comprises five wavefront sensors and two deformable mirrors. Statistics of L0(h) at Cerro Pachon from data acquired during 3 yr of campaigns show interesting resemblance to other independent results in the literature. A final analysis suggests that the impact of error sources will be substantially reduced in instruments of the next generation of giant telescopes