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

We describe an online method to estimate the wavefront outer scale profile,L0(h), for very large\udand future extremely large telescopes. The stratified information on this parameter impacts the\udestimation of the main turbulence parameters [turbulence strength, Cn\ud2(h); Fried’s parameter,\udr0; isoplanatic angle, θ 0; and coherence time, τ 0) and determines the performance of wide-\udfield adaptive optics (AO) systems. This technique estimates L0(h) using data from the AO\udloop available at the facility instruments by constructing the cross-correlation functions of the\udslopes between two or more wavefront sensors, which are later fitted to a linear combination\udof the simulated theoretical layers having different altitudes and outer scale values. We analyse\udsome limitations found in the estimation process: (i) its insensitivity to large values of L0(h) as\udthe telescope becomes blind to outer scales larger than its diameter; (ii) the maximum number\udof observable layers given the limited number of independent inputs that the cross-correlation\udfunctions provide and (iii) the minimum length of data required for a satisfactory convergence\udof the turbulence parameters without breaking the assumption of statistical stationarity of\udthe turbulence. The method is applied to the Gemini South multiconjugate AO system that\udcomprises five wavefront sensors and two deformable mirrors. Statistics of L0(h) at Cerro\udPachon from data acquired during 3 yr of campaigns show interesting resemblance to other ´\udindependent results in the literature. A final analysis suggests that the impact of error sources\udwill be substantially reduced in instruments of the next generation of giant telescopes