Online estimation of atmospheric turbulence parameters and outer-scale profiling

Abstract

Estimating the outer scale profile, L<SUB>0</SUB>(h) in the context of current very large and future extremely large telescopes is crucial, as it impacts the on-line estimation of turbulence parameters (Cn<SUP>2</SUP>(h), r<SUB>0</SUB>, θ<SUB>0</SUB> and τ<SUB>0</SUB>) and the performance of Wide Field Adaptive Optics (WFAO) systems. We describe an on-line technique that estimates L<SUB>0</SUB>(h) using AO loop data available at the facility instruments. It constructs the cross-correlation functions of the slopes of two or more wavefront sensors, which are fitted to linear combinations of theoretical responses for individual layers with different altitudes and outer scale values. We analyze some restrictions found in the estimation process, which are general to any measurement technique. The insensitivity of the instrument to large values of outer scale is one of them, as the telescope becomes blind to outer scales larger than its diameter. Another problem is the contradiction between the length of data and the stationarity assumption of the turbulence (turbulence parameters may change during the data acquisition time). Our method effectively deals with problems such as noise estimation, asymmetric correlation functions and wavefront propagation effects. It is shown that the latter cannot be neglected in high resolution AO systems or strong turbulence at high altitudes. The method is applied to the Gemini South MCAO system (GeMS) that comprises five wavefront sensors and two DMs. Statistical values of L<SUB>0</SUB>(h) at Cerro Pachón from data acquired with GeMS during three years are shown, where some interesting resemblance to other independent results in the literature are shown.