Modelling of Long Exposure Wavefront Errors for Extremely Large Telescopes

Quasi-static aberrations are wavefront distortions that vary on a timescale longer than that typically controlled by the active optics control loops used to maintain the image quality within a large telescope. The source of these errors can be due to gravitational or thermal flexure of the telescope; or poorly averaged atmospheric turbulence residuals. Following the method of Gordon et al. (2011), a simulation was used to explore the averaging rate of atmospheric turbulence residuals for a phase screen translating across the telescope aperture. Crucially, the rate at which the individual modes average out is dependent upon wind direction, meaning that both the Cn2 and wind velocity profiles can have a large effect on the modal variance of observed quasi-static aberrations. We have verified that the use of a Zernike covariance matrix library is both viable and useful when considering a multi-layered atmospheric profile with variable velocity dispersions. Using this library we tested the effects of finite averaging time in an active optics model, calculating the residual error generated by a correction from an off-axis guide star. We have used this model for varying atmospheric velocity dispersions and exposure times, for both existing telescopes and ELT scales.