Long-exposure filtering of turbulence-degraded wavefronts

The quasi-static aberrations of optical telescopes are often determined using light from a star as the reference wavefront. We calculate the exposure time necessary to determine the amplitude of the phase aberrations for a given telescope to a given accuracy in the presence of atmospheric seeing. We implement a computational simulation of the atmosphere and present the root mean square of the generated wavefront Zernike amplitudes for a given exposure time. We find the exposure time τ required to reach a desired precision is strongly dependent on telescope diameter (τ∝D(8/3)) and can be many tens of minutes in extreme cases. We present the results so τ can be calculated for a range of telescopes and atmospheric parameters.