Tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics - Reconstruction of the long exposure point spread function from control loop data

A method is presented for estimating the long exposure point spread function (PSF) degradation due to tilt anisoplanatism in a laser-guide-star-based multiconjugate adaptive optics systems from control loop data. The algorithm is tested in numerical Monte Carlo simulations of the separately driven low-order null-mode system, and is shown to be robust and accurate with less than 10% relative error in both H and K bands down to a natural guide star (NGS) magnitude of m(R) = 21, for a symmetric asterism with three NGS on a 30 arcsec radius. The H band limiting magnitude of the null-mode system due to NGS signal-to-noise ratio and servo-lag was estimated previously to m(R) = 19. At this magnitude, the relative errors in the reconstructed PSF and Strehl are here found to be less than 5% and 1%, suggesting that the PSF retrieval algorithm will be applicable and reliable for the full range of operating conditions of the null-mode system.