Efficient first-order performance estimation for high-order adaptive optics systems

Lund Observatory, Box 43, 22100 Lund, Sweden

Corresponding author: ralf@astro.lu.se

Received: 3 February 2003
Accepted: 25 April 2003

Abstract

It is shown how first-order performance estimation of high-order adaptive optics (AO) systems may be efficiently implemented in a hybrid numerical simulation by the use of 1) sparse matrix techniques for wavefront reconstruction, 2) undersampled pupil-plane turbulence-induced aberrations, and 3) analytical models that compensate – in the limit of infinite exposure time – for the errors introduced by undersampling. A sparse preconditioned conjugate gradient (PCG) method is applied for wavefront reconstruction, and it is seen that acceptable AO performance may be achieved at a relative error tolerance of 0.01, at which the computational cost of the sparse PCG scales approximately as , where n is the number of actuators in the system. Estimations of adaptive optics performance for extremely high-order systems are presented, including multi-conjugate and laser-guide-star-based systems. The scaling laws for AO performance with telescope diameter D and turbulence outer scale L₀ coupled with the use of laser guide stars are also investigated. It is shown that a single or a small number of laser guide stars (LGS) may still provide a useful level of compensation to telescopes with diameters in the range 30–100 m, if L₀ is on the order of or smaller than D. The deviations from Kolmogorov theory are also investigated for LGS AO. To the best of the author's knowledge, results presented for a case represent the largest multi-conjugate adaptive optics system simulated in full to date.