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

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  O(n1.2), 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 authorʹs knowledge, results presented for a n= 65 282 case represent the largest multi-conjugate adaptive optics system simulated in full to date.