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

It is shown how first-order performance estimation of high-orderadaptive optics (AO) systems may be efficiently implemented in a hybridnumerical simulation by the use of 1) sparse matrix techniques forwavefront reconstruction, 2) undersampled pupil-plane turbulence-inducedaberrations, and 3) analytical models that compensate - in the limit ofinfinite exposure time - for the errors introduced by undersampling. Asparse preconditioned conjugate gradient (PCG) method is applied forwavefront reconstruction, and it is seen that acceptable AO performancemay be achieved at a relative error tolerance of 0.01, at which thecomputational cost of the sparse PCG scales approximately asO(n<SUP>1.2</SUP>), where n is the number of actuators in the system.Estimations of adaptive optics performance for extremely high-ordersystems are presented, including multi-conjugate andlaser-guide-star-based systems. The scaling laws for AO performance withtelescope diameter D and turbulence outer scale L0 coupled with the useof laser guide stars are also investigated. It is shown that a single ora small number of laser guide stars (LGS) may still provide a usefullevel of compensation to telescopes with diameters in the range 30-100m, if L0 is on the order of or smaller than D. The deviations fromKolmogorov theory are also investigated for LGS AO. To the best of theauthors knowledge, results presented for a n=65 282 case represent thelargest multi-conjugate adaptive optics system simulated in full todate.