title: Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.
abstract: By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.
authors.affiliation: Department of Mathematical Sciences, Montana State University, Montana 59717-2400, USA. yang@math.montana.edu
authors.forename: Qiang
authors.initials: Q
authors.lastname: Yang
authors.forename: Curtis R
authors.initials: CR
authors.lastname: Vogel
authors.forename: Brent L
authors.initials: BL
authors.lastname: Ellerbroek