Multi-conjugate adaptive optics for a new generation of giant telescopes

A handful of groups around the world are actively working on the development of the next generation of telescopes of 30 m diameter and more. Present implementations of adaptive optics will be inadequate to realize the full resolving power of these new instruments in imaging and spectroscopy. Instead, multi-conjugate adaptive optics (MCAO) systems are being contemplated. We explore here the application of MCAO using laser guide beacons, to a 30 m telescope. Using a new simulation code, we show that reliance on the expensive lasers needed to generate sodium resonance beacons can be reduced through the use of refocused Rayleigh laser guide stars at much lower cost. We show that in the geometric optics approximation, modes of the phase distortion of order less than or equal to the number of deformable mirrors in the MCAO are correctable with no isoplanatic error. A new figure of merit is derived which predicts the relative ability of a chosen beacon/deformable mirror architecture to sense and correct wavefront aberration, based solely on knowledge of the optical geometry and the statistics of the aberration to be corrected. Numerical simulation can therefore be minimized by avoiding the exploration of unpromising beacon arrangements.