Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing

Abstract

We present a formalism for performance analyses of adaptive optics systems that use a polychromatic laser guide star to measure the tilt of atmospherically distorted wavefronts. This formalism can be applied to feasibility and design studies of polychromatic laser guide star tip-tilt systems that are used to make the adaptive optics system of a telescope independent of natural guide stars. Using a few simplifying assumptions, the results are presented in analytical form such that a range of system parameters can be studied easily. Directions for the use of more detailed models necessitating numerical calculations are also presented in case more in-depth studies of certain system aspects are desired. Along with the theoretical development, we also present examples of possible solutions of the planned ELP-OA system as well as of an implementation of polychromatic laser guide star systems at large astronomical telescopes.