Sky coverage and tip/tilt error analysis for TMT

A Monte Carlo sky coverage model for laser guide star adaptive optics systems is presented. This model provides fast Monte Carlo simulations of the tip/tilt (TT) wavefront error calculated with minimum variance estimators over natural guide star constellations generated from star models. With this simulation code we are able to generate a TT error budget for the Thirty Metre Telescope (TMT) facility Narrow Field Infra-Red Adaptive Optics System (NFIRAOS), and perform several design trade studies. With the current NFIRAOS design, the median TT error at the galactic pole with median seeing is calculated to be 65 nm or 1.8 mas