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A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.

Sky coverage estimates for adaptive optics systems from computations in Zernike space