Optical EngineeringAdaptive optics system performance approximations for atmospheric turbulence correction
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Analysis of adaptive optics system behavior often can be reduced to a few approximations and scaling laws. For atmospheric turbulence correction, the deformable mirror (DM) fitting error is most often used to determine a priori the interactuator spacing and the total number of correction zones required. This paper examines the mirror fitting error in terms of its most commonly used exponential form. The explicit constant in the error term is dependent on deformable mirror influence function shape and actuator geometry. The method of least squares fitting of discrete influence functions to the turbulent wavefront is compared to the linear spatial filtering approximation of system performance. The author finds that the spatial filtering method overestimates the correctability of the adaptive optics system by a small amount. By evaluating fitting error for a number of DM configurations, actuator geometries, and influence functions, fitting error constants verify some earlier investigations. Limitations of the approximations and scaling laws are evaluated and compared to wave optics ground-to-space propagations. Results include determination of a multiplicative conversion factor of 1.06 that should be applied to the actuator spacing whenever the spatial filtering method is used for adaptive optics system performance analysis.