Eecient Two-parameter Hankel Transforms in Adaptive Optics System Evaluations

We derive e cient approaches for two-parameter Hankel transforms. Such transforms arise, for example, in covariance matrix computations for performance modeling and evaluation of adaptive optics (AO) systems. Fast transforms are highly desirable since the parameter space for performance evaluation and optimization is large. They may be also applicable in real-time control algorithms for future AO systems. Both approaches exploit the analytical properties of the Hankel transform and result in structured matrix representations of approximate transforms. The approximations can be made to satisfy any pre-speci ed accuracy requirement. The matrix structures can then be exploited in subsequent computations to signi cantly reduce computation cost.