Photon statistics in adaptive optics

Random aberrations due to atmospheric turbulence determine the angular resolution of ground-based telescopes. Adaptive optics systems compensate the wavefront degradation before detection. Although systems with a large number of subapertures in the wavefront sensor and of actuators in the deformable mirror provide the best results, they are complicated and expensive. In contrast, simpler adaptive optics systems, (less than one actuator per atmospheric coherence diameter), compensate partially the wavefront distortions, having great potential application. The statistics of the image plane light intensity in partial compensation have been described using the Rician distribution. In order to achieve a more complete description of the phenomena, we describe the photon statistics in the whole image plane using the Poisson transform of the Rician distribution. When there is no compensation, the photon statistics follow a Bose-Einstein distribution. In partial compensation the PSF is composed by a bright core, where the photon statistics follow a Laguerre distribution, surrounded by a speckled halo with Bose- Einstein statistics. Some special cases have been studied and useful approximations have been derived. Theoretical results fit well with simulated values. This description of the light statistics as a function of the compensation may be used to extract more information about the object.