Resolving power evaluation of optical adaptive systems through the atmosphere

The resolving power is theoretically investigated of an adaptive optical system in the atmosphere. The system corrects phase and amplitude fluctuations produced by the atmospheric turbulence on an optical wave after an atmospheric path. Numerical evaluations in particular cases, of both short and long exposures for different adaptive corrections, show that even partial correction of the phase fluctuations gives rise to large increase of the resolving power. At low corrections and diameter of the system of the order of the turbulence outer scale, short exposure are more efficient and present a maximum versus the system diameter. This can be qualitatively explained by noting that, for values of the diameter sufficiently small (less than the turbulence outer scale), the aperture is smaller than a coherence area of the phase and the overall effect of the turbulence is a tilt of the wavefront over the aperture. At larger diameters both short and long exposures coincide. The main result is that, in the considered cases, even a partial correction of the phase fluctuations gives rise to a large increase of the resolving power, overcoming the saturation limit imposed by the atmospheric turbulence. These results are of interest both in astronomy and in laser atmospheric propagation.