Generalized Fried parameter after adaptive optics partial wave-front compensation

Atmospheric turbulence imposes the resolution limit attainable by large ground-based telescopes. This limit is $\mathrm{\lambda }/r_0,$ where $r_0$ is the Fried parameter or seeing cell size. Working in the visible, adaptive optics systems can partially compensate for turbulence-induced distortions. By analogy with the Fried parameter, $r_0,$ we have introduced a generalized Fried parameter, ${\rho }_0,$ that plays the same role as $r_0$ but in partial compensation. Using this parameter and the residual phase variance, we have described the phase structure function, estimated the point-spread function halo size, and derived an expression for the Strehl ratio as a function of the degree of compensation. Finally, it is shown that ${\rho }_0$ represents the diameter of the coherent cells in the pupil domain.