Atmospheric image blur with finite outer scale or partial adaptive correction

Context. Seeing-limited resolution in large telescopes operating over wide wavelength ranges depends substantially on the turbulence outer scale and cannot be adequately described by one seeing value. Aims. This study attempts to clarify frequent confusions between seeing and the full-width at half-maximum of long-exposure images in large telescopes, also often called delivered image quality. Methods. We study the effects at the focus of a telescope of finite turbulence outer scale and partial adaptive corrections, both corresponding to a reduction in the low-frequency content of the phase perturbation spectrum, by means of analytical calculations and numerical simulations. Results. If a von Kàrmàn turbulence model is adopted, a simple approximate formula predicts the dependence of atmospheric long-exposure resolution on the outer scale over the entire practically interesting range of telescope diameters and wavelengths. In the infrared (IR), the difference from the standard Kolmogorov seeing formula can exceed a factor of two. We find that a low-order adaptive turbulence correction produces residual wavefronts effectively of small outer scale, so even a very low compensation order leads to a substantial improvement in resolution over seeing, compared to the standard theory. Conclusions. Seeing-limited resolution of large telescopes, especially in the IR, is currently under estimated by not accounting for the outer scale. On the other hand, adaptive-optics systems optimized for diffraction-limited imaging in the IR can improve the resolution in the visible by as much as a factor of two