Atmospheric image blur with finite outer scale or partial adaptive correction

TL;DR

This paper investigates how finite turbulence outer scale and partial adaptive corrections influence the resolution of large telescopes, revealing that accounting for these factors significantly improves imaging performance, especially in the infrared.

Contribution

It provides analytical formulas and numerical simulations to clarify the impact of turbulence outer scale and adaptive correction on telescope resolution, highlighting the importance of these factors in performance estimates.

Findings

Finite outer scale can double the resolution difference in IR.

Low-order adaptive correction significantly improves resolution.

Standard seeing estimates underestimate large telescope performance.

Abstract

Seeing-limited resolution in large telescopes working over wide wavelength range depends substantially on the turbulence outer scale and cannot be adequately described by one "seeing" value. We attempt to clarify frequent confusions on this matter. We study the effects of finite turbulence outer scale and partial adaptive corrections by means of analytical calculations and numerical simulations. If a von Karman turbulence model is adopted, a simple approximate formula captures 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 with the standard Kolmogorov seeing formula can exceed a factor of two. We find that low-order adaptive turbulence correction produces residual wave-fronts with effectively small outer scale, so even very low compensation order leads to a substantial improvement in resolution over seeing, compared to the standard theory. 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 designed for diffraction-limited imaging in the IR can improve the resolution in the visible by as much as two times.