Progress The research history about the effect of atmospheric turbulence on optical imaging resolution was reviewed. Based on Fried's study, some investigators studied the role of turbulence outer scale in imaging resolution power. In 1973 Consortini et al. first investigated the problem and proposed that if the value of the wave structure function over the outer scale is less than 20, the turbulence does not put a limit to the resolution of an optical system. In 1990 Borgnino explored the problem mainly for long baseline interferometry and imaging in optical astronomy. In such cases, the baseline length or the telescope aperture diameter is comparable with the turbulence outer scale, and in imaging through the whole atmosphere, the turbulence strength and the outer scale vary with height. Therefore, Borgnino proposed an equivalent outer scale defined as an averaged outer scale weighted by the turbulence strength at different heights.In 1991 McKechine proposed a fresh point of view on how atmospheric turbulence affects images formed by large ground-based telescopes. This means the atmosphere can be represented by an equivalent phase screen for the two quantities that determine most of the important image properties, including the atmospheric modulation transfer function and the spectral correlation function. In 1992 McKechine investigated the imaging resolution by large telescopes and concluded that the outer scale of atmospheric turbulence is practically small and less than 1 m. Since the telescope aperture is much greater than the turbulence outer scale, the effects of turbulence on imaging can be eliminated, and thus in this case the adaptive optics is unnecessary for both astronomical imaging and laser propagation.Tatarskii and Zavorotny criticized McKechnie's viewpoint and believed that star images presented by McKechnie could well be explained with the classical propagation theory and the traditional turbulent model. However, the McKechnie model of scattering, a single-scale atmosphere with an outer scale of 35 cm, contradicts all our experience with turbulence. This comment was supported by Gurvich and Belen'kii. In 1997, Chesnokov and Skipetrov analyzed the imaging resolution ability in turbulent atmosphere. In 2012, Lukin also investigated quantitatively the effect of outer scale on the imaging resolution of large telescopes. These results could be applied to explain McKechnie's image problem. However, McKechnie insisted on his viewpoint and developed his theory in the book General Theory of Light Propagation and Imaging through the Atmosphere with the first and second editions published in 2016 and 2022 respectively.On the other hand, our understanding of the turbulence outer scale has deepened quickly. Increasingly more practical measurements at different locations reveal that the outer scale is not as large as early thought and its characteristics are very complicated. Some models for height distribution of the outer scale were proposed for theoretical use, but in-situ measurements are still needed for practical applications.Conclusions and Prospects It is well recognized that the turbulence outer scale exerts significant influence on the imaging resolution power of large telescopes, and quantitative relationships can be established based on the classical theory of light propagation through turbulence. However, some different turbulence spectrum models that can be adopted for theoretical research on different relationships between the imaging resolution and the turbulence outer scale may be obtained. Practical measurements for the outer scale and experimental studies are necessary for building a reliable relationship.As the turbulence outer scale can only be defined qualitatively, a quantitative definition should be built to investigate its properties with systematic measurements by employing related measurement techniques based on different principles. This kind of work is critical not only for imaging applications but also for other applications such as atmospheric turbulence profiling.

The effects of atmospheric turbulence on astronomical observation (optical imaging) have long been recognized. Newton proposed that the observatory should be built on the top of a high mountain to reduce the turbulence effects. In modern time Fried investigated this problem based on the Kolmogorov turbulence model and obtained analytical formulae for resolution power. The Fried parameter r₀ has been widely applied to optical engineering. If r₀ is less than the lens diameter D, the resolution power will be determined by r₀ rather than D. A typical r₀ for a good observatory site is about 0.1 m and much less than the astronomical lens diameter, and the adaptive optics (AO) has to be employed to compensate turbulence-induced phase fluctuations. However, as the AO compensation efficiency degrades with turbulence and under strong turbulence AO can not work properly, large space telescopes such as Hubble and James Webb were launched into space to avoid Earth's turbulence. Meanwhile, some investigations reveal that the outer scale L₀ affects the resolution power. If L₀ is about or even less than the lens diameter D, the turbulence effect on imaging resolution power should be greatly reduced. As increasingly larger astronomical telescopes and optical engineering lenses are planned or being built, the effect of outer scale on imaging resolution power will play an essential role in the design and performance of the optical engineering system. Thus, it is necessary to clarify the outer scale properties of practical atmosphere turbulence and its effect on the imaging resolution power of large telescopes.