Abstract

We use Mellin-transform techniques to derive generalized expressions for the piston-removed and piston-and-tilt-removed anisoplanatic error in non-Kolmogorov turbulence with a finite outer scale. We use these expressions to investigate the behavior of the anisoplanatic error when imaging over long horizontal paths where the angular extent of the scene is often many times the isoplanatic angle. By evaluating these expressions, we first find that in many cases, the anisoplanatic error saturates to a value less than $1\; {{\rm{rad}}^2}$. Next, as power law increases, the contributions due to piston and tilt dominate the anisoplanatic error expression. Last, the size of the outer scale contributes primarily to the piston and tilt terms. Together, these behaviors imply that when piston and tilt are removed, anisoplanatism is reduced by as much as 60%.

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