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%.

中文翻译：

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非Kolmogorov湍流在水平路径上的角各向异性

我们使用Mellin变换技术来推导具有有限外部比例的非Kolmogorov湍流中的活塞被去除和活塞与倾斜被去除的等平面误差的广义表达式。当在较长的水平路径上成像时，我们使用这些表达式来研究等平面误差的行为，在这种情况下，场景的角度范围通常是等平面角的许多倍。通过评估这些表达式，我们首先发现，在许多情况下，各向异性的误差饱和到小于$ 1 \的值。{{\ rm {rad}} ^ 2} $。接下来，随着幂律的增加，归因于活塞和倾斜的贡献主导了各向异性的误差表达。最后，外部刻度尺的尺寸主要影响活塞和倾斜角度。这些行为共同暗示着，当消除活塞和倾斜时，各向异性将减少多达60％。