Angular anisoplanatism in non-Kolmogorov turbulence over horizontal and slant paths

We present 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 and slant-paths paths, through a Hufnagel-Valley turbulence profile, where the angular extent of the scene is often many times the isoplanatic angle. By evaluating these expressions we first found that the removal of piston and tilt contributions causes the isoplanatic angle to increase in all cases. Relatedly, when turbulence is weighted nearer to the aperture the anisoplanatic error is more likely to saturate to a value less than 1 rad² for larger outer scales, regardless of piston and tilt removal.