Saturation of anisoplanatic error in Kolmogorov and non-Kolmogorov turbulence

Abstract

This work explores the conditions resulting in the saturation of angular anisoplanatic error. When turbulence is modeled with a von Kármán outer scale or when the piston and aperture tilt are compensated the anisoplanatic error can saturate to less than one squared radian. In Kolmogorov turbulence anisoplanatic error is limited to values smaller than one when the ratio of the Fried parameter to the outer scale is 0.349. To understand the effect of compensation on saturation both a first-order asymptotic approach and numerical integration are considered for both plane and spherical wave sources and in non-Kolmogorov turbulence. Asymptotic expressions are found to agree with the numerical results as long as the ratio of the outer scale to aperture size is less than five. For a plane wave propagating in Kolmogorov turbulence, the compensated anisoplanatic error is found to saturate when D/r0=3.9, and the outer scale is equal to the aperture size. When a spherical wave source is considered D/r0 increases to 5.8; as expected these values are related by a factor of 1.8. This work also formulates the anisoplanatic error in terms of an integrated strength parameter and the mean turbulence height allowing extension to arbitrary path geometries and power law exponents. Using this approach I find smaller power law exponents increase the mean turbulence height, thereby decreasing the isoplanatic angle; the opposite applies as the power law exponent is increased relative to Kolmogorov turbulence.