Nonlinear Dependence of the Phase Screen Structure Function on the Atmospheric Layer Thickness

TL;DR

This paper refines the understanding of the phase structure function in atmospheric turbulence, showing a nonlinear dependence on layer thickness, especially for large outer scales, through improved integral calculations.

Contribution

It introduces a refined calculation of the structure function integral, revealing a sub-linear dependence on layer thickness not captured by previous linear models.

Findings

Sub-linearity in the structure function with increasing layer thickness

Greater impact of the correction for large outer scales

Enhanced accuracy in modeling atmospheric turbulence effects

Abstract

The phase structure function accumulated by two parallel rays after transmission through a layer of turbulent air is best known by a proportionality to the 5/3rd power of the lateral distance in the aperture, derived from an isotropic Kolmogorov spectrum of the refractive index. For a von-Karman spectrum of the refractive index, a dependence involving a modified Bessel function of the ratio of the distance over the outer scale is also known. A further standard proposition is a proportionality to the path length through the atmospheric layer. The manuscript modifies this factor through a refined calculation of an integral representation of the structure function. The correction establishes a sub-linearity as the lateral distance grows in proportion to the layer thickness; it is more important for large than for small outer scales.