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

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

2011-02-27

arxiv.org/abs/1102.5513v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

10 pages, 5 PostScript figures, RevTeX4

Scientific paper

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.

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