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

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