Second Moments of Optical Degradation Due to a Thin Turbulent Layer

The effect of thin turbulent layers, including boundary layers and shear layers, on light propagation is examined from a theoretical point of view. In particular, a mathematical model is developed to describe the interaction between the aerodynamic or, more precisely, the density fluctuations and the electromagnetic field. It is assumed that the turbulence induces a normally distributed phase aberration which is a homogeneous random function in the plane of the aperture. Hypotheses concerning the density fluctuations in the layer sufficient to guarantee such a phase aberration are exhibited.

The optical degradation is described in terms of the optical transfer function (OTF) and the Strehl ratio (I/IO) which are random. Expressions for the first and second moments of these two parameters are developed from the definitions. Asymptotic ("large" aperture) approximations to these expressions are derived and discussed. Finally, the exact and approximate results are compared for several "typical" values of the ratios of aperture diameter to scale of density fluctuations and rms phase aberration to wave length respectively.