Diffraction theory of optical scintillations due to turbulent layers

An analysis is presented for the modulation indices and spatial spectra of a plane wave that propagates in a uniform medium after having been randomized by passage through a turbulent layer. The method of smooth perturbations is employed to obtain the statistical boundary condition for the wave as it passes out of the layer, and the method of rigorous diffraction theory is used in the uniform medium beyond. The diffraction theory predicts a fine structure in the spatial irradiance pattern due to a single layer, which is not found in the usual approximations. Applying the results to atmospheric turbulence, we show that the fine structure is enhanced by the amplitude fluctuations effected in the layer. However, the effects will usually be lost by aperture averaging.