This paper presents an elementary derivation of the basic phase statistics of an optical wave (both plane and spherical) propagating in a turbulent medium. The results are general in that they apply to an arbitrary passive spatially homogeneous turbulent medium. Explicit application of the analysis is directed to the atmosphere where we obtain the well known results of Tatarskii and others. The present approach provides an intuitive appreciation of the physical behavior of optical wave propagation through a medium which exhibits a spatially random index of refraction. As such, it is complementary to the rigorous mathematical derivations that appear in the literature.
H. T. Yura,
"An Elementary Derivation Of Phase Fluctuations Of An Optical Wave In The Atmosphere", Proc. SPIE 0075, Imaging Through the Atmosphere, (19 July 1976); doi: 10.1117/12.954731; https://doi.org/10.1117/12.954731