The propagation of spherical waves in a turbulent medium is considered. In particular, the case of nonstationary statistics is examined in general and then applied to the specific case of vertical propagation in the atmosphere. The analysis uses the Rytov approximation and the perturbation technique of J. B. Keller. The model of Cn2(h) variation is exponential and similar to that utilized by Tatarski.
The results are compared to other known results for plane and spherical waves in both homogeneous and locally homogeneous random media. In addition, the optimum aperture results of D. L. Fried are examined for this nonstationary case. The marked dependence on the height of the observer and parameters describing the turbulence distribution are noted.
FREDERICK P. CARLSON and AKIRA ISIHMARU, "Propagation of Spherical Waves in Locally Homogeneous Random Media," J. Opt. Soc. Am. 59, 319-327 (1969)