Abstract
Mathematical techniques, developed for the theory of turbulence, are applied to the study of the propagation of waves in a medium in which the refractive index varies slightly with position in a random manner. Both a diffraction and a ray theory are used to relate the statistical properties of the wave to those of the refractive index field, and the conditions for the validity of the ray theory are exposed. A particular result is, that, for a wave travelling in a statistically homogeneous medium where the scale of the variations in refractive index is suitably large compared with the wave length but small compared with the path length, the variations in intensity produced by the medium are proportional to the cube of the path length for short paths, but directly proportional to it for long paths.
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