Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering


Several observations of atmospheric turbulence statistics have been reported which do not obey Kolmogorov's power spectral density model. These observations have prompted the study of optical propagation through turbulence described by non-classical power spectra. This thesis presents an analysis of optical propagation through turbulence which causes index of refraction fluctuations to have spatial power spectra that obey arbitrary power laws. The spherical and plane wave structure functions are derived using Mellin transform techniques and are applied to the field mutual coherence function (MCF) using the extended Huygens-Fresnel principle. The MCF is used to compute the Strehl ratio of a focused, constant amplitude beam propagating in non-Kolmogorov turbulence as the power law for the spectrum of the index of refraction fluctuations is varied from -3 to -4. The relative contributions of the log amplitude and phase structure functions to the wave structure function are computed. If inner and outer scale effects are neglected, no turbulence exists when the power law equals -3. At power laws close to -3, the magnitude of the log amplitude and phase perturbations are determined by the system Fresnel ratio. At power laws approaching -4, phase effects dominate in the form of random tilts.

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