January 1976

Document Type


Degree Name



Dept. of Applied Physics


Oregon Graduate Center


This thesis is concerned with the statistical properties of the random processes describing optical wave propagation through the turbulent atmosphere. Of specific interest are the effects of short time averaging, necessitated by various circumstances, on the statistical measures of the random processes, most significantly the variances Cn2, the atmospheric structure constant, and σ[ subscript X, superscript 2] , the normalized variance of the log optical amplitude fluctuations. Details of the statistical properties, including probability distribution functions, power spectra and correlation functions are presented. These include the following results. Small scale atmospheric fluctuations, in the present work differential temperature fluctuations, are seen to be highly non-Gaussian, with flatness factors as high as 14. The square of the temperature difference fluctuations, related to C [subscript n, superscript 2], are nearly lognormally distributed in well developed turbulence, over a range of short averaging times. The fluctuations in the logarithm of the optical irradiance after propagation through turbulence were similarly analyzed. These fluctuations are normally distributed over a wide range of turbulence conditions. Measurements of the two point conditional distributions show that the log irradiance fluctuations may be multidimensional Gaussian only when the turbulence level is low enough that σ[ subscript X, superscript 2] is much less than the saturation value. The averaging time dependence of the mean square error in the above variance measurements due to finite averaging time is described analytically as a simple 1/t relationship. The magnitude of this 'error', the data spread, depends on characteristics of the unaveraged random process, the flatness factor and the integral scale of the correlation function. A number of characteristics of the data spread of C [subscript n, superscript 2] and σ [subscript X, superscript 2] are presented including the dependence on turbulence level, mean wind speed and averaging time. The relationship between the data spreads in measured C [subscript n, superscript 2] and σ [subscript X, superscript 2] is investigated. This relationship involves a measure of the large scale structure of the C [subscript n, superscript 2] field along the propagation path. Measurements of the various data spreads and the spatial correlation function of C [subscript n, superscript 2] support the analytically derived relationships. Finally the effects of intermittent turbulence conditions on the various statistical measurements are discussed. These results include increased relative data spread in short time averaged C[ subscript n, superscript 2] measurements and deviation from lognormality of the probability distribution function of the temperature differential squared. The effects of intermittency on the propagation problem appear to be limited to the resultant increased data spread of the σ [subscript X, superscript 2] measurements.





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