Study of autocorrelations of the fluctuations in a gaussian beam propagating through a random medium of gaussian inhomogeneity is extended in this paper to considerations of the spatially transverse autocorrelations of the log-amplitude or phase fluctuations at two off-axis positions over the cross section of the collimated and focused beams. Two-dimensional autocorrelation distributions with respect to one fixed off-axis point are obtained over the beam cross section at and near the focal position of a focused beam. The cross correlations of log-amplitude and phase fluctuations for the collimated and focused gaussian beams propagating through a random medium have also been evaluated as functions of the wave parameter, the normalized focal length, and the source-aperture size. A comparison is made among the cross-correlation coefficients for plane, spherical, and gaussian beams.
© 1969 Optical Society of America
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