STATISTICAL PROPERTIES OF LASER SPARKLE PATTERNS

Abstract
When laser light strikes a diffuse object, such as paper, the scattered light has been observed to possess a granular spatial structure. The statistical properties of these so-called 'sparkle patterns,' as seen by an observer in the far field of the scattering spot, are investigated. The first order statistics of the observed electric-field strength, the observed light intensity, and the observed light phase are examined. The electric field is reasoned to be a complex normal random variable; the intensity a real, exponentially distributed random variable; and the phase a uniformly distributed random variable. Higher order statistics of these random processes are also discussed. The autocorrelation functions of the complex field and the intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light-intensity distribution incident on the scattering surface. Spatial averages of the light intensity are considered and are found to converge to corresponding ensemble averages when either the area of the scattering spot or the average area grows large.

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