Photon-Count Distributions and Irradiance Fluctuations of a Log-Normally Distributed Light Field*

We discuss some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with large surface inhomogeneities (average size 20 μm), when the illuminated area of the scattering surface contains only a few scattering centers. Photon-count distribution measurements indicate that, to a high degree of accuracy, the field amplitude of the scattered light fluctuates as a log-normal variate. The irradiance correlation function is a gaussian function of time with a half-width at half-height that varies inversely with the angular speed of the ground glass but is largely independent of the angle of scattering. Identical functional dependence was previously found, using a ground glass with much smaller surface inhomogeneities (average size 1 μm). Finally, we report some experimental tests of a recent calculation by Mitchell concerning what has been defined as the permanence of the log-normal distribution. We find that, even when the detecting surface of the photomultiplier is illuminated by several coherence areas of the scattered field during a single counting interval, the field-amplitude distribution remains log-normal to an excellent approximation.