Skewed distribution of irradiance predicted by the second-order Rytov approximation

The first-order Rytov approximation predicts that the probability-density function for intensity fluctuations in a random medium should be a log normal distribution. Here the corrections to this prediction that arise from the second term in the Rytov series are explored. The primary effect is to skew the distribution so as to favor values that are less than the average. This effect is controlled by the Rytov variance beta0(2) alone, and the predicted distribution contains no adjustable parameters. The theoretical result is compared with numerical simulations for weak scattering of plane and spherical waves. The agreement is quite good unless the intensity fluctuations are very large or very small relative to the mean irradiance. In those ranges, the predictions require additional terms in the Rytov expansion.