Mathematical genesis of the I–K distribution for random optical fields

The recently developed I–K distribution and its connection with other distributions is examined in the context of optical waves scattered by a turbulent medium. In particular, it is shown how the I–K distribution, K distribution, and homodyned K distribution all evolve as marginal density functions from compound or doubly stochastic Gaussian optical fields. In this setting the genesis of the I–K distribution is very similar to that of the homodyned K distribution, and there is one special case (α = 1) in which the two distributions are identical. Also, both the homodyned K and the I–K distribution are shown to reduce to the K distribution in strong-turbulence regimes. The I–K distribution is further examined as a model for the irradiance when the distribution parameter α is restricted to half-integer values, leading to simpler forms of the distribution. The special case of the I–K distribution corresponding to α = 1/2 shows a particularly good fit with experimental data over a wide range of conditions of atmospheric turbulence.