Stochastic dynamics of the scattering amplitude generating K-distributed noise

We derive the stochastic dynamics of the complex valued amplitude resulting from coherent scattering from a random population of scatterers when this becomes asymptotically large. Considerations of a random walk model, introduced by Jakeman, are used to derive stochastic differential equations for the amplitude and corresponding intensity and phase stochastic processes. An analysis of the correlation structure in the fluctuations is provided and interpreted geometrically in terms of the gauge invariant properties of the field and the Markov property. A Fokker–Planck description for the evolution of the probability density is given and the equilibrium and detailed balance conditions shown to hold. Expressions for the intensity autocorrelation function and power spectral density are provided in closed form. The practical implications of the stochastic theory are discussed.