Non-Gaussian fluctuations in electromagnetic radiation scattered by random phase screen. I. Theory

The statistical, spatial and temporal coherence properties of electromagnetic radiation scattered into the far field by a deep random phase screen are investigated. It is shown that significant departures from Gaussian behaviour can occur even when the phase correlation length is much smaller than the dimensions of the scattering region-a situation in which the central limit theorem might be expected to apply. Formulae are derived relating these departures to elementary properties of the scattering structure, which may therefore be determined by measurement of the fluctuations in the scattered radiation. Application of the results to scattering from very rough surfaces is discussed.