ABSTRACT
In the previous two chapters the effect of the choice of phase spectrum on the fluctuation properties of waves scattered by joint Gaussian random phase screens was investigated. This choice of model for the phase variations was based in part on its well-known mathematical properties that facilitate analytical and numerical work. Also, in many practical situations of interest the exact nature of the phase fluctuation statistics is unknown and the Gaussian model is a plausible and convenient option that enables a qualitative understanding of the consequent properties of the scattered waves to be developed. In some situations the Gaussian model does indeed provide a fair representation of the first-order statistics, but the higher-order properties deviate from the joint Gaussian model. There is some evidence, for example, that the distribution of phase across a beam of light that has passed through a turbulent thermal plume may be gamma rather than Gaussian distributed [1]. Moreover, it is clear from common observation that there are many scattering objects introducing phase fluctuations into an incident wave that cannot be Gaussian at any level. This is particularly true of the rough interface between different media. For example, it is evident that neither the sea surface height nor its slope can generally be described by any kind of symmetric distribution since the crests of wind-driven waves are typically sharp and asymmetric while the troughs are shallow. In a completely different context, machined surfaces often consist of a series of grooves with rather irregular spacing, reflecting the imperfect nature of the cutting tool, so that the equivalent phase screen is effectively bimodal.
