Phase structure function of random wave fields

The phase properties of a complex Gaussian field, which can arise following scattering from random phase screens and through extended random media, are investigated. It is shown that the unwrapped phase of a complex Gaussian field constitutes a non-stationary process, such that the phase autocorrelation function does not exist. However, the phase structure function remains finite, allowing analytical results to be obtained for various field correlations. Methods for numerical simulation are discussed and their results found to be in excellent agreement with analytical predictions. More general considerations reveal that the phase structure function of a complex Gaussian field increases linearly with large separation distance. The results are relevant to phase-sensitive detection in fields undergoing strong intensity fluctuations.