Characteristics of the phase of Gaussian speckles are studied theoretically in both image and diffraction fields. The general analysis for these studies is given by introducing an "optical system function," and the results are applied to the analysis of the speckle phases in both fields. The speckle phase distributions are evaluated by a phase angle defined as the extent of the equiprobability density ellipse stretched from the origin in the complex plane of the speckle amplitude. In addition, several peculiar properties of the equiprobability density ellipse are summarized.
"Statistical Properties Of The Speckle Phase In Image And Diffraction Fields," Optical Engineering 25(5), 255627 (1 May 1986). https://doi.org/10.1117/12.7973876