Speckle At Various Planes In An Optical System

The statistical theory of speckle is presented in detail, including discussions of the transmission functions for a surface roughness type of diffuser and the associated characteristic function. The correlation function for the output amplitude is calculated for a variety of optical systems. These second-order moments are written for two states of position and temporal-frequency variables so that one can analyze both the spatial and the wavelength dependence of speckle. We parallel the usual cases that are treated in Fourier optics, summarizing the following configurations: space-variant, Fourier transform, far-zone, and imaging.