Non-Gaussian speckle caused by thin phase screens of large root-mean-square phase variations and long single-scale autocorrelations

Non-Gaussian speckle generated by the coherent superposition of a small number of random complex amplitudes can be physically realized through the elastic scattering of incident monochromatic radiation with a thin, nondepolarizing random phase screen. Under conditions of Gaussian-distributed phase fluctuations whose rms is much greater than 2π rad, whose lateral autocorrelation is Gaussian in shape with a correlation length z greater than twice the wavelength of the illumination, and for which the ratio of these two is less than 0.05, the Kirchhoff diffraction integral approximation can be applied. A series solution for the first and second intensity moments for the far field is derived and presented. The steepest-descents solution given by Jakeman McWhirter [ Appl. Phys. B26, 125 ( 1981)] converges to the given series solution for the mean intensity. With improved experimental technique, measurements of the normalized second moment are shown to agree with Jakeman and McWhirter’s approximation over a wide range of illuminated scattering centers. A computer simulation of this experiment for phase objects of up to 50-rad rms phase deviations is shown to agree well with predictions of the mean intensity. The second moments agree well in the low- and high-illumination limits but systematically overestimate the normalized second moment near the peak of each curve.