First-order Probability Densities of Laser Speckle Patterns Observed through Finite-size Scanning Apertures

The first-order probability density function of laser speckle patterns observed through finite size apertures is theoretically studied. An exact solution is obtained through the use of a two-dimensional Kac-Siegert analysis in terms of the spatial correlation function of the input. An approximate solution of Goodman is shown to be a limiting case of the exact theory. The probability density of the logarithm of the intensity is also derived. Representative numerical calculations are presented for a slit aperture.