Fourier description of the axial structure of speckle

Abstract

The amplitude distribution along a longitudinal axis Oz of the field diffracted by a diffusing screen is described in statistical terms taking advantage of a Fourier correspondence between the longitudinal variable 1/z and the transverse squared polar coordinate r2; considering these reciprocal spaces, the longitudinal autocorrelation function of the speckle structure may be defined as the Fourier transform of the radial energy distribution transmitted by the diffuser (Van Cittert-Zernike theorem for longitudinal correlation analysis).