Fourier projection method for measuring the two-point correlation of Laguerre-Gaussian modes

The spatial distribution and signature of vorticity of Laguerre–Gaussian modes is analysed by measuring the two-point spatial correlation function of the one-dimensional projection of the vortex field. We describe an interferometric approach, based on a Fourier projection algorithm, for the experimental determination of the two-point correlation function of the full complex vortex field at the cross-section plane of the recorded interference pattern. The two-point correlation at any transverse plane along the beam axis is retrieved by the angular spectrum of plane waves technique, allowing us to characterize the vortex structure and spatial coherencealong the direction of propagation.