Fresnel tomography and interferometric technique for characterizing Laguerre-Gaussian beams

The Fresnel tomograms of Laguerre-Gaussian beams are found and the relation of the two-point spatial correlation function with the tomographic map is discussed. The spatial distribution and signature of vorticity of Laguerre-Gaussian modes is analyzed by measuring the two-point spatial correlation function of the one-dimensional projection of the vortex field. 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 is also described; this approach allows one to characterize the vortex structure and spatial coherence along the direction of propagation.