Statistical characteristics of speckle field and orbital angular momentum of partially coherent superposition vortex beams

Abstract

The rotating speed of a target is usually measured using superposition vortex beams with opposite topological charges. Based on angular spectrum representation and Goodman’s speckle theory, the speckle characteristics of superposition vortex beams after passing through a rotating ground glass disk (RGGD) were studied. The statistical characteristics of the speckle field were analyzed using the theory of the orbital angular momentum (OAM) spectrum. The analysis determined the relationship between the spatial coherence length and the topological charge of a superimposition vortex beam and its speckle field. Moreover, the study explored the relationship between the speed of the ground glass disk (GGD) and the speckle field of the superposition vortex beam. Results show that the rotating speed of the GGD increases and the intensity distributions of generated partially coherent superposition vortex beams become increasingly uniform after passing through the RGGD. The speckles gradually disappear but the OAM spectrum becomes increasingly dispersive with increased rotating speed. These results might be useful for practical applications of the rotational Doppler effect in remote sensing and metrology.