Twist direction and degree of interference fringes collected in double-slit interference experiment can be used to determine the topological properties of vortex beams, and the modulation depth of interference fringes indicates the spatial coherence of vortex beams. The effects of distance between double slits and the initial coherence length of the beam on the visibility and the twist degree of interference fringes in the partially coherent vortex beam topological charge interference measurement are analysed by adjusting the double-slit distance and the coherence length of the partially coherent vortex beam under near-field conditions. The study found that the interference fringes are distorted with the increase of the double slit distance, but the interference fringes and their distortion are not obvious when the initial coherence length of the partially coherent vortex beam is shorter than the beam width. Visible interference fringes will appear when the initial coherence length is longer than the beam width and the twist degree of interference fringes also increase. The coherence length has little effect on the visibility and distortion of the interference fringes when the initial coherence is greater than the size of the light spot on cross-section where the double slits are located, but the distance between the double slits still affects the observation to the visibility of interference fringes and distortion phenomenon. The research results may be useful for the measurement of orbital angular momentum of partially coherent vortex beams.
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.