Measuring the topological charge (TC) of optical vortices is crucial for advancing applications in areas such as optical communication and quantum information processing. Although various interferometric and non-interferometric techniques have been developed for coherent and partially coherent beams, most of these methods are ineffective for fractional-vortex beams, especially when the beam gets perturbed. In this work, we propose and experimentally demonstrate a simple, non-interferometric technique based on autocorrelation for assessing and quantitatively measuring the TC of fractional vortex beams. We generated fractional optical vortex beams using computer-generated fork-shaped holograms and then obtained the corresponding random optical patterns after scattering through a rough surface. The autocorrelation rings of random patterns provide the TC of fractional vortex beams, and the asymmetry gradually becomes symmetric as the TC approaches an integer value. Additionally, by examining the divergence of the first dark ring with respect to propagation distance, we can quantitatively estimate the fractional TC. The measured divergence closely matches theoretical results, achieving an accuracy of over 98 %. The proposed method eliminates the need for phase retrieval, coherence modulation, or interferometry, providing a practical and robust solution for measuring fractional TCs, even in the presence of perturbations such as scattering and mild atmospheric turbulence, which are common in free-space optical communication systems.
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