Deep-Learning-Enabled Continuous Regression of Fractional Topological Charge from Speckle Patterns

Optical vortex beams that carry orbital angular momentum are widely used in optical communication, quantum information, and optical manipulation, where precise detection of the topological charge is essential, but existing machine learning approaches treat topological charge detection as a discrete classification problem, which limits the extraction of fractional topological charge, as it varies continuously and requires a regression-based model. Here, we developed a customized model for extracting the charge of fractional optical vortices using their perturbed intensity distribution, i.e., speckles, obtained by scattering them through a rough surface. When evaluated on experimentally generated speckle patterns, the fully supervised model achieved a mean absolute error (MAE) of 0.0394 and an R2 value of 0.9997. To assess its interpolation capability, the model was trained using sparse data, specifically integer and half-integer charges, and successfully detected previously unseen fractional topological charges, achieving an MAE of 0.122 and a mean absolute percentage error of 3.11%. These results demonstrate the potential of the model as a non-interferometric method for fractional topological charge detection in scattering environments, particularly under data-scarce conditions.