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We obtain a complete characterization of a vectorial, random light beam carrying orbital angular momentum (OAM) across L modes in its 2 L -dimensional polar Fourier space defined by the Modelization Matrix (MM), whose elements are scalar radial field correlations filtered at the pairs of OAM and polarization components. The MM is shown to encode a fully structured state uniquely represented by an ellipse, providing a geometrical signature of the beam. Various measures quantifying the modal weight distribution and coupling of the beam are introduced. A numerical example is presented for visualization.
Laatikainen et al. (2026) studied this question.