Abstract
We obtain a complete characterization of a vectorial, ran-dom light beam carrying orbital angular momentum (OAM) across L modes in its 2L-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. Vari-ous measures quantifying the modal weight distribution and coupling of the beam are introduced. A numerical example is presented for Visualization. (c) 2026 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (Al) training, and similar technologies, are reserved.