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We derive an exact formula for the angular Schmidt spectrum of the orbitalangular momentum (OAM)-entangled states produced by parametric down-conversion(PDC). We show that our formula yields true theoretical spectrum without anyconvergence issue as has been the case with the previously derived formulas.Furthermore, we use this formula to experimentally characterize the angularSchmidt spectrum for non-collinear PDC. We report the measurements of verybroad angular Schmidt spectra corresponding to angular Schmidt numbers up to233, which, to the best of our knowledge, is the highest number reported sofar. Our studies can be very important for OAM-based quantum informationapplications.

Angular Schmidt spectrum of entangled photons: derivation of an exact formula and experimental characterization for non-collinear phase matching