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