We describe a method for off-line analysis of spectra measured by two-
dimensional angular correlation of annihilation radiation (2D-ACAR) po
sitron spectroscopy. The method takes into account, at all its stages,
two salient data features: the piecewise constant discretization of t
he 2D physical momentum distribution into square pixels, performed by
the setup, and the occurrence of a characteristic 2D projected symmetr
y of the positron-electron pair momentum distribution. Several validat
ing criteria are derived which secure significantly increased reliabil
ity of the output. The method is tested on 2D-ACAR spectra measured on
(R)Ba2Cu3O7-delta (R123; R = Y, Dy) single crystals. It resolves ridg
e Fermi surfaces (Fs) up to 3rd Umklapp components on both kinds of R1
23 spectra. Moreover, on a c-axis-projected Y123 spectrum, measured at
300 K, it resolves a small but clear signature of the pillbox Fs at t
he S point of the first Brillouin zone as well.