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The technique of spatially resolved cross-correlation spectroscopy (CCS) was used to carry out systematic diagnostic measurements of the barrier discharges (BDs) in Ar/N2 mixtures at atmospheric pressure. The spatio-temporal distributions of the light emission intensities for several selected spectral indicators (λ = 309, 337, 727, 751, 764 nm) corresponding to the volume part of the discharge as well as to the surface part of the BD were recorded. In the diffuse mode, the spatio-temporal distributions of the radiation intensities of different spectral indicators in the BD in Ar/N2 mixtures were found to be very similar to the corresponding distributions in pure nitrogen. In the filamentary mode, the surface discharges were found to propagate from the gap over both electrodes to a distance of about 1 cm.