Studies on the dielectric surface parameters and dielectric barrier discharges (DBD) characteristics considering the influence of gases in DBD on the surface charge distribution are scarce. Thus, to overcome this research gap, this study measured the potential distributions of AC-driven surface DBD in oxygen (O2), synthetic air and nitrogen (N2) as background gases using the Pockels effect. The results showed that the patterns of the filamentary discharges generated during the positive voltage polarity phase differed depending on the O2 ratio. In addition, the electrostatic repulsion forces between the residual charge and the newly created filament were analysed from the measured potential distribution and the greatest effect was observed in air, rather than in N2 and O2. The potential distribution was transformed into a charge density distribution and compared with the discharge luminescence in air and N2. The results showed that the shape of the filament tip differed between the charge density and discharge luminescence only in the case of air, which was attributed to the effect of attachment reactions on the formation of residual charge. The measurements showed that in a surface discharge, similar to the case in a volume discharge, the photoionisation and ionisation coefficients significantly affected the geometrical properties of the discharges.