© 2019 IOP Publishing Ltd. Gas density perturbations generated by an alternating-current dielectric-barrier-discharge plasma actuator (ac-DBDPA) are quantitatively visualised using the background-oriented schlieren (BOS) method. A method of setting the optimum boundary condition for solving the Poisson equation in the BOS method is studied, and an integration method for the boundary condition in the vicinity of the plasma where the density change is steep is proposed. The BOS method is applied in two cases with different voltage amplitudes, and the variation in the absolute value of the density is discussed with the discharge properties. The results show a decrease in density in the synthetic jet induced by the ac-DBDPA and a spatiotemporal variation indicating a step-wise gas-heating phenomenon due to plasma discharge.