The ozone production process in a pulsed positive dielectric barrier discharge (DBD) is studied by measuring the spatial distribution of ozone density using a two-dimensional laser absorption method. DBD occurs in a 6 mm point-to-plane gap with a 1 mm-thick glass plate placed on the plane electrode. First, the propagation of DBD is observed using a short-gated ICCD camera. It is shown that DBD develops in three phases: primary streamer, secondary streamer and surface discharge phases. Next, the spatial distribution of ozone density is measured. It is shown that ozone is mostly produced in the secondary streamer and surface discharge, while only a small amount of ozone is produced in the primary streamer. The rate coefficient of the ozone production reaction, O + O2 + M → O3 + M, is estimated to be 2.5 × 10-34 cm6 s-1.