Dielectric barrier discharges, particularly micro cavity plasma arrays, offer significant potential for plasma-catalytic research due to their ability to ignite plasma in direct contact with a catalytic surface, enabling the observation of plasma-surface interactions. A key factor in their application is the generation of reactive species, such as atomic oxygen, within the cavities. These species can interact with both, the surface (e.g., for activation or cleaning) and the gas being treated (e.g., for oxidation). Given the central role of oxygen atoms in plasma catalysis and their use as a model for more complex species, this work investigates the transport of these atoms out of the cavities. Two-photon absorption laser induced fluorescence (TALIF) spectroscopy with picosecond resolution is performed in the volume above the cavities. The results are compared with a basic diffusion model. The reactor operates with a He/O2 mixture at a flow rate of 1slm and atmospheric pressure. Densities of up to 10^16cm^-3 are measured near the surface. Time-dependent measurements show that, at a distance of 350µm from the surface, a density equilibrium is reached within less than 3ms of reactor operation. Decay times due to ozone formation after the reactor is turned off are on a similar scale. Spatially resolved measurements show that the oxygen density decreases exponentially from the surface but remains detectable up to approximately 1mm above the surface, indicating significant application potential. Variations in the O2 admixture show a density maximum at 0.4%, confirming previous helium state enhanced actinometry measurements within the cavities.