Two-photon absorption laser-induced fluorescence (TALIF) is used to measure the absolute density of atomic oxygen (O) in a coaxial microwave jet in ambient air at atmospheric pressure, operated with a mixture of He and a few per cent of air. The TALIF signal is calibrated using a gas mixture containing Xe. A novel method to perform calibration in situ, at atmospheric pressure, is introduced. The branching ratios of several Xe mixtures are reported, to enable us to perform the Xe calibration without the need for a vacuum vessel. The O densities are measured spatially resolved, and as a function of admixed air to the He, and microwave power. The electron density and temperatures are measured using Thomson scattering, and the N-2 and O-2 densities are measured using Raman scattering. O densities are found to have a maximum of (4-6) x 10(22) m(-3), which indicate that O-2 is close to fully dissociated in the plasma. This is confirmed by the Raman scattering measurements. O is found to recombine mainly into species other than O-2 in the afterglow, which is suggested to consist of O-3 and oxidized components of NO.