A method for the practical determination of the absolute concentration of single (a1delta(g)) oxygen is discussed. The method is based on sensitive off-axis integrated-cavity-output spectroscopy (ICOS). Off-axis ICOS allows narrowband, continuous-wave lasers to be used in conjunction with optical cavities to record sensitive absorption measurements. The details of the method as well as spectroscopic data confirming the first observation of the (1, 0) band of the b1sigma(g)(+) - a1delta(g) Noxon system are presented. The absolute transition probabilities for the b1sigma(g)(+) - a1delta(g) Noxon system, which are not known precisely from experiments, are determined by quantum chemistry theory.