Updated analyses of several singlet Rydberg states of O2 via spectra involving excitation from the metastable a1Δg and b1Σg+ states are presented. The high quality FT-VUV spectra available from the DESIRS beamline at the SOLEIL synchrotron gives significantly improved spectra compared to previous work. The Rydberg states analysed include 3pπ1Σu+ v=0-4, 3pσ1Πu v=0-2, 3pπ1u v=0-2, 4pπ1Σu+ v=0-1, 4pσ1Πu v=0 and 4pπ1Δu v=0. This is complemented by high quality ab initio calculations on the 1Σu+ and 1u Rydberg states to determine the transition moments providing the first quantitative cross sections for Rydberg – b1Σg+ transitions. These are validated against the experimental data. The results suggest the most promising candidate for determining b1Σg+ number density is likely to be the 1-0 band of the 4pπ1Σu+ – b1Σg+ transition at 131.3 nm.