A proof of principle experiment was performed by recording the cavity enhanced absorption spectrum of the weak b- X transition of molecular oxygen in the atmosphere using a Ti:Sa femtosecond laser as an absorption source and a high resolution continuous scan Fourier transform interferometer. The cavity was mode matched and either continuously scanned or stabilized at the so-called magic point. An optimal rms noise equivalent absorption of 3 × 10 -7 cm -1 Hz -1/2 was reached in the latter case, corresponding to αmin = 3 × 10 -7 cm -1.