Cavity-enhanced absorption spectroscopy is explained in terms of the transmission function of a rapidly swept interferometer, and the integrated transmission is shown to be proportional to the cavity ringdown time. The technique is demonstrated on the b1∑g+ - X3∑g- (1,0) band in molecular oxygen at 687 nm using a tunable diode laser and a relatively high-Q optical cavity (finesse ≈ 4000). A detection limit of 3 × 10-8 cm-1 s1/2 is achieved for a 0.8 cm-1 scanning range