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 b(1)Sigma(g)(+) - X(3)Sigma(g)(-) (1,0) band in molecular oxygen at 687 nm using a tunable diode laser and a relatively high-Q optical cavity (finesse approximate to4000). A detection limit of 3 x 10(-8) cm(-1) s(1/2) is achieved for a 0.8 cm(-1) scanning range.