When the frequency of light coupled into a cavity is suddenly shifted, the radiation emanating from the input port of the previously excited cavity can beat with the reflection of the frequency-shifted input on the surface of a photodetector. When the beat frequency is stable, the time decay of the resulting optical heterodyne signal can be used to measure intracavity absorption spectra with near quantum-limited sensitivity. (C) 2000 Optical Society of America OCIS codes: 300.6360, 120.6200, 040.2840, 300.6310.