Oxygen determination based on luminescence quenching of fluorescent dye is effected by using the frequency output of an offset-phase locked loop (15) to calculate the time constant for the exponential decay of fluorescence. An offset phase angle between a periodic stimulus signal used to excite the dye and a response signal based on fluorescence detection is predetermined to optimize signal-to-noise ration for a wide range of time constants. An offset-phase locked loop (15) is used to vary the frequency of a periodic stimulus signal until the predetermined phase relationship is established, and the frequency forms a measure of the decay rate. Where the stimulus and response signals are substantially sinusoidal, the offset phase angle is ideally about 49.3°, although substantially optimal performance is achieved using a more conveniently generated 45°. The 45° angle offset can also be used with a square-wave stimulus signal.