text: Cavity ring-down spectroscopy is a form of laser absorption spectroscopy.  In CRDS, a laser pulse is trapped in a highly reflective (typically R > 99.9%) detection cavity. The intensity of the trapped pulse will decrease by a fixed percentage during each round trip within the cell due to absorption, scattering by the medium within the cell, and reflectivity losses.  The intensity of light within the cavity is then determined as an exponential function of time.
  The principle of operation is based on the measurement of a decay rate rather than an absolute absorbance. This is one reason for the increased sensitivity over traditional absorption spectroscopy, as the technique is then immune to shot-to-shot laser fluctuations. The decay constant, τ, which is the time taken for the intensity of light to fall to 1/e of the initial intensity, is called the ring-down time and is dependent on the loss mechanism(s) within the cavity. For an empty cavity, the decay constant is dependent on mirror loss and various optical phenomena like scattering and refraction:
  where n is the index of refraction within the cavity, c is the speed of light in vacuum, l is the cavity length, R is the mirror reflectivity, and X takes into account other miscellaneous optical losses. This equation uses the approximation that ln(1+x) ≈ x for x close to zero, which is the case under cavity ring-down conditions.  Often, the miscellaneous losses are factored into an effective mirror loss for simplicity. An absorbing species in the cavity will increase losses according to the Beer-Lambert law. Assuming the sample fills the entire cavity,
  where α is the absorption coefficient for a specific analyte concentration at the cavitys resonance wavelength. The decadic absorbance, A', due to the analyte can be determined from both ring-down times.
  Alternatively, the molar absorptivity, ε, and analyte concentration, C,  can be determined from the ratio of both ring-down times. If X can be neglected, one obtains
  When a ratio of species' concentrations is the analytical objective, as for example in carbon-13 to carbon-12 measurements in carbon dioxide, the ratio of ring-down times measured for the same sample at the relevant absorption frequencies can be used directly with extreme accuracy and precision.