Optimal Signal Processing in Cavity Ring-down Spectroscopy

In this chapter, the authors present a systematic statistical analysis of cavity ring-down signal extraction. The traditional uncorrelated least squares fit can be generalized to the situation with data correlation (e.g. caused by data filtering, which is essential to minimize noise). If the data is sufficiently highly sampled, the effect of the data correlation can be included by introducing an effective variance of the data. This correction has substantial influence on the estimation of the standard error of the fit parameters for correlated data, especially for the fitted decay rate k0, because this determines the final sensitivity. For both the white noise dominated and the shot noise dominated situations, the sensitivity limit is given. The authors found that the bias of k in the white noise situation is normally very small and can be neglected. The authors also compared several commonly used alternative algorithms in cavity ringdown community. These mathods include linearized weighted least squares fit, determining the decay rate by Fourier transform, corrected successive integration (CSI)