This paper discusses the application of a discrete-time extended Kalman filter (EKF) to the problem of estimating the decay time constant for a Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The data for the estimation process is obtained from a CRDS experimental setup in terms of the light intensity at the output of the cavity. The cavity is held in lock with the input laser frequency by controlling the distance between the mirrors within the cavity by means of a proportional-integral (PI) controller. The cavity is purged with nitrogen and placed under vacuum before chopping the incident light at 25KHz and recording the light intensity at its output. In spite of beginning the EKF estimation process with uncertainties in the initial value for the decay time constant, its estimates converge well within a small neighborhood of the expected value for the decay time constant of the cavity within a few ring-down cycles. Also, the EKF estimation results for the decay time constant are compared to those obtained using the Levenberg-Marquardt estimation scheme.
In this paper we report on the development of a Fourier-transform based signal processing method for laser-locked Continuous Wave Cavity Ringdown Spectroscopy (CWCRDS). Rather than analysing single ringdowns, as is the norm in traditional methods, we amplitude modulate the incident light, and analyse the entire waveform output of the optical cavity; our method has more in common with Cavity Attenuated Phase Shift Spectroscopy than with traditional data analysis methods. We have compared our method to Levenburg-Marquardt non linear least squares fitting, and have found that, for signals with a noise level typical of that from a locked CWCRDS instrument, our method has a comparable accuracy and comparable or higher precision. Moreover, the analysis time is approximately 500 times faster (normalised to the same number of time domain points). Our method allows us to analyse any number of periods of the ringdown waveform at once: this allows the method to be optimised for speed and precision for a given spectrometer.