Low pass filter model-based offline estimation of ring-down time for an experimental Fabry-Perot optical cavity

This paper presents offline extended Kalman filter (EKF) estimation results for the decay time-constant for an experimental Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The decay time for an optical cavity is defined as the amount of time it takes for the light intensity inside the cavity to decay to 1/e times its original intensity in the absence of a sustained light source. An estimation of the decay time for a cavity depends upon the absorbing species inside the cavity along with other miscellaneous losses due to the elements used to construct the cavity. Once the miscellaneous losses are computed experimentally, the decay time due to the absorbing species can be directly computed. The decay rate, as a function of wavelength, can be used to identify trace gas elements such as chemicals and their compounds. For estimation purposes, the cavity is modeled as a low pass filter with unity DC gain and the experimentally obtained light intensity at the output of the cavity is used as measurement. During the process of recording the intensity data, the cavity's resonant frequency is held in sync with the input laser frequency via a proportional-integral (PI) controller. Finally, the estimation results for the decay time of the cavity using the low pass filter model presented in this paper, are compared with the estimation results using a quadrature model for the cavity from a previous work. The estimation results are also compared on filter execution times.