Nonlinear estimation of a Fabry-Perot optical cavity for cavity ring-down spectroscopy

This paper considers the application of a discrete-time extended Kalman filter (EKF) to a problem of estimating the ring-down time constant of a Fabry-Perot optical cavity for the purpose of cavity ring-down spectroscopy (CRDS). The ring-down time corresponds to the time taken by the light inside an optical cavity to decay to 1/e of its initial intensity. The online estimation of ring-down time (or decay time) for a cavity is a direct indication of the absorbing species contained in it and can be used to detect improvised explosive devices and concealed explosives. Two cases are considered for EKF design depending on whether the resonant frequency of the optical cavity is perfectly locked to the input laser frequency, or not. In the case of a perfect lock, a three-state EKF is designed to estimate the magnitude and phase quadrature components of the cavity and the ring-down time. In the other case where there is not a perfect lock between the two frequencies, leading to non-zero detuning, a four-state EKF is designed to estimate the detuning parameter in addition to the magnitude and phase quadrature components of the cavity and the ring-down time. The detuning parameter gives an indication of the deviation of laser frequency from the resonant frequency of the cavity, which can then be used by a controller to maintain detuning at zero.