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

Abstract

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 25 KHz 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.

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

“…It was also shown in [9] that the EKF performed better than the LM method with similar error in initial conditions. However, in [9], [10], the cavity was modeled in terms of amplitude and phase quadratures, starting from an annihilation-creation operator framework. This led to a third order system which was computationally expensive.…”

“…In order to overcome these issues and keeping in mind the real-time requirements for trace gas element detection, the use of an extended Kalman filter (EKF) was proposed in [8], in simulation. Furthermore, it was applied to a set of experimentally obtained light intensity data at the output of a Fabry-Perot optical cavity to estimate τ in offline mode in [9], [10]. It was also shown in [9] that the EKF performed better than the LM method with similar error in initial conditions.…”

“…Furthermore, it was applied to a set of experimentally obtained light intensity data at the output of a Fabry-Perot optical cavity to estimate τ in offline mode in [9], [10]. It was also shown in [9] that the EKF performed better than the LM method with similar error in initial conditions. However, in [9], [10], the cavity was modeled in terms of amplitude and phase quadratures, starting from an annihilation-creation operator framework.…”

“…In this paper, we model the cavity as a low pass filter (LPF) which is a simpler model than the cavity dynamics presented in [9], [10]. This is motivated by the fact that the optical cavity operates as an LPF as described in [11], [12].…”

“…This is motivated by the fact that the optical cavity operates as an LPF as described in [11], [12]. This model leads to a second order system for estimation purposes and has a smaller execution time than the model described in [9], [10]. Also, the LPF model for the cavity can be used for both pulsed as well as continuous-wave laser inputs and can handle both DC-as well as AC-coupled inputs.…”