An analytical model for analyzing multi-channel intracavity spectroscopy technology (ICST) is established based on rate equations of Er-doped fiber laser. With the consideration of the amplified spontaneous emission, how the mode competition influences the iterative process for a stable output is analyzed. From the perspective of iterative times, the sensitivity-enhanced mechanism of the ICST is explained. Moreover, the theoretical modeling is employed to analyze the role that the mode-competition effect plays in switching the sensing channel automatically. It is demonstrated that, owing to the mode-competition effect in the laser cavity, the modulation of the cavity loss can be used to tune the sensing channel automatically. Furthermore, our proposed theoretical modeling is verified using a multi-channel ICST sensing system. It is indicated that the calculated estimates agree well with those data from the experimental absorption spectra. The principle will play a significant role in realizing the multiplexing of ICST.

The nonlinear model of torsion pendulum is presented by considering the nonlinear damping force and nonlinear restoring force. The analytic solution of the nonlinear model is calculated to analyze the relationship between the characteristics of torsion pendulum and the nonlinear factors. The instantaneous characteristics of nonlinear torsion pendulum are analyzed by instantaneous undamped natural frequency and instantaneous damping coefficient. The instantaneous characteristics can be used for the parameter estimation of nonlinear torsion pendulum system. The nonlinear characteristics of the torsion pendulum are validated by the torsion pendulum based on the air-hovered turntable. The parameter estimation method based on the instantaneous characteristics is validated by the moment of inertia measurement system based on the torsion pendulum.

In this study, a high-precision rotation angle measurement method based on polarization self-mixing interference (SMI) is proposed. The higher signal-to-noise ratio SMI signal can be obtained by the differential processing of two polarized SMI signals with opposite phases. In order to reduce the influence of the speckle effect, the envelope signal is used to normalize the SMI signal. The fringe subdivision method is used to improve the accuracy of the rotation angle measurement. The experimental results show that the error of the rotation angle measurement is within ±0.5%, and the measurement range can reach up to 20°.