Objective Optical fiber sensors have been investigated extensively for crustal strain observation owing to their advantages of high resolution and excellent environmental resistance. Currently, the most typically used high-resolution optical fiber static strain sensing technologies include frequency sweep detection and the Pound-Drever- Hall detection. In a frequency sweep detection scheme based on a tunable laser and fiber Bragg grating resonator, the frequency sweep range of the laser is relatively small and realizing the simultaneous multiplexing of multiple fiber Bragg grating resonator sensors in a single detection optical path is difficult. Generally, in the Pound-Drever-Hall detection scheme, a single-frequency laser source can only be frequency locked to a fiber Fabry- Perot resonator; therefore, this technology can only be used for single-sensor detection. Hence, achieving large-scale multiplexing using the current nano-strain optical fiber static strain sensing technology is difficult. In this study, time- division multiplexing and ellipse- fitting reference compensation techniques are proposed for high-resolution multiplexing optical fiber static strain sensing. Methods A optical fiber Michelson interferometer is used as a sensor and each sensing interferometer is attached to a reference interferometer to compensate for the effects of temperature fluctuation and laser frequency drift. Time- division multiplexing technology is used to realize sensor multiplexing as it offers the advantages of high device utilization and high multiplexing gain. The sensor signal is demodulated using a phase- generated carrier ( PGC) scheme. In this scheme, the measurement and correction of the phase modulation depth and carrier phase delay in orthogonal signals are key to reducing nonlinear errors and improving the consistency of the phase demodulation results. Therefore, an improved ellipse-fitting algorithm, referred to as the bias-corrected ellipse- specific fitting (BCESF) algorithm, is adopted to suppress the effects of phase modulation depth and carrier phase delay. The curve equation of the Lissajous figure composed of two orthogonal signals is solved using an ellipse-fitting method and the coefficients of the ellipse are obtained. Subsequently, these coefficients are used to correct the signal demodulation results to eliminate the effects of the phase modulation depth and carrier phase delay as well as to improve the consistency between the reference and sensing interferometers. Thus, the compensation effects of the temperature fluctuation and laser frequency drift are optimized, and the resolution for static strain sensing is improved. Results and Discussions We place the interferometer in a sound and vibration isolation box (Fig. 3) and perform the experiment in a 5 m deep basement. To verify that the ellipse- fitting algorithm can improve the consistency of the demodulation phases of both the reference and sensing interferometers, we place the sensing arms of the reference interferometer and the sensing arm of the sensing interferometer around a piezoelectric phase modulator (PZT). Next, we apply a sinusoidal signal to the PZT using a signal generator. Based on the classical PGC-ARCTAN demodulation algorithm, the amplitudes of the sinusoidal signal demodulation results of the sensing and reference interferometers differ significantly [Fig. 4(a)]. The processing results using the ellipse- fitting algorithm show that the peak-to- peak value of the difference between the two sinusoidal signals decreases significantly [Figs. 4(a) and 4(b)]. The experimental results show that the ellipse-fitting algorithm can improve the consistency of the demodulation phase between the reference and sensing interferometers. Next, the multiplexed channels in the time division multiplexing (TDM) sensor array are expanded into four channels. Based on the elliptical fitting and reference compensation calculation, the peak-to-peak values indicated by the phase demodulation results of four channels are consistent within 10 min (Fig. 7), and the static strain resolution of each channel exceeds 0. 26 ne. Compared with other types of fiber-optic sensing systems (Table 1), the proposed time-division multiplexing system based on elliptical-fitting reference-compensation technology offers a high strain resolution during the multiplexing of multiple sensors. Conclusions Herein, we propose a high- resolution static strain sensing technique that uses a fiber Michelson interferometer as the sensor and utilizes time- division multiplexing and ellipse- fitting reference compensation techniques to achieve multiplex static strain sensing. A time- division multiplexing system with four channels is constructed, and the static strain resolution of each channel exceeds 0. 26 ne. The proposed time-division multiplexing and ellipse-fitting reference compensation technologies are confirmed to be feasible for high-resolution static strain measurements and can satisfy the requirements of network multiplexing in crustal strain observation.
