Objective Ultraprecise time synchronization plays an important role in scientific research and commercial applications. Owing to the advantages of optical fiber’s low transmission loss, high reliability, and stability, optical fiber time synchronization has been considered as a promising solution for high-precision time synchronization. This paper adopts a highly precise optical fiber time comparison scheme proposed by Shanghai Jiao Tong University, which uses bidirectional time-division multiplexing transmission over a single fiber with the same wavelength (BTDM-SFSW). The scheme can effectively suppress both effects of the Rayleigh backscattering and dispersion-induced bidirectional asymmetry simultaneously, whereas it does not achieve time synchronization. This study, which realizes time synchronization, adopts the scheme to obtain the time difference between two clocks and uses the clock servo technique to eliminate the time difference between two clocks.

Methods A time synchronization experimental system is set up based on the BTDM-SFSW time comparison scheme and clock servo technique (Fig. 1). After using the BTDM-SFSW time comparison scheme to obtain the time difference between two clocks (Fig. 2), the difference between setpoint value and the time difference is used as error signal of proportion-integral-differential (PID) controller (Fig. 3), which is processed and summed by proportional, integral, and derivative units to obtain the output of the controller. The voltage-controlled crystal oscillators (VCXO's) frequency is adjusted according to the frequency correction algorithm and the controller’s output to change the phase of one pulse per second (1PPS) derived from the pulse per second (PPS) generator. New 1PPS is used by BTDM-SFSW time comparison to obtaining a new time difference between two clocks, which is treated as the feedback value of the controller. The above steps constitute a feedback control for the elimination of the time difference.

The time synchronization system adopts the same optical fiber and wavelength, which fully guarantees delay symmetry of the bidirectional link. After the calibration of time-synchronized terminals, there is no need to calibrate the optical fiber link.

Results and Discussions In an air-conditioned laboratory, time-synchronized terminals are connected by a 1 m optical fiber, and the calibration of terminals is completed by modifying the PID controller’s setpoint value to adjust the convergence position of the time difference so that the average value of time difference after synchronization is stabilized near zero. After calibration, the PID parameters such as setpoint value, proportional gain, integral time, and derivative time are no longer changed. The average value of time difference after time synchronization is less than 1.5 ps, 3 σ time difference is less than 228 ps (Fig. 4 (a)), and time deviation (TDEV ) of time difference is better than 15 ps/s and 1.5 ps/10⁴ s respectively (Fig. 4 (b)). Compared with TDEV of time difference without synchronization, the long stability of time difference after synchronization is significantly improved.

Time-synchronized terminals, which have been calibrated over a 1 m optical fiber, are connected by 30, 50, 80, and 100 km standard single-mode optical fibers respectively to perform experiments. The average value of time difference after synchronization is less than 10 ps (Fig. 5). Results of the experiment show that the system can achieve high-precision time synchronization over optical fiber links, that have different lengths by using a short optical fiber to complete calibration of terminals without calibration of the optical fiber link.

The field test is conducted over a standard single-mode optical fiber link between Minhang and Xuhui campuses of Shanghai Jiao Tong University. The length of the optical fiber link is about 60 km, and the total attenuation of the link is about 24 dB. The average value of time difference after time synchronization is less than 9 ps, 3 σ time difference is less than 285 ps (Fig. 6 (a)), and TDEV of time difference is better than 16 ps/s and 7 ps/10⁴ s respectively (Fig. 6 (b)). Compared with the TDEV of time difference after synchronization using a 1 m optical fiber to connect terminals, the short stability of the field test’s time difference does not change significantly, whereas the long stability worsened over the field optical fiber link. It is reasonable since the long-term stability is mainly related to the fluctuations of propagation delay asymmetry caused by variations in temperature and wavelength difference, which are proportional to optical fiber length. The “bump” of TDEV near 10 s is caused mainly by hysteresis of VCXO frequency adjustment. It indicates that the steering corrections are unable to compensate for the frequency drift completely at certain averaging times.

Conclusions In this study, a time synchronization system is designed based on the BTDM-SFSW time comparison scheme and clock servo technique. The system takes advantage of the high bidirectional transmission delay symmetry of BTDM-SFSW time comparison without calibration of the optical fiber link. Laboratory and field optical fiber link tests are conducted, and results of the experiment show that after completing calibration of time-synchronized terminals, the average value of time difference after synchronization is less than 10 ps over different lengths of optical fiber links, and using a field optical fiber link of about 60 km, the average value of time differences after time synchronization is less than 9 ps, 3σ time difference are better than 285 ps, and TDEV is better than 16 ps/s and 7 ps/10⁴ s respectively.