## 1 Introduction  
Phase-sensitive optical time-domain reflectometry technology is widely used in distributed optical fiber sensing systems for intrusion detection, pipeline condition monitoring, oil and gas exploration, etc. [1; 2; 3]. In early research, much effort was put towards detecting the interfering amplitude resulting from the external vibration signal. However, these intensity demodulation methods cannot restore the full scale external vibration signal information for the nonlinearity between the changed interfering amplitude and the demodulated magnitude of vibration-induced perturbation. To overcome this obstacle, so-called fiber-optic distributed acoustic sensing (DAS) has been proposed, making DAS a research hotspot in recent years [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21].  
With external vibration reaching the sensing fiber, the local refractive index and length will modulated, which leads to the relative linear phase change. Unlike intensity demodulation methods, DAS technology focuses on detecting the phase that directly represents the external vibration signal. Up to now, DAS systems contain two different demodulation schemes; direct detection [6; 7; 8; 9; 10] and coherent detection [11; 12; 13; 14; 15; 16]. The system demonstrated in Reference [6] has a spatial resolution of 2 m with a frequency range of 500-5000 Hz. The system in Reference [7] is based on PGC demodulation, which has a maximum sensing length of 10 km and a spatial resolution of 6 m. Reference [8] introduces a distributed temperature and strain system by using linearly chirped pulses, which can achieve a 1 mK/4 ne resolution with a spatial resolution of 10 m over 1 km. Reference [15] reports a system based on I/Q demodulation and homodyne detection, which has a sensing range of 12.56 km and a spatial resolution of 10 m. These above systems' spatial resolution are in the range of tens of meters or meters, which cannot satisfy the high spatial resolution demand in some special applications, for example, the crack detection. To further improve the spatial resolution, an improved optical arrangement and a new signal processing procedure are used in the system in Reference [9], which can detect dynamic perturbations in 5 km with a spatial length of 50 cm. Three independent photodiodes, operated in synchronism, are required in this scheme. The spatial resolution of this scheme is still limited by the path difference of imbalanced Mach-Zehnder interferometer (MZI). With an optical frequency swept pulse, the system in Reference [16] achieved a sensing distance of 19.8 km and a spatial resolution of 30 cm and a signal-to-noise ratio (SNR) of 10 dB for vibration sensing. The spatial resolution of the optical frequency swept pulse optical time-domain reflectometry (\(\varphi\)-OTDR) is determined by the frequency sweeping range. The authors use a moving differential technique to determine the phase change, which can only be used to determine the change in amplitude of the backscattering and has a low SNR. In addition, this scheme requires a relatively high bandwidth photodetector and a high sampling rate data acquisition card, thus introducing difficulty in real-time measurement.  
In this article, we introduce an alternative to improve the spatial resolution of a \(\varphi\)-OTDR system by using double interferometers, which breaks through the limits set by the path difference of Michelson interferometers (MIs). Two MIs with different path length differences are used in the system. One is 10 m, the other is 9.2 m. Trough precise time control and PGC algorithm, the phase of Rayleigh scattering (RS) light along the sensing fiber can be obtained in an adjacent time. After using a heterodyne and 2-D bilateral filtering algorithm, a 0.8 m spatial resolution over 1.9 km is demonstrated in the experiment.