Contents I. Introduction
Optical fiber displacement sensors possess advantages such as chemical resistance, immunity to electromagnetic interference, high sensitivity, flexibility, and compactness. Due to these inherent advantages, they have garnered extensive attention in recent years [1]. They play crucial roles in various fields, including construction, gravitational wave detection, manufacturing, and satellite towing technology [2], [3]. Recently, fiber optic displacement sensors based on different principles have been proposed [4], [5]. Abdul Ghaffar et al. introduced a linear displacement sensor based on structural interference, which detects displacement by monitoring the relative motion between an LED band (LB) and the fiber, using a power meter to measure intensity changes for unique detection. This sensor has a sensitivity of 1.532 nW/mm and can achieve linear displacement measurements of up to 1 m [6]. Yong Zheng et al. studied a spring-shaped fiber optic displacement sensor based on bending loss, employing an Optical Time Domain Reflectometer (OTDR) as both transmitter and receiver. They investigated the structural design and sensing principle related to changes in light intensity with displacement, achieving a sensitivity of 0.0202 dB/mm and a measurement range of 30 mm [7]. Yongxing Guo et al. proposed a fiber Bragg grating (FBG) displacement sensor suitable for alternating positive and negative displacement measurements, featuring a measurement range of ±50 mm and a sensitivity of 29.373 pm/mm, along with good performance for minute displacement measurements [8]. Jingxian Cui et al. presented a two-dimensional vector displacement sensor capable of simultaneously distinguishing the direction and magnitude of displacement, enhancing performance through the powerful machine learning algorithm, Random Forest, with a wider measurement range (0 to 45 mm) and reduced measurement errors [9]. Furthermore, fiber optic displacement sensing is not limited to single-point measurements; multi-point displacement sensing is gaining attention in structural health monitoring, civil engineering, aerospace, and robotics [10]. Xuehui Zhang and Wout Broere developed a novel joint monitoring system utilizing Distributed Optical Fiber Sensors (DOFS), designed with a specific sensor layout to simultaneously measure horizontal joint openings and vertical uneven settlement [11]. Tao Hu et al. proposed a new Roof Settlement Displacement (RSD) monitoring sensor, utilizing pre-stretched optical fiber (PSOF) arranged horizontally at fixed points, characterizing RSD qualitatively and quantitatively through distributed fiber strain measurement [12]. Jianli Li et al. introduced a distributed POS six-dimensional deformation measurement method based on FBG sensors, proposing a strain decoupling method to enhance strain measurement accuracy for irregular cross-section lever arms, establishing an axial displacement model to further achieve six-dimensional deformation measurement [13]. Liehr et al. proposed a new technique based on Optical Frequency Domain Reflectometry (OFDR) for measuring quasi-distributed length changes between reflective points in optical fibers. This technique can measure length changes with a resolution superior to 1 micron and supports static and dynamic measurement capabilities of up to 2 kHz [14]. These technologies allow simultaneous displacement measurement at multiple points, but their drawbacks include high costs, complex installation and maintenance processes, and performance instability in high-temperature or harsh environments [15]. In experiments, FLRD was combined with optical fiber sensors to address these issues. The fiber loop ring-down technique has recently received significant attention due to its advantages of being independent of light source fluctuations, enabling remote measurements, and exhibiting high detection sensitivity [16], [17]. It can be used to detect various physical quantities such as liquid levels, magnetic fields, currents, biological media, refractive indices, temperatures, concentrations, and pressures [18], [19], [20]. However, FLRD faces challenges such as high system costs, complex manufacturing, significant cavity losses, and difficulties in multi-point displacement measurement [16], [21]. These issues limit its applications.
