# Optical accelerometers for Detecting Low-Frequency Micro-Vibrations
## 6 Optical Wavelength Modulation

Table 3: Parameters of the accelerometer based on optical phase modulation. can be obtained on the basis of drift value. [PERSON] et al. proposed an accelerometer with a cantilever FBG [78]. This accelerometer consists of an L-shaped rigid cantilever beam, a seismic mass, a spring, and FBG. In the design of [PERSON] et al., FBG is not directly fixed onto the L-shaped cantilever beam, but instead, a point contact is used with the cantilever beam to ensure the consistency of the strain applied to the entire FBG. A similar design was made by [PERSON] et al. [79,80]. FBG has good multipoint measurement capability. [PERSON] et al. designed a distributed optical accelerometer based on FBG [81,82]. This distributed optical accelerometer is realized by using pairs of vibration-sensitive mechanical structures and paired FBGs with different Bragg wavelengths. In the design of [PERSON] et al., up to six optical accelerometers can be combined for measurement. In recent years, many researchers have started to focus on improving the performance of FBG optical accelerometers. In their research, they have exerted effort on two perspectives: the design of FBG and the design of a vibration-sensitive mechanical structure. [PERSON] et al. used a tilted FBG (TFBG), as shown in Figure 18, to produce a biconical accelerometer, avoiding the difficulty of demodulation of the output optical wavelength signal when the traditional FBG accelerometer is used, and its reflected optical power is proportional to the acceleration [11]. A similar design was developed by [PERSON] et al. [83]. The advantage of TFBG over FBG is that the optical fiber does not require stretching and can be embedded directly into the solid base, improving the reliability of the optical accelerometer and reducing its size. Other researchers have increased the sensitivity of FBG accelerometers by improving their mechanical design. As shown in Figure 19a, [PERSON] et al. increased the sensitivity of a cantilever FBG accelerometer by using a simple method, i.e., adding a polyimide patch to the cantilever beam that does not affect its resonant frequency [84,85]. This polyimide patch increased the distance between the central axis of the cantilever beam and FBG, improving the sensitivity of the accelerometer. The design is simple in structure, but it improves sensitivity without affecting bandwidth and other characteristics. [PERSON] et al. Figure 17: FBG-based accelerometer: (**a**) elastic material and (**b**) two simply supported beams. Figure 18: TFBG-based accelerometer [11]: (**a**) schematic and (**b**) photograph. and [PERSON] et al. designed an FBG accelerometer based on an isosceles triangular cantilever beam [86; 87]. [PERSON] et al. designed a compact accelerometer based on an organic double semicircular cantilever beam and double FBGs [88], as illustrated in Figure 19b. These studies were conducted to suppress the FBG chirp effect and improve the sensitivity of FBG optical accelerometers. Elastic diaphragms with high mechanical sensitivity have also been applied to FBG accelerometers. [PERSON] et al. designed a double diaphragm-based FBG accelerometer with FBGs mounted on the upper surface of the diaphragm along the circumferential direction; this design can effectively prevent the FBG chirp effect [89]. When acceleration acts on the sensor, a uniform strain is generated, leading to an FBG wavelength shift. The photonic crystal (PHC) accelerometer is also an optical wavelength modulated accelerometer. The displacement sensing unit of a PHC accelerometer is usually a one- or two-dimensional PHC waveguide. PHC waveguides have a photonic bandgap that is selective for the wavelength of the passing light [90]. Acceleration deforms the periodic photonic structure, thereby destroying and altering the selectivity. Thus, PHC accelerometers obtain acceleration values by detecting changes in wavelength. PHCs can be classified into one-dimensional and two-dimensional forms depending on the form of lattice composition.