# Optical accelerometers for Detecting Low-Frequency Micro-Vibrations
## 3 Optical Path Modulation  
An optical accelerometer based on the optical path modulation principle senses acceleration by directly modulating the optical path. When external acceleration acts on the accelerometer, seismic mass in the accelerometer is inertially displaced, directly altering the laser optical path. This type of accelerometer exhibits the advantages of a simple structure and low cost. A focus error sensor (FES) based on a DVD pickup head is a high-precision optical path modulation sensing system. Figure 2 shows a focus sensor modified from a red-ray DVD pickup head by removing the voice coil motor and using a rectangular prism to turn the optical path. It exhibits the advantages of high resolution and high accuracy. This modified sensor can be used in nanoscale measurement after calibration. As shown in Figure 3a, [PERSON] et al. designed a cantilevered high-sensitivity optical accelerometer with a sensitivity of 12.3 V/g on the basis of focus error sensing [20]. As shown in Figure 3b, [PERSON] et al. improved the design of [PERSON] et al. by using the moving part of the voice coil motor inside a DVD pickup head as the elastic mechanism; they reduced the size of the accelerometer while improving its sensitivity to 24.4 V/g [21]. The resonant frequency in the \(x\) and \(y\) directions of a cantilevered beam is not significantly greater than the resonant frequency in the \(z\)-direction, and vibrations in the \(x\) and \(y\) directions exert a greater effect on the output of the accelerometer. Therefore, [PERSON] et al. designed an accelerometer with a fully symmetric leaf spring (as shown in Figure 4); it has a resolution of 0.3 mg and measurement uncertainty as low as 0.07 mg (K = 2) [22]. To improve the sensitivity of optical accelerometers, [PERSON] et al. modeled an optical accelerometer by using sensitivity analysis and improved its sensing optical path to achieve a resolution as low as 4 ug [23]. The FES is based on a modified DVD pickup head, and its internal optical components are irreplaceable and exhibit poor maintainability. Laser triangulation (LTG) is a method for achieving position detection on the basis of the change in optical path. As depicted in Figure 5, when the position of the reflector changes \(\Delta h\), the position of the spot on the photodetector will also change \(\Delta l\). The relationship between \(\Delta h\) and \(\Delta l\) is  
\[\Delta l=\frac{\Delta h}{\sin\alpha}, \tag{10}\]  
where \(\alpha\) is the angle between the incident laser beam and the reflector. Therefore, the LTG method can amplify the displacement \(1/\sin\alpha\) times. This method is widely used in micro/nano measurement instruments, such as micro/nano contact probes [24], scanning probe microscopes [25], and optical accelerometers (Figure 6) [7]. With the development of technology, the resolution of photodetectors has reached the submicron order. For example, the photodetector (SPOT-4, OSI Optoelectronics Co., Ltd., Hawthorne, CA, USA) used in the literature [7] has a position resolution of 0.1 \(\upmu\)m, and with optical lever amplification; this displacement sensor has a resolution of 70 nm. An optical accelerometer based on the LTG method and a fully symmetrical leaf spring-type elastic mechanism can achieve a low-frequency response down to 0.4 Hz and a high resolution of 0.3 mg.  
Figure 3: Cantilevered accelerometers: (**a**) leaf spring and (**b**) voice coil. Reprinted with permission from Ref. [21]. Copyright 2008 IOP. Figure 2: FES: (**a**) structure schematic and (**b**) sensing principle. Reprinted with permission from Ref. [26]. Copyright 2019 Springer Nature. Common 1D accelerometers cannot meet the requirements of the aerospace, robotics, and other multidimensional measurement fields due to the complexity and multidimensionality of vibration. Therefore, research on 2D accelerometers has been increasing gradually. The key to 2D optical accelerometers is 2D angle sensing. Figure 7 presents the schematic of a 2D angle sensor modified from a DVD pickup head [26].