# Ultra-Small Fiber Bragg Grating Accelerometer
## 3 Experiments  
Figure 1 shows the packed FBG accelerometer in comparison with a coin. Its length, width and height were 23, 18 and 17 mm, respectively. The insets show the schematic diagrams of the inside. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Length of the** & **Mass of the** & **Crest-to-Trough** & **Resonant** & **Vibration Direction of the** & \\
**Vibration Arm** & **Inertial Object** & **Sensitivity** & **Frequency** & **Inertial Object (Axial: Along the Fiber, Transverse:** & **Ref.** \\ (mm) & **(gram)** & **(pm/g)** & **(Hz)** & **Perpendicular to the Fiber)** & \\ \hline
7 & 4.41 & 244 & 90 & transverse & here \\
24 & 3 & 770 & 41 & transverse & Ref. [15] \\
30 & 1.29 & 16 & 1300 & axial & Ref. [14] \\
40 & 4.8 & 1.7 & 3600 & axial & Ref. [12] \\
47 & 1.76 & 23 & 900 & axial & Ref. [13] \\
47 & 1.76 & 545 & 34 & transverse & Ref. [13] \\
50 & 5.71 & 1290 & 26 & transverse & Ref. [15] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of FBG accelerometers using the optical fiber to hold the inertial object. The FBG was fixed by its two ends, and an inertial object was hung in the middle. It was not fixed on the FBG, and could move almost freely along the FBG. The inertial object and shell were made of stainless steel. The distance between the two fixed ends of the FBG was 7 mm. The values used here were selected based on a few principles. Firstly, the Bragg grating should not be too short; otherwise, it may fail to provide adequate reflection for practical applications. Secondly, the distance between the two fixed ends should only be slightly longer than the length of the Bragg grating. The shorter the distance, the better the performance of an accelerometer. But the distance must be longer than the FBG to avoid chirping. Lastly, the inertial object should be heavier enough to overcome the friction, and its size should not be bulky, so the accelerometer can be compact. Bearings were used to reduce the frictions between the inertial object and the shell. There were two bearings lined up horizontally on one side, and two vertically on the other side. This design may reduce the shaking of the inertial object. This accelerometer was only sensitive in one transverse direction. The inertial object could move almost freely along the axial direction, only subjected to friction. Its motion in the other transverse direction is restricted by restricting the distance between the inertial object and shell. The Bragg grating was 5 mm in length, 3 db bandwidth less than 0.3 nm, reflectivity 91%, side-mode suppression ratio 10 dB, and free state resonant wavelength 1529.05 nm (Da Hui Photoelectric Inc., Jinan, China). The resonant wavelength was 1530.43 nm at equilibrium after the inertial object was hung. The mass of the inertial object was 4.41 g. The stretch at equilibrium was \(1530.43-1529.05=1.38\) nm, which was due to both the pre-stretch when the FBG was fixed by its two ends and the stretch induced by the weight of the inertial object. The room temperature was within 10 to 25 \({}^{\circ}\)C during the experiments. Figure 2 shows the experimental setup. The FBG accelerometer and a piezo accelerometer were put together on top of a shaker. The shaker was feed with a sinusoidal wave generated by a signal generator (MFG2160 MR, Gwinstek Inc., Taiwan). Both accelerometers were sampled at 500 Hz. The Piezo accelerometer (CT1010L, Chengke Inc., Shanghai, China), connected to a constant current adaptor (CT5204, Chengke Inc., Shanghai, China), a Data Acquisition (DAQ) card (USB_HRF4626, Hengruifeng Inc., Suzhou, China), and a computer, shown a resolution of 0.001 g; the FBG interrogator (SAI-1127 AF, Casstk Inc., Shenzhen, China) shown a resolution of 1 pm. Figure 3 shows the results of the two accelerometers at 5 Hz at 6 different accelerations and their corresponding FFTs. The frequency of the input signal of the shaker was fixed at 5 Hz, and 6 different amplitudes were applied.