## 1 Theoretical Background
However, the error of this approach can be significant in cases where the structure under study experiences a sizeable out-of-plane displacement [39]. Recently, the US rail bridge inspection manuals proposed a noncontact displacement measuring system for railroad inspections [40]. This system is a sensor fusion of a camera and a laser. The camera used in the system corrects the translation and rotation of the laser during its measurements. This new methodology can acquire the dynamic movement of the structure, which a laser or camera alone cannot collect. The experimental test showed up to 20% error, which can decrease with further development of this method. Miyashita et al. presented a vital literature review on vibration measurements using a Laser Doppler Vibrometer (LDV) and MEMS-based technologies [41]. This paper describes various noncontact distance measuring tools for bridges. Furthermore, it presents a custom \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sensor Name** & **Sensor Type** & \begin{tabular}{c} **Reading Frequency** \\ **(Hz)** \\ \end{tabular} & \begin{tabular}{c} **Distance** \\ **Range** \\ **(cm)** \\ \end{tabular} & \begin{tabular}{c} **Dimension** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Limitations** \\ **Voltage** \\ \end{tabular} & \begin{tabular}{c} **Input** \\ **Application** \\ \end{tabular} & \begin{tabular}{c} **Used** \\ **(EUR)** \\ \end{tabular} \\ \hline HC-SR04 [26] & Ultrasonic & 40 & 2–400 & 45.0 \(\times\) 20.0 \(\times\) 1.5 & \begin{tabular}{c} Complex objects, low \\ frequency and sensitive \\ to temperature \\ variation \\ \end{tabular} & 5.0 & Robotics [27] & 2.5 \\ \hline GP2Y0A21 YK0F [28] & IR & 26 & 10–80 & 29.5 \(\times\) 13.0 \(\times\) 13.5 & \begin{tabular}{c} Low frequency and \\ sensitive to ambient \\ light and surface color \\ \end{tabular} & 5.0 & \begin{tabular}{c} Air levitation \\ [29] \\ \end{tabular} & 7.8 \\ \hline Lite v3 [24] & LiDAR & 500 & 5–4000 & 48.0 \(\times\) 40.0 \(\times\) 20.0 & \begin{tabular}{c} Dangerous to eyes, \\ expensive \\ \end{tabular} & 5.0 & Drones [30] & 109.0 \\ \hline V153l0x [31] & ToF & 500 & 3–200 & 13.0 \(\times\) 18.0 \(\times\) 2.0 & \begin{tabular}{c} Sensitive to surface \\ color and ambient light \\ \end{tabular} & 3.3 & \begin{tabular}{c} Rail gap \\ measurement \\ [32] \\ \end{tabular} & 5.4 \\ \hline V153l1x [33] & ToF & 500 & 2–400 & 13.0 \(\times\) 18.0 \(\times\) 2.0 & \
\begin{tabular}{c} Sensitive to surface \\ color and ambient light \\ \end{tabular} & 3.3 &
\begin{tabular}{c} Water level \\ monitoring \\ [34] \\ \end{tabular} & 12.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of different distance sensors. made triaxle accelerometer with a sampling frequency of 100 Hz used on the experimental analysis of a bridge. Bhowmick et al. presented a novel method for accurate continuous movement measurement of a one-dimensional vibrating beam using video recording [42]. This paper uses the camera of an iPhone SE in slow-motion mode. The Root Mean Square (RMS) difference of measurements of a vibrating beam using a commercial LDV sensor and the phone camera is about 0.4 mm. The authors illustrated the first three mode shape evaluation of a two-story scaled structure using this technique [43]. It is noted that this type of distance measurement imposes some challenges (such as data storage and transmission). They discussed and solved these issues by the proposed method using reconstructed full-field Lagrangian displacement response [44]. A paper addressing the status monitoring of tall structures describes a fusion of a Terrestrial Laser Scanner (TLS) and a Ground-Based Real Aperture Radar (GB-RAR). This system can provide the Eigen frequencies and oscillation amplitudes of high-rise structures such as wind towers. The comparison of numerical and experimental analysis using TLS and GB-RAR system fusion shows a precision displacement measurement with about 5 mm of error.