# Full-Field Vibration Measurements by Using High-Speed Two-Dimensional Digital Image Correlation
## 2 Principle of the Method
### Sensitivity of the In-Plane Displacement and Out-of-Plane Displacement Measurements  
In 2D-DIC measurements, the in-plane displacement sensitivity is majorly related to the DIC algorithm, which can generally reach 0.02 pixels [29]. Therefore, it is varied with the imaging resolution of the 2D-DIC system. If the imaging resolution is 0.1 mm/pixel, the in-plane displacement sensitivity \(\delta U\) and \(\delta V\) can be estimated; i.e., 0.02 pixel \(\times\) 0.1 mm/pixel = 2 \(\upmu\)m. However, the field of view (FOV) is generally predetermined in practical measurements. Thus, the imaging resolution and the in-plane displacement sensitivity are limited by the pixel numbers of the camera sensor.  
The out-of-plane measurement sensitivity is associated with the object's distance \(Z\) and the measured strain, as shown in Equation (3), which can be represented as  
\[\delta W=-Z\cdot\delta\varepsilon, \tag{4}\]  
where \(\delta\varepsilon\) is the strain sensitivity; i.e., the minimum strain that a 2D-DIC can accurately measure. Therefore, \(\delta\varepsilon\) can be represented as \(\delta\varepsilon=\delta U/L_{x}\) or \(\delta\varepsilon=\delta V/L_{y}\), where \(L_{x}\times L_{y}\) corresponds to the size of the FOV. Since the displacement sensitivity of the DIC measurement can generally reach 0.02 pixels, the strain sensitivity is also determined by the number of pixels on the camera sensor. When considering a camera with 1000 \(\times\) 1000 pixels, \(\delta\varepsilon\) can be estimated; i.e., 0.02 pixel/1000 pixel = 20 \(\mu\varepsilon\). Further, considering that the object distance is 1 m, the sensitivity of the out-of-plane displacement can be estimated; i.e., 1 m \(\times\) 10 \(\mu\varepsilon\) = 20 \(\upmu\)m. Compared with the in-plane displacement sensitivity, the out-of-plane displacement sensitivity is one order of magnitude lower. The proposed 2D-DIC-based vibration measurement method is mainly suitable for measuring large amplitude vibrations. From the analysis, it is noted that, both in-plane and out-of-plane displacement sensitivities are related to the pixel numbers of the camera sensor. Therefore, a high-resolution camera or even a camera array can be employed to enhance the displacement sensitivities [30]. In addition, if the measurement condition is permitted, the out-of-plane displacement sensitivity can be further improved by decreasing the object's distance.  
In conclusion, the steps of choosing adequate imaging parameters can be summarized as follows:  
* Determining the FOV and the minimum object distance according to the practical measurement needs;
* Setting the distance between the camera and the measured object to the predetermined minimum object distance for obtaining the maximum out-of-plane displacement sensitivity;
* Choosing a high-resolution camera or a camera array for ensuring a high in-plane displacement sensitivity;  
Figure 2: Schematic of the virtual in-plane displacement induced by the specimen’s out-of-plane motion.  
Selecting the focal length of the imaging lens that allows the camera to image the full range of the predetermined FOV at the minimum object distance.