*2.2. Double-Sided Calibration*

Camera calibration plays an important role in DIC measurement, as its quality directly affects measurement accuracy. The principle of camera calibration is to establish the relationship between the position of the camera image pixel and the scene point position. According to the camera imaging model, the relationship between the image coordinate system and the world coordinate system is as follows [21]:

$$
\stackrel{\rightharpoonup}{\text{sm}^2} = A \begin{bmatrix} r \ t \end{bmatrix} \stackrel{\rightharpoonup}{\text{M}} \tag{2}
$$

⃑⃑ = [ ] ̅ = [, , 1] ̅ = [, , , 1] [ ] ̅ = [, , 1] ̅ = [, , , 1] [ ] ' where *m* = [*u*, *v*, 1] *T* is the image homogeneous coordinate system, *M* = [*X*,*Y*, *Z*, 1] *T* is the world homogeneous coordinate system, *s* is the scale factor, *A* is the camera internal parameter matrix, and [*r t*] is the camera external parameter matrix. Both the internal and external parameters of the camera can be calculated by Zhang's calibration method [21].

⃑⃑

' The double-sided calibration strategy uses a double-sided calibration plate to calibrate the front and back dual-camera DIC systems simultaneously. The schematic of the doublesided calibration strategy is shown in Figure 3. Figure 3 shows two typical two-camera stereo vision subsystems, and these two subsystems are linked through calibration. Figure 4 shows the design of the calibration plate. The role of this calibration is to connect these two subsystems into one single global system. The world coordinate system of the front camera is taken as the reference global coordinate, and the back camera coordinate system is transformed to the reference global system. This transformation can be expressed as follows:

(3)

−1 0 0 0

**Figure 3.** Schematic of double-sided calibration strategy.

**Figure 4.** Double side calibration plate (front and back side).

In this equation, *d* is the thickness of the double-sided calibration plate.
