## 3 Temperature Compensation Methods for Photo Mechanics Measurements
### Compensation Specim Method  
The image error forms discussed in Section 2 indicate that the compensation specimen method cannot eliminate all types of measurement errors in photo mechanics measurements. This method requires that the thermal-induced error form of the region in the tested specimen shown in the image is the same as that of the compensation specimen, which depends on the responses of the thermal behaviours of the camera system to temperature variations. For the camera system investigated in this study, the image error form generated because of temperature variations is the same in any region of the captured images. Therefore, the compensation specimen method is suitable for correcting the measurement results obtained via photo mechanics methods when using the investigated camera system. In this case, the compensation specimen method requires that an unloaded specimen is placed on the side of the tested specimen. During photo mechanics measurements, images of both the specimens are simultaneously captured by the camera system. For the tested specimen, the results of photo mechanics measurements contain the real mechanical information and the thermal-induced error. However, for the compensation specimen, the measurement result only represents the thermal-induced error. In particular, for correcting the measurement results of photo mechanics methods, the result of the compensation specimen should be subtracted from the result of the tested specimen. The principle of this method is shown in Figure 15.  
Figure 14: Experimental investigation for avoiding thermal-induced error using the preheating method: (**a**) experimental layout, (**b**) temperature variation of the camera case, (**c**) a thermal-induced strain error, and (**d**) a thermal-induced translation error. Next, the feasibility of the compensation specimen method was verified for correcting the results of photo mechanics measurements. For strain measurements, the experimental arrangement used is shown in Figure 16a. A low-carbon-steel specimen (having a volume of \(45\times 45\times 60\) mm\({}^{3}\)) with speckles and a strain gauge was compressed using the testing machine (WDW-100, at 0.005 mm/min). The deformation of the specimen was measured using the resistance strain measurement method with temperature compensation. In addition, an identical specimen with speckles was placed next to the tested one. During the experiment, the images of both specimens were captured by the investigated camera system. The measurement results of both specimens were obtained using the DIC method, as shown in Figure 16b. The corrected result obtained from DIC for the tested specimen was calculated by subtracting the measurement result of the compensation specimen from the measurement result of the tested specimen. The corrected result of the tested specimen aligns well with the result of the strain gauge, shown in Figure 16b, which indicates that this compensation method can correct the strain measurement results obtained using photo mechanics methods. For translation measurements, the experimental layout is shown in Figure 17a. The tested planar specimen with speckles was moved along the \(x\)-direction with the motion of the electric translation platform, and the compensation specimen remained stationary. Furthermore, the images of the tested and compensation specimens were captured by the camera system. Then, using a matching algorithm, the translation of the tested and compensation specimens along the \(x\)-direction was tracked and calculated. Furthermore, using the compensation specimen method, the corrected photo mechanics result was obtained. The reference result was calculated using the motion rate of 0.625 \(\upmu\)m/min of the electric translation platform, which is equal to 0.0237 pixels/min in the captured images. The experimental results are shown in Figure 17b, which indicate that this compensation method can correct the translation measurement results in photo mechanics methods.