## 3 Temperature Compensation Methods for Photo Mechanics Measurements
### Model Compensation Method  
The model compensation method is based on the error models discussed in Section 2, which clarify the relationship between the environmental temperature and measurement error of photo mechanics methods. Its compensation principle is explained in Figure 11. When using this method to correct measurement results, the responses of the thermal behaviours of camera components to temperature and thermal parameters in Equation (13) need to be calibrated as in the case of the error model discussed earlier. Second, the imaging parameters given in Equation (1) need to be obtained before performing measurements. Then, images of the tested object are captured by the camera system, and the environmental temperature is recorded. Finally, the thermal-induced measurement error calculated using the determined error models is subtracted from the direct results of the images obtained using photo mechanics methods to acquire the corrected results.  
Figure 10: Investigation of relationship between the image error and measurement error of fringe analysis methods.  
In this study, the feasibility of the model compensation method is verified for correcting strain and translation measurement results obtained using the investigated camera system. For strain measurements, the experimental arrangement is shown in Figure 12a. A granite specimen (having a volume of \(20\times 20\times 40\) mm\({}^{3}\)) containing speckles and a strain gauge was compressed using the testing machine (WDW-100, at 0.005 mm/min), and the deformation of the specimen was measured by the resistance strain measurement method with temperature compensation. Meanwhile, the images of the granite specimen were captured by the camera system, and the environmental temperature of the region around the camera was recorded using a thermal sensor. Using the environmental temperature, given in Figure 12b, and the determined error model, the strain measurement error was calculated. The direct measurement result was obtained using DIC to analyse the captured speckle images. The corrected result from DIC was calculated by subtracting the strain measurement error from the direct measurement result. The experimental results are shown in Figure 12c, which indicate that this compensation method can correct the strain measurement results obtained using photo mechanics methods.  
Figure 11: Compensation principle of the model compensation method.  
Figure 12: Experimental verification of model compensation method for compensating strain measurement error: (**a**) experimental arrangement, (**b**) environmental temperature during experiment, and (**c**) experimental results.  
The experimental layout used for translation measurements is shown in Figure 13a. The checkerboard, a rigid body, was moved along the negative \(x\) direction with the motion of the electric translation platform (ZOLIX SC300-2A, at 0.625 \(\upmu\)m/min). Meanwhile, the images of the checkerboard were captured by the camera system, and the temperature of the environment around the camera was recorded. Using the environmental temperature, indicated in Figure 13b, and the determined translation error model, the translation measurement error was calculated. The direct measurement result was obtained using the Harris algorithm to analyse the captured images. The corrected result was calculated by subtracting the translation measurement error from the direct measurement result. The reference result for translation was calculated using the motion rate of the electric translation platform, which is equal to 0.0227 pixel/min in the captured images. The experimental results are shown in Figure 13c, which indicate that this compensation method can correct the translation measurement results obtained using photo mechanics methods.