## 4 Experiments and Results
### Characteristics of Distortions due to Heat Waves  
Next, an experiment was conducted to investigate how heat waves affect DIC measurements. First, an image of the specimen was taken without the influence of a heat source as a reference image. The hot plate was turned on and the temperature set to 300 \({}^{\circ}\)C by the controller. After the temperature of the hot plate was stabilized at 300 \({}^{\circ}\)C, 200 images of the specimen were recorded at 1 Hz. The 200 images taken through heat waves and the reference image were used for DIC measurement. The result of the DIC measurement of the image taken at 100 s is shown in Figure 9.  
Comparing Figures 8 and 9, the effect of heat waves on the DIC measurement results is evident. The spatial and temporal standard deviations of the displacement fields and strain fields under the influence of heat waves are shown in Table 2. It can be seen from Table 2 that the spatial standard deviation and temporal standard deviation are significantly increased due to the effect of heat waves. The spatial standard deviation was increased by nearly ten times, and the standard deviation of the displacement fields was more than 0.05 pixels, which is unacceptable.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Spatial STD** & **Temporal STD** \\ \hline _U (pixels)_ & 0.0037 & 0.0023 \\ _V (pixels)_ & 0.0040 & 0.0024 \\ \(\varepsilon_{xx}\) (\%) & 0.0077 & 0.0040 \\ \(\varepsilon_{xy}\) (\%) & 0.0047 & 0.0027 \\ \(\varepsilon_{yy}\) (\%) & 0.0076 & 0.0039 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Baseline noise floor for the experimental setup, without the purposeful introduction of a heat source, quantified by spatial and temporal standard deviations (STD) of the data.  
Figure 9: Representative contour plots of the displacements and strains computed in DIC measurement affected by heat waves: (**a**) Displacement in U direction; (**b**) displacement in V direction; (**c**) strain \(\varepsilon_{xx}\); (**d**) strain \(\varepsilon_{xy}\); (**e**) strain \(\varepsilon_{yy}\).  
Figure 10 shows the variation of the displacement of the ROI central subset over time. It can be seen that the swing of the curves of the displacement in both directions of U and V are not surrounding zero, but there is an offset, the Mu and Mv, as shown in Figure 10. The offsets are the main distortion mentioned above, and the swing around the main distortion is random distortion.  
Next, the situation in which the temperature of the heat source changes drastically was analyzed. The heat source temperature was adjusted to 100, 150, 200, 250, 300 degrees Celsius, respectively. At each temperature, 200 unloaded sample images were taken; the calculated main distortion is shown in Figure 11. As the temperature increases, the main distortion tends to increase, but at different temperatures, this offset is different. Therefore, in the case where the temperature of the heat source changes drastically, the method of correcting the main distortion based on the BOS technique is no longer applicable. But the time-average method can also be used to improve the accuracy of the measurement.  
\begin{table}
\begin{tabular}{c c c} \hline
**Component** & **Spatial STD** & **Temporal STD** \\ \hline _U (pixels)_ & 0.0516 & 0.0108 \\ _V (pixels)_ & 0.0365 & 0.0069 \\ \(\varepsilon_{xx}\) (\%) & 0.1100 & 0.0336 \\ \(\varepsilon_{xy}\) (\%) & 0.0490 & 0.0139 \\ \(\varepsilon_{yy}\) (\%) & 0.0590 & 0.0149 \\ \hline \end{tabular}
\end{table}
Table 2: Mean error of displacements and strains caused by imaging through heat waves, quantified by spatial and temporal standard deviations (STD) of the data.  
Figure 10: Displacement of the center subset as a function of time: (a) U direction; (b) V direction.