## 3 Results and Discussion  
### Correlation between an IR and a DSLR Camera to Determine the Zone Length  
In order to confirm the accuracy of the zone length measurement via an IR camera, a parallel determination of the zone length was conducted using a conventional DSLR camera (Canon D600 with the lens EF-S 18-55 mm) as a reference. Both cameras were positioned with an inclination of 45\({}^{\circ}\) from the molten zone surface and a height of 500 mm and 400 mm, respectively, from the crucible region direct below the induction heating coil (see Figure 4). The special position of the cameras in terms of inclination and distance point of view leads to a perspective observation of the zone length. Therefore, the correct measurement of the molten zone length had to be adjusted based on the characteristics of the camera such as sensor dimensions, view angle, pixel resolution, etc. By using this information together with the obtained pixel distance from the beginning and end of the molten zone, it was possible to calculate the length of the molten zone in millimeters. For the DSLR measurement, both the start and the end of the molten zone were determined by analyzing the pictures (see Figure 5b);  
\begin{table}
\begin{tabular}{c c c c c c} \hline Temperature (\({}^{\circ}\)C) & 650 & 668 & 674 & 683 & 692 & 699 \\ \hline Emissivity (\(\epsilon\)) & 0.47 & 0.42 & 0.41 & 0.39 & 0.36 & 0.32 \\ \hline \end{tabular}
\end{table}
Table 1: Experimental data for the emissivity values at different temperatures of lightly oxidized Al, based on the above-mentioned conditions.  
Figure 3: Sketch of the zone refining process in the experiment.  
while for IR patterns (Figure 5a), these regions were determined automatically based on the melt temperature of the recorded area (see Section 3.2 for a detailed explanation).  
During the trial, several DSLR pictures were taken, and at the same time, the IR camera recorded the whole process. This trial was conducted for a duration of 5 min while the coil remained static at the middle of the crucible and the induction heating was kept at 11 kW. During this period, a molten zone of around 130 mm was kept in the middle region of the bar. Since the coil remained static and gave power continually, a slight increase to around 180 mm in the length of the molten zone during the 5-min period was observed.  
Figure 4: (a) Horizontal zone refining equipment with a single induction heater at IME Institute of RWTH University showing the position and (b) technical details of an infrared, as well as a DSLR camera.  
Figure 5: Comparison between the IR thermography (a) with the DSLR camera picture (b) showing the molten zone in the aluminum bar.  
Equation (1), as well as Figure 6 show the mathematical background behind the calculation in MATLAB in order to obtain the length of the molten zone for both the DSLR and IR cameras (for example, through taking one frame per 10 s).  
\[\text{Zone Length}=L_{2}(FB)-L_{1}(FA)=f(n_{2})-f(n_{1}) \tag{1}\]  
where \(n_{1}\) is the pixel number of the beginning of the molten zone; and \(n_{2}\) is the pixel number of the end of the molten zone. The calculation of the function \(f(n)\) can be seen in Appendix A.  
According to the aforementioned calculations, the zone lengths obtained by both cameras were plotted in comparison with each other (Figure 7). The results show a good correlation of both values and demonstrate the reliability of the measurement procedure for both camera systems. The maximum difference observed between measurements was around 20 mm (10% divergence) and can be ignored. As a conclusion, the IR camera is reliable enough to deliver as accurate results for the molten zone length as a real visual observation. That means the temperature values on the surface were detected correctly, as well.  
Figure 6: Geometrical illustration of the conversion of zone length distance from pixels to millimeters.  
Figure 7: Values of molten zone length obtained via the IR camera and the DSLR camera.