## 2 Materials and Methods
### Characterization Methods
#### 2.2.4 Temperature Distribution  
The FOV was adapted to the width of the cut kerf considering a maximum reachable frame rate. Set #1, the static beam shaping, utilized FOV 1 (see Figure 6b). As the cut kerf width decreased for beam oscillation, FOV 2 was applied. As it covered more than half of the process zone, flipping the image at the symmetry axis complemented the missing information. With this method, the frame rate significantly enhanced. The parameters of both FOVs are summarized in Table 3.  
The relation between process emission and temperature is shown in Figure 8. The camera recorded gray value images comparable to Figure 8a within the selected FOV. The gray values were converted into the temperature distribution of the process zone using the calibration curve of Figure 3 with the emission coefficient of e = 1. The choice of e = 1 was made deliberately, because the genuine emission coefficient cannot be determined. Additionally, it is not uniform within the process zone. As a consequence, the real temperature will always be higher than the calculated values (within the uncertainty range; see Figure 4). However, working with absolute temperatures allows for more advanced evaluations, such as estimating the melt pool size. The transformed result projected into the cut kerf is shown in Figure 8b. The camera recorded a sequence of single images over a time period of 500 ms. Each single gray value image was written as matrix Tij(t). These matrices had the dimensions m \(\times\) n according to Table 3 and were evaluated in different ways, as described in the following. Figure 8: Correlation between thermographic and geometric information of the process: (**a**) Gray value of the process light during the cut; (**b**) Conversion of the gray value into corresponding temperature distribution super positioned with geometry of the cut kerf. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **FOV 1** & **FOV 2** \\ \hline set & \#1 & \#2-\#4 \\ m \(\times\) n [px] & 1200 \(\times\) 300 & 1200 \(\times\) 80 \\ image size [mm\({}^{2}\)] & 3.6 \(\times\) 0.9 & 3.6 \(\times\) 0.24 \\ frame rate [FPS] & 488 & 1360 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of the camera’s FOV in dependence of the analyzed sets. Extracting single rows T\({}_{\text{i}}\)(t) out of the matrices along the cut front (red dashed line in Figure 8b) enabled spatially resolved temperature profiles. These provided e.g., the position of the laser beam regarding the cut front. Calculating the average \(\overline{\text{T}}_{\text{ij}}\) and maximum T\({}_{\text{ij}}^{\text{max}}\) temperature matrices out of all single images within a sequence surveyed the characteristic temperature distribution of each set:  
\[\overline{\text{T}}_{\text{ij}}=\frac{1}{0.5\cdot\text{f}\text{r}\text{r} \text{a}\text{r}\text{a}}\sum_{0\leq\text{t}\leq 0.5\text{s}}\text{T}_{\text{ij}}( \text{t}), \tag{4}\]  
\[\text{T}_{\text{ij}}^{\text{max}}=\max_{0\leq\text{t}\leq 0.5\text{s}}\big{(} \text{T}_{\text{ij}}(\text{t})\big{)}. \tag{5}\]  
To validate the temperature volatility, the mean value of a smaller submatrix \(\overline{\text{T}}_{\text{p,p}}(\text{t})\) out of T\({}_{\text{ij}}\)(t) was calculated:  
\[\overline{\text{T}}_{\text{p,p}}(\text{t})=\frac{1}{\text{p}^{2}}\sum_{\text {i=a}\text{j=b}}^{\text{a+p,b+p}}\text{T}_{\text{ij}}(\text{t}). \tag{6}\]  
The calculations utilized p = 20 pixels, which corresponds to an area of 60 \(\times\) 60 \(\upmu\)m\({}^{2}\), which are located around the hottest pixel of the cut front. The location is defined by the start coordinates a and b. Plotting \(\overline{\text{T}}_{\text{p,p}}(\text{t})\) versus time visualized a temporally resolved temperature sequence. This sequence revealed the temperature at a fixed position with respect to the moving cut front. To analyze the melting progress, respectively the heating up and cooling periods, a fixed material position was analyzed as well.