## 2 Materials and Methods
### Experimental Setup
#### 2.1.3 High Spatially and Temporally Resolved Temperature Measurement of the Process Zone  
The camera unit was coaxially integrated into the beam path with a dichroic mirror, as illustrated in Figure 1. The temperature measurement used the thermal process light emitted by the process zone. An optimal magnification ratio of the relatively small process zone on the camera sensor ensures a high spatial resolution. For this reason, the measurement setup included a magnifying objective. An adjustable focusing of the magnifying objective provided the necessary information about the depth from the cut kerf. The beam path contained a band-pass filter to ensure that the camera detected only the thermal process light. The specifications of the camera unit are summarized in Table 2.  
The measurement setup necessarily required calibration to comply temperature conformity. For this purpose, an LED-based calibration source was used, which was developed at the Fraunhofer IWS [42]. This LED array emitted infrared radiation in a very small spectral band in the wavelength range of 740 nm \(\pm\) 10 nm, which was directly tuned to the sensitivity range of the camera sensor. The LED array was tested and certified as a calibration standard at the Physikalisch-Technische Bundesanstalt on a black body. For this LED array, the correlation between emitted radiation and corresponding temperature is known. For the developed temperature measuring setup, a known temperature of the LED array was assigned to each measured gray value of the camera signal. In this way, a temperature-gray value-characteristic was determined for the temperature measuring setup, as shown in Figure 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristics** & **Data** \\ \hline wavelength & 740 nm \(\pm\) 10 nm \\ sensor & CMOS 1/1.2\({}^{\prime\prime}\) (1936 \(\times\) 1216 px\({}^{2}\)) \\ magnification & 2:1 \\ dynamic range & 73 dB \\ quantum efficiency & appx. 30\% (@740 nm) \\ sensitivity threshold & 7.2 e\({}^{-}\) \\ saturation capacity & 32,000 e\({}^{-}\) \\ \hline \end{tabular}
\end{table}
Table 2: Characteristics of the developed camera-based temperature measurement setup.  
Figure 3: Temperature–gray value–calibration curves for different emission coefficients.  
According to this procedure, the calibration was valid for the emission coefficient e = 1. The real emission coefficient is decisive to evaluate absolute temperatures. Therefore, Figure 3 contains further calibration curves, where the cut material was assumed as a diffusive gray body with different emission coefficients.  
As the emission coefficient depends on the material, the radiation angle (defined by the cut front topography), and the temperature, it is non-uniform within the process zone. This means a complete consideration of the real influence is impossible, and an uncertainty analysis of the temperature measurement is mandatory. When using the emission coefficient e = 1 for evaluation, Figure 4 shows that the measured temperature is always below the real temperature. In addition, the measurement uncertainty grows at an increasing temperature or decreasing emission coefficient.