## 2 Materials and Methods
### Synchronization of the Measuring Signals  
Regarding the geometrical characteristics of the melt pool generated during deep-penetration laser welding, including the vapor capillary, the different regions that are probed along the welding axis can obviously be of very short extent. The Knudsen layer, with a theoretical thickness in the order of magnitude of \(L_{\mathrm{K}}\)-10 \(\upmu\)m [13], is the thinnest characteristic keyhole region to be distinguished in the literature. Welding at welding velocities in the range of 30 mm/s up to 65 mm/s therefore corresponds to very short time intervals of about \(t_{\mathrm{K}}\)\(\sim\)100 \(\upmu\)s in which the characteristic behaviors can be probed. Due to this temporal restriction, not only are high sampling rates necessary but, also, the synchrony of the employed measuring devices must be assured within strict tolerances. The employment of different measuring devices is always affected by a time delay \(\delta t\) between the different signals resulting from the inner runtimes of the respective devices. Therefore, even though the signals are sampled simultaneously by the FPGA controller, they do not necessarily correspond to the same real-time event. Figure 8 shows a schematic of the signal paths from the experimental setup. The internal runtime and signal processing of the high-speed camera and the pyrometer lead to a delay between both signals, preventing a synchronous correlation within the strict tolerances required by the spatial extent of the investigated system. Figure 7: Influence of positioning errors on the pyrometric measurements: (**a**) geometric deviation of the measuring spot, and (**b**) resulting relative temperature deviation exemplarily for the emissivity of tantalum. In order to analyze these internal delays, an experimental setup has been designed in which an event is created that triggers the applied measurements simultaneously during well-defined and short time intervals, as depicted in Figure 9. The continuous heat source that is to be detected by the pyrometer is implemented by a tungsten lamp with an operating temperature of approximately T\({}_{\mathrm{W}}\approx\) 2000 \({}^{\circ}\)C. The detectable event for the high-speed camera is given by the visibility of the illumination laser spot. A shutter disk with a radius of \(R=47.5\) mm is used to interrupt the corresponding beam paths with a frequency defined by the rotation speed and the diameter of the semicircular notches. The beam path of the illumination laser and the focus of the pyrometer are arranged in such a way that the camera and the pyrometer can detect the event at the same angular position of the shutter disk. Based on the factual synchronicity of the physical events, it is now possible to match the measured signals and thereby find the systematic delay between the measured signals. The accuracy of the synchronization process is calculated from the angular velocity \(\omega\) of the shutter disk, the radius of the disk \(R\), and the radius of the notches \(r\) at the disk rim. \[\delta t=\frac{2\cdot\arctan\left(\frac{r}{R}\right)}{\omega} \tag{9}\]  
Figure 8: Schematic of the signal paths in the experimental setup. Figure 9: Experimental setup for synchronizing the measuring devices. hs: high-speed. The high-speed recording during the synchronization setup is performed at a frame rate of \(f_{\rm HS}\) = 100 kHz, matching the adjusted sampling rate of the FPGA controller. The signals from both the pyrometric and high-speed images are postprocessed with threshold values and thereby transformed into binary data indicating the detection of the event or the idle time, respectively. The shift between the recorded signals is analyzed by cross-correlation, showing a significant peak at the configuration of a maximal overlap between the input curves.