## 2 Materials and Methods
### Surface Wave Analysis  
A stationary laser beam from a fibre laser (IPG YLR-15000, IPG Photonics, Burbach, Germany, wavelength 1070 nm) was aimed towards a steel plate (Docol 200, SSAB, Stockholm, Sweden), illuminated by a laser pulse of 1 s duration with 1.5 kW laser output power at a defocussed spot size of \(\sim\)2.1 mm (Figure 1). Argon shielding gas at a flow rate of \(\sim\)10 L/min was used. The metal surface was observed using a high-speed camera (Photron Fastcam Mini UX100 type 800K-M-16G, Reutlingen, Germany) at 10,000 fps with a bandpass filter that only transmits the reflections from the processing zone of the used illumination laser (Cavitar, continuous wave, 808 nm wavelength, multimode, no preferred polarization, spot diameter on the material of \(\sim\)10 mm).  
When a surface event occurred on the surface, e.g., initiated by a degassing gas bubble, the resulting surface waves were observed and evaluated. Their frequencies \(f\) and wavelengths \(\lambda\) were determined from the video frames (Figure 1). The assumptions were that small values of disturbance occur, the surface tension is constant over the oscillating surface, and the liquid is uniform in depth, incompressible and irrotational at small wave amplitudes. These assumptions enable the use of the Kelvin equation [40]. Due to the small wavelengths of the capillary waves compared to the liquid film depth, reliable surface tension data \(\sigma_{k}\) can be derived by [40]  
\[\sigma_{k}=\frac{\rho}{k^{3}}.\left(4\pi^{2}.f^{2}-g.k\right) \tag{2}\]  
while \(f\) is the frequency related to the angular frequency \(\omega=2\pi\cdot f\) and \(k=\frac{2\pi}{\lambda}\) the wave vector. The error in measuring the frequencies and wavelengths \(\lambda\) leads to uncertainties in the surface tension measurements. Type B uncertainties were estimated. Deviation \(\Delta\)  
Figure 1: Set-up to create a controlled melt pool using laser beam heating, observed by an RGB camera for temperature calculations and a high-speed camera to observe melt pool surface wave propagations.  
was assumed to be symmetrical. Uncertainties \(u_{B}\) were derived for each surface tension measurement according to  
\[u_{B}=\frac{\Delta}{\sqrt{3}} \tag{3}\]  
The relative uncertainties \(\widetilde{u}_{B}\) were derived as  
\[\widetilde{u}_{B}=\frac{u_{B}}{value} \tag{4}\]  
The total relative uncertainty of one measurement was given as  
\[\widetilde{u}_{B,tot}=\sqrt{\sum u_{B}^{2}} \tag{5}\]  
For the surface wave measurements, Equation (2) contains the parameters and assumed deviations \(\Delta\) given in Table 1.  
Since the surface waves propagate over a certain surface area, the related temperature was determined as the average of temperatures within the propagation area. Temperature fields were recorded using an RGB-camera (DFK 23 GM021, TheImagingSource, Bremen, Germany) at a recording rate of 30 fps, exposure time of 1/200,000 s and a gain of 0 dB. An IR filter was installed to avoid damage to the sensor by the laser light process reflections. The temperature in each pixel of the camera sensor was determined by calculating the intensity ratios between the red and blue pixel intensity values assuming gray body emission (with calibrated offset) and considering the sensor spectral sensitivity curves. Within the measuring area, the minimum and maximum values showed deviations between 2% and 9% from the average values.