## 2 Materials and Methods
### OCT Setup  
The measurement system is based on SD-OCT technology. In SD-OCT, the frequency spectrum of the interference of back-reflected light from a sample arm and a reference arm with a stationary mirror is evaluated. The interferential spectrum contains the entire depth information of a scan in frequency-coded form, which means that axial scanning is not necessary and very high lateral scanning frequencies can be achieved. The SD-OCT developed for this work is based on a fiber-based Michelson interferometer setup consisting of three main components: Preicte's IDM (Preicte GmbH & Co.KG, Gaggerau, Germany), which combines a broadband light source and a customized spectrometer with a linear CCD camera, a scanning unit integrated in the LMD-w head with a dichroic beam splitter, and an external reference path that is shielded from any environmental influences and interference by the fiber-based coupling to the rest of the system. A central wavelength of \(\lambda_{0}\) = 1550 nm was chosen with a spectral bandwidth of 80 nm. In previous spectral emission tests, it was found that the process emissions have no influence on the interference signal of the measurement system. The light is guided through an optical fiber to a fiber coupler which splits the light in a ratio of 50/50 into the reference arm and the sample arm. The sample arm consists of a collimator, a telescopic beam expander, and a pair of galvo scanners. Inside the processing head, the measuring beam runs coaxially with the process laser after it passes the dichroic beam splitter; both the measuring beam and the process beam pass through optical prisms and the focusing lens, which focuses the beam onto the workpiece. The measuring range in the z-direction is 10 mm, the z-position of the workpiece can be determined with a repeatability of approx. 1 \(\upmu\)m. The theoretical spot size in the focus plane was calculated to be 30 \(\upmu\)m. A circular scanning pattern was necessary due to the presence of the coaxial nozzle and wire in the center of the objective lens. The circular scanning diameter of the measuring laser over the sample can be varied by adjusting the galvo parameters. In non-scanning mode, absolute height values can be read from the depth scan, the so-called A-Scan. With the use of the integrated galvo scanners, the measuring beam is scanned over the workpiece so that a 2D cross-sectional image of the sample is created. The A-Scan rate for the system used in this work was 70 kHz. A volume scan results from an additional scanning direction (e.g., in the direction of the process). For this application, a maximum scan field with a scanning-diameter of 3 mm (r = 1.5 mm) was required to capture the complete width of the weld beads (shown in Figure 3). With a maximum galvo frequency of \(\omega\) = 200 Hz and a measuring frequency of \(f\) = 70 kHz (t\({}_{\text{min}}\)\(=1.42857~{}\times~{}10^{-5}\) s), the lateral spacing \(\Delta\text{Y}_{\text{max}}\) can be calculated using  
\[|\Delta\text{Y}_{\text{max}}|=\text{r}\,*\,\omega*\text{t}_{\text{min}} \tag{1}\]  
to be -4.3 \(\mu\)m. If the maximum feed rate \(v\) of the process head is also considered, the spacing of the scanning points increases to 4.5 \(\mu\)m through additional path changes, using  
\[|\Delta\text{Y}_{\text{max}}|=\text{r}*\omega*\text{t}_{\text{min}}+v\,\text{ t}_{\text{min}}. \tag{2}\]  
At the same time, the feed motion of the head causes the spot to be laterally washed out within the integration time of the camera of the spectrometer. This washing-out effect does not occur in conventional OCT because the measuring head or the object are not moved during acquisition. This effect plays a role when the lateral offset is greater than \(\lambda/4\)[17]. With the integration time of the camera of 10 \(\mu\)s used here and a maximum feed rate of \(\sim\)1000 mm/min, the lateral offset lies within this range. It was found that at feed rates of 1000 mm/min maximum, no contrast degradation of the signal is to be expected, so that the effect is negligible at these process speeds.