## 3 Selected Results of Optical Metrology Techniques
### Techniques Based on Geometrical Optics Suitable for In-Process and In Situ Applications
#### 3.2.2 In-Process Measurement and Evaluation of Laser Added Manufacturing Processes for Metals
The results show a significant dependence of porosity on the thickness difference, as would be expected from the discussion of Figure 11. It should be noted, that the goal of this study is to determine the suitability of the measurement principle demonstrated here for an in-process characterization of the quality of the laser beam melting. An optimization of the PBF-LB/M process itself is beyond the scope of this study. Our results demonstrate, however, for the first time, the suitability of precise thickness evaluation using Fringe Projection for the in-process detection of the material quality created by an PBF-LB/M process. For the assessment of the recorded data, usually surface parameters such as mean roughness (Sa), RMS roughness (Sq), Peak to Valley (PV) value (Sz), skewness (Ssk) or kurtosis (Sku) are determined according to Reference [55]. However, it turns out that the structure function (SF) [56] is much more useful for assessing 3D surface characteristics to reveal process deviations compared to the parameters stated above. The SF of order \(d\) depends on the separation parameter \(n\) for a one-dimensional discrete set of height values \(z_{i}\) with \(i=1,\ldots,N\) and is defined by  
\[S_{d}(n)=\frac{1}{N-n}\sum_{i=1}^{N-n}(z_{i}-z_{i+n})^{d}. \tag{10}\]  
The SF that represents the mean distance of each spatial distance (separation) does not refer to a statistical expectation of the data and is therefore independent of the measurement  
Figure 15: Porosity measured by X-CT of structures created by PBF-LB/M as a function of the height difference measured in-process by Fringe Projection. The values represent measurements using samples presented in Figure 14 after further growth to layer 20. The values of the height difference are taken from layer 20, the center of the cubes, which consist of 40 layers at the end of the growth process. For an easier overview, the material with the highest degree of porosity was used as a height reference with height difference = 0. Measured values follow the tendency that the height difference increases with the degree of sample porosity. The value of the structure located individually in the upper part of Figure 14a was not taken into account because the z-values do not appear plausible due to the large distance between the melted tracks (compare Figure 14b). Sample parameters are given in Table 1 of Appendix A.  
system. One of the important advantages that apply here is the significantly high sensitivity of the SF for roughness differences. In Reference [57], we therefore proposed a method for the in-process evaluation of powder beds used in PBF-LB/M based on the SF analysis. We have indicated that when comparing metallic powder height distributions, which differ only by 3 \(\upmu\)m in their standard deviations, differences in roughness and waviness can be evaluated using SF. Our results [57; 58] demonstrated that the SF can be interpreted as a criterion of the frequency content of the surface with respect to roughness and waviness, in which a periodicity within the sample surface is again represented by a periodicity in the SF. For more detailed definitions of the one- and two-dimensional SF, we refer to [59; 60]. The following result demonstrates the successful assessment of the quality of the powder distribution on the basis of height values, which are shown in Figure 16 using the (x, y, z) values of layer 10, as described in the analysis above. The powder recoating procedure took place from right to left. For evaluation purposes, the geometric coordinates (z) of the point cloud are calculated perpendicular to the (x, y) plane. Two areas of 25 \(\times\) 25 mm in size were selected out of the powder bed to compare and assess the even distribution. These areas are denoted as area 1 (right) and area 2 (left) in Figure 16. The calculated mean roughness Sa of the absolute of the ordinate values show a small difference of 1 \(\upmu\)m only. The color values of the areas have been adjusted to make the height values more recognizable.