## 2 Materials and Methods  
### X-ray Computed Tomography Measurements  
The specimens used for the investigation in this study are cylindrical internal channels (N1 and N2) fabricated by L-PBF that were built as a part of an industrial case study from Baker Hughes, Italy. The part was manufactured vertically with an orientation perpendicular to the build platform. The material used for fabrication was INCONEL 718, an austenitic nickel-chromium-based superalloy commonly used for high-temperature applications in gas turbines [3; 5]. The channels were cut out from the whole part to obtain separate specimens using Wire Electrical Discharge Machining and individually scanned with CT. The channels consist of an integrated straight and inclined section with an inclination angle of 60\({}^{\circ}\) from the horizontal axis and a bend radius of 3 mm. The nominal diameter of channel specimens N1 and N2 are 1.5 mm and 1 mm, respectively. Figure 1 displays the (a) fabricated case study, (b) drafting with the dimensions of the case study and (c) one of the CT-scanned volumes of the individual channel specimen to visualise the 60\({}^{\circ}\) bend in the centre of the specimen visualised with respect to the \(y\)-axis. The specimens were scanned using a metrological CT system Nikon MCT 225 (Nikon Metrology X-Tek, Herts, UK), where only the centre part of each specimen was in the field of view to avoid potential defects induced by the cutting and to achieve the highest resolution to resolve and visualise the microscale surface features on the internal surface of the channel. The part was positioned as close as possible to the X-ray source, while it was ensured that the specimen's complete projection was inside the field of view of the detector at any rotation position. In this way, an 8 mm high section centred around the bend of the channels could be acquired with a voxel size of 4 \(\upmu\)m. The optimised scan parameters for the scans are shown in Table 1 and were not altered for the different samples. To reduce beam hardening artefacts due to the high density of the material, a 0.5 mm tin filter was used. The acquired images were reconstructed with the reconstruction software provided by the CT system manufacturer without any additional software filtering or artefact reduction. Subsequently, the volumes were imported in VGStudio MAX 3.3 for further analysis. Figure 1: Industrial case study with nominal channel diameters of 1.5 mm and 1 mm: (**a**) picture of the geometry produced by L-PBF; (**b**) drafting with dimensions of the case study; (**c**) cut section of CT-scanned case study volume to visualise the 60\({}^{\circ}\) bend, with the blue box indicating the created Region of Interest. After the surface was determined, a Region of Interest (ROI) was created comprising only the internal channel (cf. yellow rectangle in Figure 2) to perform the wall thickness analysis in two different modes (background and material) using the Ray and Sphere methods implemented in VGStudio. Figure 2a shows a schematic representation of the working directions (blue material mode and red arrow background mode) of the different wall thickness analyses on the cross-section of the specimen shown in Figure 1c, while Figure 2b illustrates the creation of individual ROIs for the straight and inclined sections of the channel specimen. Within the ROIs, analyses applying different combinations of both working directions and the Ray and Sphere approaches were conducted, resulting in four data sets that were further processed to determine \(d_{man}\) and \(d_{eq}\). Regardless of whether the Ray or Sphere method was used, the background mode operated only on the internal volume of the channels (i.e., non-material voxels) using the determined surface on one side as the starting point to find the closest surfaces within a pre-defined opening angle that was set to 15\({}^{\circ}\). On the other hand, the Sphere method is based on spheres that are incrementally expanded throughout the ROI until the sphere touches two points of the surface.