## 2 Materials and Methods
### X-ray CT and Image Analysis  
The X-ray CT scans were conducted using a metrological CT system (Nikon Metrology MCT225), with a micro-focus X-ray source having a minimum achievable focal spot size of 3 \(\upmu\)m, a 16-bit X-ray detector with a 2000 \(\times\) 2000 grid of 0.2 mm squared pixels, a controlled cabinet temperature (20 \(\pm\) 0.5 \({}^{\circ}\)C), and a maximum permissible error (MPE) for length measurements equal to (9 + \(L/50\)) \(\upmu\)m (where \(L\) is the length in mm). Each channel was scanned once, except for the channel 6 mm A, which was scanned five times for repeatability and reproducibility analysis. The scanning parameters used to acquire X-ray bi-dimensional projections were kept fixed for all scans for a better comparison of results. A total of 3141 projections were acquired with an exposure time equal to 1.415 s per projection and using a 0.1 mm Cu filter, a voltage of 200 kV, and a power of 8 W. The reconstruction of 3D models starting from the acquired projections was conducted with the CT Pro 3D software version 3.1.9 (Nikon Metrology Inc., Dusseldorf, Deutschland), which implements the filtered-back projection algorithm [28]. A beam hardening correction was applied across all scans using the preset index 2 which utilizes a second-order polynomial of the form:  
\[y=0.75x+0.25x^{2} \tag{1}\]  
where \(x\) is the initial gray value and \(y\) is the corrected gray value. In addition, a noise median filter with a 3 \(\times\) 3 kernel size was applied to all the acquired X-ray projections before reconstruction. The obtained voxel size was equal to 9 \(\upmu\)m.  
\begin{table}
\begin{tabular}{c c c} \hline \hline Layer Height, \(\Delta z_{\text{lager}}\) & 60 \(\upmu\)m \\ \hline Particle Size & 20–63 \(\upmu\)m \\ \hline Hatch Parameters & Volume & Down skin \\ \hline Laser Power, \(P_{L}\) & 650 W & 200 W \\ \hline Scanning Speed, \(v_{\text{scant}}\) & 1850 mm/s & 1700 mm/s \\ \hline Hatch Spacing, \(\Delta y_{\text{match}}\) & 170 \(\upmu\)m & 100 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Process parameters for LPBF manufacture of the channel samples.  
Figure 1: **(a)** LPBF aluminum cooling channel sample; **(b)** end-view of the different investigated channel diameters; **(c)** sketch of the channel sample showing the nominal dimensions and locations for five holes intended for thermocouples. \(D_{\text{norm}}\) varied between investigated channels.  
The scanned region, with a height approximately equal to 18 mm, was the same for each of the nine channels. To do this, the third thermocouple hole from the left (Figure 1b) was positioned in the middle of the scan. The reconstructed volumes were individually realigned and cropped using the analysis and visualization software VGSTUDIO MAX 3.2 (Volume Graphics, Heidelberg, Germany). The volumes were cropped so that a total channel length of 9 mm was represented equally on either side of the thermocouple hole. The cropped volume was subsequently exported as a stack of cross-sectional TIFF images along the length of the channel, with step width equal to 9 \(\upmu\)m. Each image from the exported stack represented a cross-sectional view of the channel as the one shown in Figure 2. For each of the nine reconstructed volumes, a stack consisting of 2000 images was generated, of which the middle 500, representing a channel length of 4.5 mm, were used for analysis. The 500 slices were selected as the default stack size for the general investigations as they could be analyzed within an acceptable computation time.