## 2 Materials and Methods
### The Reference Measurements and Cumulative Error  
A GOM ATOS II Triple Scan (GOM GmbH, Braunschweig, Germany) 3D coordinates measuring system and a Mitutoyo Legex 9106 (Mitutoyo Corporation, Kawasaki, Japan) CMM with tactile-probing systems were used to conduct reference measurements, as shown in Figure 1.  
The optical 3D coordinates measuring system follows the structured light and stereo vision techniques built on the principle of camera-camera and camera-projector triangulation. Two calibrated reference gauge blocks were used to establish a traceability to the SI unit during the optical measurements. The measurements were performed in a room with a temperature range of 22.0-23.3 \({}^{\circ}\)C. The results of the measurements were compensated with the subsequent thermal expansion. The CMM consists of a fixed bridge structure and uses the scanning and touch-trigger probing principles. The CMM is periodically verified with the interferometrically calibrated gauge blocks ensuring a maximum permissible error, E\({}_{0,\,\mathrm{MPE}}\) value of 0.35 \(\upmu\)m + L/1000 \(\upmu\)m where L is length in \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ISO/ASTM** & **Machine** & **Software** & **Material** & **Layer** & **Other Parameters** & **Post Processing** \\
**Method** & & & & & & \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Powder \\ bed fusion \\ \end{tabular} } & SLM & Materialise & \multirow{3}{*}{0.03 mm} & \multirow{3}{*}{
\begin{tabular}{c} Standard process parameters \\ \end{tabular} } & Heat \\  & Solutions & Magics & & & Platform heating: 200 \({}^{\circ}\)C & Treatment and \\  & 125 HL & 22.0 & & & Particle size: D\({}_{v}\)(10) = 32.5 \(\upmu\)m, & manual \\  & & & & D\({}_{v}\)(50) = 44.3 \(\upmu\)m, D\({}_{v}\)(90) = 59.9 \(\upmu\)m & support \\  & & & & Number of layers: 1460 & removal \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Additive manufacturing (AM) parameters for the end-use implant. Figure 2: The print orientation and location of four identical implants on the build platform illustrating supports in blue. mm. The CMM measurements were performed in an automated climate-controlled laboratory with a temperature stability of 20 \(\pm\) 0.2 \({}^{\circ}\)C [68]. In this study, uncertainty was calculated according to the principles of Guide to the expression of uncertainty in measurement (GUM) [52]. Independent measurements were compared with the reference measurement of the specimens to calculate geometric variation using GOM Inspect 2018 (v2.0.1, GOM GmbH, Braunschweig, Germany) software, which is tested and certified by the National Institute of Standards and Technology (NIST) and the National Metrology Institute of Germany (PTB). Inaccuracy of the CT system was calculated in terms of linear error in the x-, y-, and z-axis and orthogonal error in the x-y, x-z, and y-z planes. The linearity and orthogonality are estimated by establishing a coherent local coordinate system for the CT-scanned Phantom and the tactile-probed Phantom. The coherent local coordinate system enabled measurements of their deviations. The linear error in the x- and y- axis is estimated by linear regression analyses. These are conducted by measuring distance deviations from hole-to-hole center points with respect to positions in the local co-ordinate system. The linear error in z-axis is calculated by evaluating the distance deviation of the hole-to-hole center points situated in the x-z and y-z planes. It is presumed that the effects of thresholding the CT-scanned Phantom are negligible due to the custom-designed geometrical features and the selected measuring principles. The 3D thresholding error is analyzed by relying on a mean distance deviation which is estimated by comparing surfaces of the segmented SD head and the optically scanned dry skull. The 3D modeling error is investigated by evaluating the absolute accuracy of the modeling software. Potential sources of error in AM are analyzed in terms of a mean distance deviation and a magnification error.