## 3 Results  
The comparison between the positions achieved with the proposed method and the currently applied clinical workflow within the CT bunker is depicted in Figure 8b, which summarizes the positioning of the fixation light extracted from the ETS geometry in cases of OM in the left and right eyes for the nine patients treated in CNAO. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Diseased Eye** & **Fixation Eye** & **Polar** [\({}^{\circ}\)] & **Azimuth** [\({}^{\circ}\)] \\ \hline L & L & 28 & 90 \\ L & L & 28 & 90 \\ L & L & 28 & 0 \\ R & R & 27 & 0 \\ L & L & 28 & 20 \\ R & R & 28 & 180 \\ L & L & 25 & 80 \\ L & L & 28 & 40 \\ L & L & 26 & 180 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fixation angles of the patients treated at CNAO considered in the study. Left eye (L) and right eye (R). Figure 8: Representation of polar and azimuthal angles that identify the fixation point (**a**). Aligned position of the fixation point of the nine patients treated in CNAO, comparison between clinical results (blue) and the results of the proposed method (Test, in green) (**b**). All nominal fixation points of the complete dataset (in red, real patients are highlighted) considered in the study (**c**). The 3D distance of the corresponding markers in the two ETS configurations (clinical and test) had a median value of 3.33 mm with an interquartile range (IQR) of 2.18 mm. The corresponding deviations on polar and azimuthal gaze angles were 0.37 \(\pm\) 1.12\({}^{\circ}\) (median \(\pm\) IQR) for the polar angles and 0.32 \(\pm\) 1.33\({}^{\circ}\) for the azimuthal angles. Figure 9 shows the boxplots that detail the positional deviations affecting the ETS-mounted markers calculated for the clinically applied procedure and the proposed test procedure, with respect to the nominal prescription coming from the treatment plan and the ETS modeling described in Section 2.1 (step #2). The corresponding median differences in terms of gaze direction were \(-\)1.10\({}^{\circ}\) (IQR = 1.13\({}^{\circ}\)) for the polar angles and \(-\)0.24\({}^{\circ}\) (IQR = 1.28\({}^{\circ}\)) for the azimuthal angles, when the clinical procedure was considered. Conversely, median angular deviations were \(-\)1.47\({}^{\circ}\) (IQR = 1.09\({}^{\circ}\)) for the polar angles and \(-\)0.11\({}^{\circ}\) (IQR = 0.75\({}^{\circ}\)) for the azimuthal angles, when the proposed procedure was applied. The augmented dataset including simulated clinical-like cases is reported in Table 2.  
When the deviation analysis was performed on this dataset, we found a median difference of 0.01\({}^{\circ}\) (IQR = 0.96\({}^{\circ}\)) for the polar angles and \(-\)0.32\({}^{\circ}\) (IQR = 1.47\({}^{\circ}\)) for the azimuthal angles between the clinical and test methods. When comparing the clinically applied procedure and the nominal prescriptions, we estimated a median difference of \(-\)1.32\({}^{\circ}\) (IQR = 1.19\({}^{\circ}\)) for the polar angles and \(-\)0.40\({}^{\circ}\) (IQR = 1.09\({}^{\circ}\)) for the azimuthal angles. When the ETS configuration obtained with the proposed method and the nominal prescriptions were compared, a median difference of \(-\)1.33\({}^{\circ}\) (IQR = 0.91\({}^{\circ}\)) for the polar angles and 0.16\({}^{\circ}\) (IQR = 0.99\({}^{\circ}\)) for the azimuthal angles were found. When less frequent fixation angles were included in the dataset (Table 3), we estimated a median difference of \(-\)0.13\({}^{\circ}\) (IQR = 0.98\({}^{\circ}\)) for the polar angles and 0.16\({}^{\circ}\) (IQR = 1.75\({}^{\circ}\)) for the azimuthal angles between the clinical and test method. Figure 9: Boxplot of the differences between the reference and the clinically applied procedure, and between the reference and the proposed test procedure in the medio–lateral (x), antero–posterior (y) and cranio–caudal (z) directions.