## 4 Results and Discussion
Both are crucial for optimal lens performance, affecting visual clarity and prescription accuracy. As stated previously, measurements were also performed for the pantoscopic angle as well as the vertex distance (distance between the pupil and the plane of the lens). Results have shown that similar to interpupillary measurements, vertex distance is affected by the distance at which the images are captured. This is shown in the other measurements discussed further in the paper. The behavior is best observed in the latter, with the measurements \"drifting\" towards lower values, with the increase in distance between the tablet and the markers. However, very little, if any, effect of distance over the pantoscopic angle was observed. Regarding these measurements, since the mannequin does not feature any asymmetrical characteristics, the measurements were considered identical for each side. These are also shown in Figure 16a-f for each distance, along with Figure 16g, which offers a general overview of the trend in the obtained values. Figure 13: Comparative analysis of obtained results regarding the interpupillary distance measurement. Figure 14: (**a**) Interpupillary measurement at 50 cm; (**b**) Interpupillary measurement at 60 cm; (**c**) Interpupillary measurement at 70 cm; (**d**) Interpupillary measurement at 80 cm; (**e**) Interpupillary measurement at 90 cm; (**f**) Interpupillary measurement at 100 cm; (**g**) Comparison chart of error distribution obtained for interpupillary distance. The following will present the main interpretations and findings resulting from the experimental determinations according to the obtained parameters. Analyzing the graphs in Figures 12 and 13 and Table 2, it is clearly seen how the measured average ID increases and deviates from reality as the distance to the target increases. The same general tendency can be observed in the case of average absolute errors and standard deviations. Therefore, for a distance of 50 cm from the target, the following data were obtained for the interpupillary distance: average measured distance of 51.115 mm with a standard deviation (SD) of 0.416 and with maximum and minimum values of 52.23 mm and of 50.34 mm, respectively and absolute average error from the actual distance of 0.503 mm, appearing to be the most optimal distance from the target among those investigated for the correctness of the measurements of this parameter. If at 60 cm to target, the deviations from reality do not seem to increase significantly, being comparable to those at 50 cm, starting with a distance to target of 70 cm, the results of the measurements become more and more distant from the actual data, for example at 90 and 100 cm to target, having an average absolute error of 2.438 mm and 2.374 mm, almost five times higher compared to a distance of 50 cm to target. Regarding the determined semi-distances ((IDL and IDR) Figures 14 and 15 and Tables 3 and 4), it was found, in general, a greater predisposition to errors for IDR--starting with a distance of 60 cm to target--the average absolute errors exceed 1.25 mm (for IDL, the average absolute error exceeds 1 mm compared to the real data only for the distance of 100 cm to target). Also, at a distance of 100 cm, some significantly different results appear compared to the rest of the measurements, this being visible on the graphs in Figure 14f,g through the points further away from the rest of the data--very large distance to target representing an amplification of possible errors caused by the human factor. When it comes to the pantoscopic angle (Figures 16 and 17 and Table 5), there is generally a tendency to decrease the measured angle and move away from the real angle when the distance to the target increases. The closest results to reality this time, too, are obtained for the distance to the target of 50 cm.