## 5 Influence of Detection Angles on Detection Distances
### Results  
As mentioned, the actual detection angles would not be the same as assumed prior to the study, since the positions of the detection dummies were fixed and since the detection distance would change from one subject to another. Figure 7 therefore shows the calculated detection angles for each dummy location for all test subjects and test runs. Angles were calculated by taking the arctangent of the ratio between the dummy's lateral offset distance from the center of the driving lane and the detection distance to the dummy. As shown, a single dummy position can, due to the vastly different detection distances among the test subjects, also lead to different detection angles. The mean detection angles are 3.2, 6.1, 7.8, and 10.5\({}^{\circ}\). As an example, the dummy furthest away from the road (10.5\({}^{\circ}\)) is responsible for detection angles between 7\({}^{\circ}\) and 15\({}^{\circ}\). Figure 6: Schematic test set-up to investigate the influence of different detection angles on detection distances. The test dummies are placed at 5.0, 9.6, 12.5, and 15.5 m from the center of the driving lane. The detection distances were measured as 93.5, 95.5, 97.9, and 84.1 m for the corresponding dummy positions 5.0 m (3.2\({}^{\circ}\)), 9.6 m (6.1\({}^{\circ}\)), 12.5 m (7.8\({}^{\circ}\)), and 15.5 m (10.5\({}^{\circ}\)). It is directly obvious that the detection distances remain fairly consistent over the central positions. Even if detection distances at angles smaller than 3.2\({}^{\circ}\) had been measured and were much longer than at angles of 3.2\({}^{\circ}\) or larger, this would imply that a lower intensity would be needed to detect objects at these small angles. Higher intensities would still support detection of these objects. However, this seems unlikely given the very small differences in detection distances between 3.2\({}^{\circ}\) and 7.8\({}^{\circ}\). However, due to the nature of automotive headlight distributions, the light output from headlights at larger detection angles is far lower than immediately adjacent to the road, where, within a few degrees of the line of sight in the parafoveal region of the retina, the targets were more or less viewed on-axis with little change expected in the required intensity. The dummy on the outside therefore has the lowest detection distance due to the least amount of light reaching the dummy under this angle. Since the absolute detection distances are not the focus of this part of the study, but rather the relative required luminous intensity compared to the center of the light distribution, the luminance at each test dummy was measured for these detection distances. From this, using Equation (2), the illuminance required for the detection angles can be calculated as:  
\[I=E\cdot r^{2}\text{ and }L=\frac{\rho}{\pi}\cdot E \tag{2}\]  
which follows:  
\[I=\frac{L\cdot\pi}{\rho}\cdot r^{2}. \tag{3}\]  
Based on this analysis, the required luminous intensities were calculated as follows: 154,453 cd, 76,787 cd, 67,240 cd, and 39,551 cd for the corresponding detection angles. Figure 8 shows these data interpolated in blue and normalized to a value of 1. Extrapolated from this are the data for the left side of the road, assuming a similar relationship between angle and intensity as along the right side. Figure 7: Calculated detection angles for the measured detection distances for all test subjects over the given target positions of 5.0 m (3.2\({}^{\circ}\)), 9.6 m (6.1\({}^{\circ}\)), 12.5 m (7.8\({}^{\circ}\)), and 15.5 m (10.5\({}^{\circ}\)). The red bars show the mean distances. The blue bars indicate 50% of all data. The black bars show the range of normal distributed data. Red data points were classified as outliers. These data will now represent the baseline headlight distribution. The horizontal data were taken directly from the data in Figure 8. For the vertical distribution, a Gaussian distribution is added that extends the vertical range of this distribution to have 10% intensity at \(\pm 5^{\circ}\), which is standard in current headlights.