## 3 Results
The result of this analysis is shown in Figure 12 and indicates, with a coefficient of the determination of \(\mathrm{R}^{2}=0.984\), that there is a correlation between the Visibility Level and the proportion of object positions with a detection probability of the gray card of at least 90 %. From Figure 12, it can be observed that a Visibility Level of 13.35 is required for the reliable detection of the gray card on 90% of the object positions. If a Visibility Level of about 4.95 is provided to the vehicle driver, a reliable detection of the gray card on 50% of the object positions is achieved. In this context, the 50% threshold represents the critical threshold for object detection in nighttime road traffic, since the number of detections and the number of missed detections are equal here. In order to analyze the influence of the environmental conditions, the results of the investigation on the closed test site are presented here. For this purpose, the Visibility Level required at the various object positions for reliable object detection is first considered in Table 4.  
Table 4 shows that the required Visibility Level is in the range of 2.585 to 25.439 and thus higher Visibility Levels are required for the reliable detection on the closed test site, which is a realistic representation of nighttime road traffic. To consider the influence of the environment in more detail, the results for the closed test site are also analyzed using the simplified psychometric function. Figure 13 shows the relationship between the Visibility Level and the proportion of object positions on which the gray card is reliably detected. Figure 12: Relationship between the Visibility Level VL and the proportion of object positions in the light tunnel at which the gray card is reliably detected; to reliably detect the gray card at 90% of the object positions, a Visibility Level of 13.35 is required. As Figure 13 shows, the relationship between the Visibility Level and the proportion of reliably detectable object positions on the closed test site can also be described via the psychometric function (R\({}^{2}=0.959\)). The increase in the required Visibility Level for the reliable detection of the gray card to 90% of the object positions from Table 4 is confirmed by considering the psychometric function. Thus, at the closed test site, a Visibility Level of about 25 is required to reliably detect the gray card at 90% of the object positions. This corresponds to an increase in the Visibility Level by a factor of 1.87 compared to the light tunnel. In addition to the 90% threshold, the Visibility Level of 13.35 from the investigation in the light tunnel is indicated by the vertical dashed line in Figure 13. Looking at the percentage of reliably detectable object positions at the Visibility Level of 13.35, it can be observed that the gray card is reliably detected on more than 70% of the object positions. Thus, the critical 50% threshold, which is reached at a Visibility Level of about 8.8, is exceeded by using the Visibility Level determined in the light tunnel. For the design of motor vehicle headlamp light distributions, a Visibility Level of 13.35 must therefore be guaranteed as an absolute minimum requirement in order to produce passable detection conditions (\(p>70\) %) for vehicle drivers in nighttime road traffic in non-urban areas.