## 3 Results
The result of this evaluation is shown in Figure 11. To describe the correlation between the eccentricity angle \(\Theta\) and the required Visibility Level, a Gaussian function with two terms after Equation (8) is used due to the data set. \[f(x)=a_{1}\cdot exp\bigg{(}-\left(\frac{x-b_{1}}{c_{1}}\right)^{2}\bigg{)}+a_{ 2}\cdot exp\bigg{(}-\left(\frac{x-b_{2}}{c_{2}}\right)^{2}\bigg{)} \tag{8}\]  
Here, \(x\) describes the independent variable and \(f(x)\) the angle-dependent Visibility Level. \(a_{1}\) and \(a_{2}\) are the maximum values of the respective Gaussian functions. Via \(b_{1}\) and \(b_{2}\), the horizontal displacement of the Gaussian functions related to the eccentricity angle of \(0^{\circ}\) is described. \(c_{1}\) and \(c_{2}\) define the width of the respective Gaussian functions. The evaluation of the data with this equation shows that there is a Gaussian correlation between the eccentricity angle \(\Theta\) and the Visibility Level, which is required for reliable object detection. Thus, the findings from previous studies by [PERSON] [18] and [PERSON] [34] are confirmed by the study conducted in the present work. The angle dependence of the Visibility Level for reliable object detection shown in Figure 11 results from the distribution of the receptors (cones and rods) on the retina [44; 45; 46; 47]. Due to the fact that the examinations were performed in the mesopic range typical for nighttime road traffic, the rods are activated in addition to the cones by the adaptation time of \(15\,\mathrm{min}\). Since the rods, which are more light-sensitive than the foveally concentrated cones, are concentrated in the peripheral area of the retina, the brightness sensitivity of mesopic vision is higher in the peripheral area and the contrast perception is improved compared to the foveal vision [44; 45; 46; 47]. The Gaussian relationship between the eccentricity angle \(\Theta\) and the required Visibility Level shown in Figure 11 shows that for the design of optimized luminous intensity distributions, the foveal area represents the critical area (\"worst-case\"). Thus, the luminous intensity must be determined on the basis of the required Visibility Level for the foveal area and then adopted for the peripheral area. In order to determine the required Visibility Level over the different object positions and thus create a common basis for the design of the headlamp light distributions, the relationship between the proportion of detected object positions and the Visibility Level is  
Figure 11: Angular dependence of the Visibility Level VL; as the eccentricity angle \(\Theta\) increases, the required Visibility Level for reliable object detection decreases. considered. For this consideration, the object positions are included again at an offset of 4.50 m, and thus all 20 object positions in the light tunnel are analyzed. The detected object positions are evaluated using the calculated Visibility Levels in Table 3. Thus, the proportion of detected object positions is determined by summing, at the respective Visibility Level, the number of object positions at which the gray card is detected with a probability \(p\) of at least 90 %. While at a Visibility Level of 1.505, only the gray card is detected on the object position 1; at a Visibility Level of 5.140, there are already 10 object positions on which the gray card is detected with a probability of 90 %. In order to detect the gray card on all object positions considered, a Visibility Level of 21.500 is necessary. This procedure yields the Visibility Level as an independent variable and the proportion of object positions as a dependent variable. To test these two variables for correlation, again, the simplified psychometric function of [PERSON] et al. [43] is used (Equation (5)).