## 2 Materials and Methods  
The aim of the detection investigations in non-urban areas is to determine the minimum Visibility Level required for reliable object detection (\(p\geq 90\,\%\)) as a function of the object position. For this purpose, not only the distance dependence but also the angle dependence of object detection in nighttime road traffic is investigated. Furthermore, the general influence of environmental conditions on the Visibility Level required for detection is considered. The study for object detection in non-urban areas was divided into two parts and conducted statically. Thus, on the one hand, the study took place under highly controlled conditions in a light tunnel and, on the other hand, the study was conducted on a closed test site. This separation was performed to determine the influence of distance and angle on object detection under controlled conditions. Conducting the study on the closed test site served the purpose of the more realistic replication of the traffic situation on rural roads. A total of eleven drivers (age range: 18 to 59 years) participated in the study in the light tunnel, and 15 drivers (age range: 18 to 34 years) participated in the study on the closed test site. All drivers were in possession of a valid driving license at the time of the study and wore their visual aids when required. Thus, a visual acuity of at least 0.7 required for driving a motor vehicle was assumed and no additional visual acuity testing was performed. To ensure that the performed studies represent worst-case scenarios, 20 cm \(\times\) 20 cm large gray cards with a reflectance of about 4 % were used as detection objects following previous studies [31; 40]. A low reflectance was chosen because, according to studies by [PERSON] and [PERSON] [41] or [PERSON] [42], the winter clothing of pedestrians, in particular, have low reflectance values of less than 10 %. For the variation of the distance and the angle between the detection object and the observer, the gray card was set up on fixed positions of measuring grids. The measuring grids were thereby adapted to the available total dimensions of the respective experimental area. Thus, in the light tunnel, there was a usable area of 120 m \(\times\) 12 m available, while a width of about 20 m was available on a roadway with a length of more than 1 km on the closed test site. Based on these limitations, the measurement grids, which can be observed in Figure 5, were designed for the partial studies. The distances to the object rows of the measurement grids were 40 m, 60 m, 80 m, and 100 m for both studies. Due to the limitation of the light tunnel, as shown in Figure 5 on the left, a 4 \(\times\) 5 measurement grid was feasible, with which a total of 20 object positions were  
Figure 4: Required light intensity \(I\) for a detection object at a distance of about 90 m as a function of the eccentricity angle \(\Theta\) according to the field investigations of [PERSON] [34]; with increasing eccentricity angle, the required light intensity decreases, and the coefficient of determination of the correlation is R\({}^{2}\) = 0.96 [34]. investigated during the detection study. At the closed test site, a total of 24 object positions were considered in a \(4\times 6\) measurement grid (see Figure 5 on the right). Tables 1 and 2 show the exact positions of the gray cards in front of the test vehicle in the respective measuring grids. Here, negative horizontal distances represent an offset to the left with respect to the longitudinal axis of the vehicle and positive horizontal distances represent an offset to the right with respect to the longitudinal axis of the vehicle. Table 1 shows that in the light tunnel, a width of \(\pm 4.50\) m was spanned by the measuring grid, where the horizontal distance between two grid points is \(2.25\) m. Furthermore, in each object row, there was one object on the longitudinal axis of the vehicle (offset: \(0.00\) m). Thus, at a constant angle, only the distance between the \(40\) m and \(100\) m was varied here.