## 3 Results
In the context of the present work, reliable object detection is considered to occur at a detection probability of 90 %. Other relevant thresholds are the 50 % threshold (\"critical threshold\") and the 70 % threshold (\"passable detection\"). The evaluation of the object detection probability with the psychometric function is shown in Figure 10 for object position 1 in the light tunnel. For all other object positions, the evaluation is performed in the same way. Figure 8: Luminances \(L\) (**left**) and Weber contrast \(C_{\text{W}}\) (**right**) of the gray card at object position 1 in the light tunnel; due to the linear increase in the luminance difference \(\Delta L\) and the background luminance \(L_{\text{B}}\), the contrast gradient enters saturation. Figure 9: Luminance \(L\) (**left**) and Visibility Level VL (**right**) of the gray card at object position 1 in the light tunnel; both luminance and Visibility Level increase with higher PWM levels. Figure 10 shows that the relationship between the existing Visibility Level and the detection probability is very well represented by the psychometric function (R\({}^{2}=0.994\)). If the detection probability of the gray card at position 1 shown in Figure 10 is considered, it can be observed that from a Visibility Level of 1.505, the detection probability is at least 90 % and is thus called \"reliably detected\". In this way, all further object positions are evaluated, and a spatially resolved distribution of the required Visibility Level is determined, which is shown in Table 3.  
From Table 3, it can be observed that the required Visibility Level ranges from 1.505 to 21.500. The value of 21.500 represents an outlier resulting from the proximity of the object position to the fixation object. Looking at the measurement series at the individual distances, it is striking that the required Visibility Level decreases at the transition from the foveal visual field (offset: 0.00 m) to the peripheral visual field. An exception is the horizontal offset of 4.50 m to the right. Here, the Visibility Level increases again. As stated by the drivers, the potential cause for this is the proximity of the objects to the wall of the light tunnel (see Figure 7 on the left). Thus, the drivers indicate that this proximity to the wall of the light tunnel makes the detection of the objects significantly more difficult. For this reason, the object positions on the far right are not considered further when considering the angle dependence. The angle dependence of the Visibility Level is determined after removing these data points. For this purpose, the eccentricity angles to the respective measurement grid points are determined, and the data for the different distances are summarized. The summarization of the data is made possible by the fact that the distance is already taken  
Figure 10: Relationship between the detection probability \(p\) and the Visibility Level VL of the gray card at object position 1 in the light tunnel; to achieve a detection probability \(p\) of 90 %, a Visibility Level of 1.505 is required. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Offset to Longitudinal** & \multicolumn{4}{c}{**Distance to Vehicle in m**} \\
**Axis of Vehicle in m** & **40** & **60** & **80** & **100** \\ \hline \(-4.50\) & 1.505 & 2.029 & 2.480 & 3.454 \\ \(-2.25\) & 2.384 & 2.173 & 6.380 & 4.804 \\ \(0.00\) & 7.760 & 6.295 & 21.500 & 9.920 \\ \(2.25\) & 3.252 & 5.140 & 4.300 & 6.610 \\ \(4.50\) & 10.955 & 8.220 & 7.450 & 15.030 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Required Visibility Level on the different object positions in the light tunnel. into account in the calculation of the threshold luminance difference \(\Delta\mathrm{L_{th}}\) with the STV model and the object size \(\alpha\) required for this purpose (see Equation (7)). \[\alpha=arctan\left(\frac{D}{d}\right) \tag{7}\]  
Here, \(D\) describes the extension of the object in \(\mathrm{m}\) and \(d\) the distance to the test vehicle in \(\mathrm{m}\).