## 1 Introduction
Studies by [PERSON] [15] and [PERSON] [18] demonstrate that the threshold luminance difference for positive and negative contrast is of the same magnitude but lower for negative contrast than for positive contrast. Figure 1: Contrast polarities; (**left**) The object appears brighter than its background (positive contrast); (**right**) The object appears darker than its background (negative contrast) [8]. Figure 2: Age influence on the threshold luminance difference \(\Delta L_{\text{th}}\) according to [PERSON] and [PERSON] [33]; the observer’s age has a significant influence on the required threshold luminance difference \(\Delta L_{\text{th}}\); especially from an age of 64 years, the age influence increases significantly [33]. These influence parameters were transferred by different researchers and research groups into detection models, in order to allow a statement about the detectability of objects [31; 37; 38; 39]. One of the most used models is the Small Target Visibility (STV) model by [PERSON] (see Equation (2)) [31]. The threshold luminance difference \(\Delta L_{th}\) is calculated according to the following formula. \[\Delta L_{\text{th}}=k\cdot\left(\frac{\sqrt{\Phi}}{\alpha}+\sqrt{L}\right)^{2 }\cdot\frac{a(\alpha,L_{B})+t}{t}\cdot F_{CP}\cdot AF \tag{2}\]  
where  
* \(\Delta L_{\text{th}}\): Threshold luminance difference;
* \(k\): Detection probability factor;
* \(\left(\frac{\sqrt{\Phi}}{\alpha}+\sqrt{L}\right)^{2}\): Luminous flux and luminance function according to [PERSON]'s and [PERSON]'s law;
* \(\alpha\): Plane object size in angular minutes;
* \(a(\alpha,L_{B})\): Blondel-Rey constant;
* \(t\): Observation time in seconds;
* \(F_{\text{CP}}\): Contrast polarity factor;
* \(AF\): Age factor. This threshold luminance difference applies to a certain probability under laboratory conditions. To transfer this to the complexity of a real traffic situation, the Visibility Level VL is used as a multiplier. The Visibility Level is determined as the ratio of the currently prevailing luminance difference between the object and its background and the calculated threshold luminance difference (see Equation (3)). \[VL=\frac{\Delta L}{\Delta L_{\text{th}}} \tag{3}\]  
To determine such a Visibility Level, [PERSON] [18] performed both laboratory and field tests. The studies were conducted on both a closed test site and in real road traffic at night. The results of the studies show that for each increase in the complexity level, for instance by the additional driving task, the locality (highway, country road, city) or the position of the objects, the detection conditions become more difficult. Thus, for the transition from the laboratory test to the static field test, a threshold contrast that is 12.7 times higher is needed in order to detect the objects. This factor is called the field factor and is comparable to the Visibility Level. Furthermore, [PERSON] confirms the dependence of the required thresholds on the object size in the field test, as shown in Figure 3 on the left side. On the right side of Figure 3, on the other hand, the dependence of the required object luminance \(L_{\text{O}}\) on the eccentricity angle \(\Theta\) is shown. To obtain the presented data, the data from the investigations of [PERSON] were mirrored at the eccentricity angle \(0^{\circ}\). Here, it is noticeable that the dependence of the object luminance \(L_{\text{O}}\) on the eccentricity angle \(\Theta\) can be described by a Gaussian function and thus the required object luminance \(L_{\text{O}}\) decreases with the increasing eccentricity angle \(\Theta\)[18]. A similar field study was conducted by [PERSON] [34]. Here, the detection object was realized by a pedestrian, which was positioned at different eccentricity angles of \(\Theta\) next to the roadway. The field study was conducted in two parts with older and younger drivers and a test vehicle with activated high beam headlamps. In the quasi-static test, the driver sat in the driver's seat and the object moved toward the test vehicle.