# Influence of Headlight Level on Object Detection in Urban Traffic at Night
## 1 Introduction
The threshold luminance difference \(\Delta L_{th}\) is calculated according to the following formula:  
\[\Delta L_{th}=k\cdot\left(\frac{\sqrt{\Phi}}{\alpha}+\sqrt{L}\right)^{2}\cdot \frac{a(\alpha,L_{B})+t}{t}\cdot F_{CP}\cdot AF \tag{1}\]  
where  
* \(\Delta L_{th}\): 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 laws
* \(\alpha\): Object size in angular minutes
* \(a(\alpha,L_{B})\): Blondel-Rey constant
* \(t\): Observation time in seconds
* \(F_{CP}\): 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 VL is determined as the ratio of the currently prevailing luminance difference between the object and its background and the calculated threshold luminance difference. In the European area, the European standard EN 13201 is used for the planning of street lighting systems, and defines the adaptation level in individual streets by specifying street lighting classes (M1 to M6), roadway luminance levels, and illuminance levels [39; 40; 41; 42; 43]. The design of motor vehicle headlights and their light distributions are regulated by international standards. It should be noted that the design of motor vehicle headlights is independent of the ambient lighting conditions. This means that when designing a low beam headlight, no distinction is made between driving on an unlit country road or highway or on an urban street illuminated by street lighting. Similarly, the design of street lighting systems does not consider the additional light provided by automotive headlights, highlighting the problem of lack of communication between automotive lighting technology and street lighting technology [39; 40; 41; 42; 43; 44; 45]. Especially in urban areas, the interaction of different street lighting systems and different vehicle headlight distributions creates a wide variety of lighting situations that influence detection behavior, thereby directly affecting the safety of urban road traffic at night [46; 47; 48; 49; 50]. In illuminated streets, there is a transition from negative contrast to positive contrast, as the detection object appears darker than its background due to the luminous intensity of the street lighting coming from above. This negative contrast disappears and changes into a positive contrast due to the frontal light of the vehicle headlights. The effect of this transition on detection conditions has been investigated in various studies [13; 25; 35; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61]. [PERSON] et al. [51; 52] performed a study on the interaction of street lighting and automotive lighting regarding the visibility of flat detection targets. For this purpose, they positioned a flat target at a distance of 40 m in front of the vehicle on an illuminated road and determined the Visibility Level for the scenarios street lighting alone, automotive lighting alone and combination of street and automotive lighting. The results show that street lighting alone provides sufficient visibility and the addition of automotive lighting does not improve visibility. Thus, it can be concluded that street lights or low beams used alone provide better visibility than when they are used together [51]. In another study, [PERSON] et al. found a correlation between the calculated Visibility Level and the subjects' assessment of object detectability. This showed that detection objects on the roadway can be detected at a Visibility Level of 7 or higher [52]. [PERSON] showed that the influence of vehicle headlights depends on the illumination level of the stationary roadway lighting by determining the visibility of objects at the right edge of an illuminated roadway at 60 and 120 feet in front of the test vehicle.