## 2 Materials and Methods
### Diffuse Luminance Coefficient Qd and Surface Reflectance Coefficient RL  
EN 1436 [39] defines Qd as the ratio of the luminance of a surface area under diffuse illumination in proportion to the illuminance at the surface plane. Qd is measured using the spectral distribution of illumination according to a standard illuminator representing daylight and an observation angle of 2.29\({}^{\circ}\) representing a geometry (observation distance) of 30 m. A representation of the measurement of Qd is represented by the diagram below (Figure 2).  
Surface reflection is strong in situations corresponding to driving against the sun. The usual bounce is strong in situations corresponding to riding with the sun back. Suitable light for a standard road configuration when confronted with dry and wet surface conditions is assessed by optimising the lighting distribution function [40]. The degree of reflectivity of a road surface traditionally depends on the averaged luminance coefficient Qo [12] and the mirrored reflectivity S1 [41]. The average luminance expressed by the luminance factor Qo, although still used, is a parameter that is difficult to measure in the small space of a portable instrument. Therefore, from the 1990s onwards, the Qd factor was introduced to characterise the reflectivity of road markings in daylight or under road lighting. Portable units are available and are used widely for road markings and can also be applied to road surfaces. However, no portable instrument determines the precise mirroring coefficient. The luminance factor Qd, used in this study, takes into account the mirror effect, but to a lesser extent than Qo. Therefore, the Qd parameter can be regarded as a reasonable approximation of the Qo value for determining the illuminance required for road lighting design. The Qd factor is also relevant when daylighting is poor (e.g., twilight) [40].  
The standardised luminance coefficient Qd for the pavement, associated with the r-table, can be determined using laboratory methods from a cut sample of the pavement under field conditions using a reflectometer or by modern digital image analysis techniques [42]. It is worth mentioning that the maximum luminance that can be obtained for a given area when the surroundings have a constant luminance L is 318 mcd\(\cdot\)m\({}^{-2}\cdot\)k\({}^{-1}\). In contrast, a value of approximately Qd = 52 mcd\(\cdot\)m\({}^{-2}\cdot\)lx\({}^{-1}\) is attributed to \"black\" pavements [41]. This type of luminance factor determines daytime visibility.  
Another measure of luminance is the surface reflectance RL (mcd\(\cdot\)m\({}^{-2}\cdot\)lx\({}^{-1}\)). It is defined as the quotient of the luminance L of the marking surface in the direction of observation by the illuminance E in a plane perpendicular to the direction of incident light and to the area of that reflective surface. The definition of RL is very similar to that of the luminance ratio Qd and has the same unit. Typically, the surface reflectance coefficient RL determines the reflectivity of pavement or horizontal markings illuminated by the light of vehicle lamps. It is also referred to as night visibility. It is important in the absence of road lighting. A diagram of its designation is shown in Figure 3.  
Figure 2: Luminance coefficient in diffused light Qd.  
Road surfaces generally have RL values in the range of 10 to 30 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\). In comparison, surfaces intended for road marking (containing glass spheres) can usually achieve at least RL = 150 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\).