# Statistical Analysis of the Crosswalk Lighting Design Correctness
## 2 State of the Art
### Technical Background: Lighting Design and Performance  
**Roadway lighting. ** From the practical point of view, the core action of the roadway lighting design is calculating values of several photometric quantities depending on geometric properties of a situation, light distribution and road reflectance. Those values are computed for all nodes of a rectangular calculation grid covering the road surface and located between two consecutive poles (see Figure 2). Since all required photometric quantities are computed, one can verify whether a considered lighting installation performance fulfills lighting standard requirements. Those photometric quantities include:  
* \(L_{\text{avg}}\)--average luminance: refers to luminous flux reflected by the road surface,
* \(U_{o}\)--overall luminance uniformity: the ratio of minimum and average values of \(L\),
* \(U_{l}\)--the minimum maximum value of \(L\), calculated on the points located at a lane axis,
* \(f_{\mathbf{TI}}\)--threshold increment (disability glare),
* \(R_{\mathbf{EI}}\)--lighting of surroundings. Verification of installation performance is accomplished by examining the values of the above parameters against the reference ones. The lighting standard EN 13201-2:2015 \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Class**} & \multirow{2}{*}{\(L_{avg}\) [**cd/m\({}^{2}\)**] **(min. *)**} & \(\mathbf{U_{o}}\) & \(\mathbf{U_{l}}\) & \(f_{TI}\) [\%] & \(R_{EI}\) \\  & & **(min. *)** & **(min.)** & **(min.)** & **(max. **)** & **(min.)** \\ \hline M1 & 2.00 & 0.40 & 0.7 & 10 & 0.35 \\ M2 & 1.50 & 0.40 & 0.7 & 10 & 0.35 \\ M3 & 1.00 & 0.40 & 0.6 & 15 & 0.30 \\ M4 & 0.75 & 0.40 & 0.6 & 15 & 0.30 \\ M5 & 0.50 & 0.35 & 0.4 & 15 & 0.30 \\ M6 & 0.30 & 0.35 & 0.4 & 20 & 0.30 \\ \hline \end{tabular} \({}^{*}\)min.: minimum allowed value; ** max.: maximum allowed value.  
\end{table} 
Table 1: M-lighting classes (for traffic routes, dry surface condition) according to the CEN 13201-2 standard [2]: \(L_{avg}\)—min., average luminance maintained; \(U_{o}\)—min., overall uniformity; \(U_{l}\)—min. longitudinal uniformity; \(f_{TI}\)—max., disability glare; \(R_{EI}\)—min., lighting of surroundings. Figure 2: Calculation grid [3]: 1—poles; 2—width of relevant area; 3—field of calculation; 5—lamp spacing; \(d\)—the spacing between poles in the transverse direction; \(D\)—the spacing between poles in the longitudinal direction; \(N\)—the number of calculation points in the longitudinal direction. for roadways [2] distinguishes six classes enumerated from M1 (highways, expressways) to M6 (local residential streets). Table 1 presents those requirements. **Pedestrian crossing lighting. ** An inherent element of roadway illumination planning is pedestrian crossing lighting (Figure 1), and as mentioned before, crosswalk illumination is a critical component of public lighting due to the accident risk. There are multiple methods aimed at improving pedestrian safety. Their common goal is to enhance pedestrian visibility. It can be achieved by increasing the contrast, raising a driver's concentration by applying different color temperatures of light in a crosswalk area, setting an \"approaching zone\" (with increased luminous flux intensity) ahead of a crosswalk or setting a different height for dedicated, pedestrian crossing luminaires. Another supplementary method of focusing driver attention is embedding LED road markers alongside a pedestrian crossing. It is worth noting that there is no consensus among experts regarding applying dynamic (adaptive) lighting to crossroads. Blinking or dynamically dimmed lighting may be confusing for a driver (and thus ignored) as similar to the illumination used for road works or as caused by some device failure. The problem of appropriate crosswalk illumination was considered by [16; 17]. For human safety reasons, the lighting must satisfy special qualitative and quantitative requirements, including contrast issues, light color temperature and others (see [18]).