## 4 Application  
We measured feature points of three road lighting environments in a block in Shenzhen, China, in Figure 12 and reconstructed the illuminance distributions using our proposed approach in Figure 13. The illuminances in the transverse directions of each road are reconstructed with linear functions and longitudinal directions with sine functions. Luminaires may sometimes be missing or not in operation in some parts, and the double-/staggered-type distributions may be regarded as single-type in such situations. The accuracy of reconstruction work is therefore robust when applied to streets with missing luminaires. The average illuminances for the three roads are 8.9, 10.0, and 14.3 lx, respectively. For the three roads, the same type of luminaire is used. The spectral power distribution of the luminaires, namely typical LEDs, is shown in Figure 14.  
Figure 12: Road lighting measurements. (**a**) Three roads, Road 1, 165 m \(\times\) 16 m, Road 2, 100 m \(\times\) 16 m, and Road 3, 180 m \(\times\) 12 m, are measured (**b**) Luminaire distributions are as follows: for Road 1, 10 luminaires, for Road 2, 7 luminaires, and, for Road 3, 9 luminaires. Figure 13: Illuminance reconstructions of three roads using linear function in the transverse direction and sine function in the longitudinal direction. To study the mesopic luminance performance, the illuminance should be transformed to photopic luminance using a rule-of-thumb formula [40] in Equation (3), where q\({}_{0}\) is the surface luminance coefficient [41] equal to 0.0700 sr\({}^{-1}\) for a standard road. S/P ratio [42], the quotient of luminous efficacy in isotopic vision and photopic vision, is necessary information in calculation of mesopic luminance. The corresponding S/P ratio of the LED luminaires is 1.33. In the calculation of mesopic luminance processes, an adaptation field [42] should be applied. However, for a long road, it is difficult to define such an adaptation field. Therefore, we transform the photopic adaptation luminance to mesopic luminance [43] point to point. \[\mathrm{L=q_{0}E.} \tag{3}\]  
For the calculation of equivalent melanopic lux [31], the corneal illuminance or vertical illuminance is required. For commercial roads, the corresponding illuminance ranges are 10-20 lx horizontally and 2-4 lx vertically at a 1.5 m height [1]. The vertical illuminance is about 0.2 times the horizontal illuminance. Some standards [44] recommend lighting classes for pedestrians and pedal cyclists to have average horizontal-vertical illuminance values as follows: 15-5.0 lx for the P1 class, 10-3.0 lx for the P2 class, 7.5-2.5 lx for the P3 class, 5.0-1.5 lx for the P4 class, 3.0-1.0 lx for the P5 class, and 2.0-0.6 lx for the P6 class, respectively. The vertical illuminances are about 0.2-0.33 times the horizontal illuminance. There is no research work studying the relationship between the corneal illuminance and horizontal illuminance, and it is impossible to obtain big data of vertical illuminances with the present technology. Based on the relation of horizontal illuminance and vertical illuminance recommended in standards, we assumed a linear relation between them as shown in Equation (4), where E\({}_{\mathrm{c}}\) is the corneal illuminance, and \(\alpha\) is the coefficient within 0-1.0. In reference to the relation for commercial roads [1], we set the coefficient \(\alpha\) as 0.2 in this work. This result can be refined if new research results on horizontal-vertical illuminance are given. \[\mathrm{E_{c}=\alpha E.} \tag{4}\]  
Based on the reconstructed illuminance, the mesopic luminance and equivalent melanopic lux are shown in Figure 15. According to Chinese road lighting standards [28], the three roads are classed as secondary roads, and luminance should reach 1.0 cd/m\({}^{2}\). The average mesopic luminance of Road 3 reaches the standard. For the melanopic illuminance, it is better to be small for nighttime applications.