## 3 Experimental Setups and Analysis
Luminous intensity function: In order to improve the primary curved CCR further, the add-on ray tracing simulation tool OptisWork (Optis SAS, La Farlede, France), embedded in SolidWorks mechanical design software, was used to search for suitable variable parameters to get an optimized curved CCR, using \(\mathrm{d_{i}}\) to elevate its performance and \(\mathrm{D_{i}}\) to fit the reference curve for the outlook of curved CCR smoothly. The constraint of each variable parameter is determined by the curvature of the curved CCR surface. The lighting performances, such as intensity distributions, illumination uniformity, and optical efficiencies of curved CCR, can be accomplished to meet targets by using optimization. In the study, the luminous intensity function serves as the object function, and the value \(\mathrm{R_{I}}\) at the upper 0.33\({}^{\circ}\) is targeted to be maximum in the solution searching process. We search for an approximation of the luminous intensity (\(\mathbf{R_{I}}\)) I(\(\varphi\), \(\mathrm{a}\), \(\mathrm{b}\), \(\mathrm{c}\)) as the object function, which is at the polar angle \(\Phi\) in Equation (9), where K is the number of functions. Figure 5:3  
In order to set the target value of the optimization, the simulation experiment with a flat regulated CCR was exercised to find the reflected light power as the reference by a 1000 lumen incident beam. The resulting power was 850 lm and this was used as the target for the subsequent searching of the optimized curved CCR. By running the scheme in optimization steps, manually limited to 600 searching steps to quickly find a better solution, the best results were determined in step 18 (SAE curve) and step  
Figure 5:4 The height difference between the neighboring pins in a double-pin group. 79 (ECE curve). The final intensity sensor values were shown to be 742.51 lm (SAE curve) and 802.1 lm (ECE curve), which were also the output powers reflected by the optimized curved CCR. In the initial optimization process, the mathematical equation for the intensity distribution of reflected light entered into the program is expressed in the measurement value of the intensity sensor. The luminous intensity \(\mathbf{R_{I}}\) is defined by I (\(\varphi\), a, b, c) at the polar angle of \(\varphi\), shown in Equation (9). The target of the optimization process was defined as a value corresponding to the retro-reflective light intensity on the retro-reflector plane. During the optimization, to have the curved CCR meet the requirement of the ECE (0.33\({}^{\circ}\)) and SAE 0.2\({}^{\circ}\)) standard and maximum reflection efficiency, the values of \(\delta\) and \(\mathrm{d_{i}}\) were found through the workflows shown in Figures 13 and 14, respectively. As the optimization is terminated by the program, the optimized curved CCR with the same curve as the commercial one was obtained. After the optimization process, the optimized curved CCR was analyzed for comparison with the commercial reflector by simulations. The distance from the light source to the curved CCR is set as 30.5 m, and the diameter of the laser beam is 25 mm. The curved CCR is kept with its car driving direction at 0\({}^{\circ}\), 10\({}^{\circ}\) (up, down) vertically, and 20\({}^{\circ}\) (left, right) horizontally with the incident light, respectively, to perform the optical tests of SAE and ECE regulations. The resulting intensity distributions by 0\({}^{\circ}\) incident light to the anterior, central, and posterior regions sequentially are shown in Figures 15 and 16. The results showed that the optimized curved CCR could contribute much higher sufficient light intensity than that of the commercial design (no effective retro-reflection at 0.2\({}^{\circ}\) (SAE), 0.33\({}^{\circ}\) (ECE) up), as shown in Figure 15c for regular SAE curved CCR and shown in Figure 16c for regular ECE curved CCR.