# Enhancement of ECE SuperPin Curved Reflex Reflector by the Use of Double Pins with Corner Cubes
## 4 Optics Design and Verification  
In order to remedy the ineffective posterior working area of the commercial design, two groups of pins were connected together as the double pins group to compose the CCCR, as shown in Figure 13. Fifteen pieces of double-pin groups were arranged in parallel to the car driving direction to compose the primary CCCR; one pin group touches the curve reference surface and the other one is free to translate in the car driving direction. The height difference between the neighboring pins in a group of double pins and the double pin group are named \(\mathrm{d_{i}}\) and \(\mathrm{D_{i}}\), respectively. The object function \(f\) defined by the Equation (7) was determined in the optimization process. The optimization process encompassed three fragments. Object function: The equation that describes the value of the object function of the optimization program established by genetic algorithms is as follows:  
\[f(i,j)=\sum_{i,j=1}^{n}\sqrt{w_{i}(m_{i}-t_{i})^{2}+w_{j}\big{(}m_{j}-t_{j} \big{)}^{2}} \tag{7}\]  
where \(w_{i}\) is the weight parameter of the object function, \(m_{j}\) is the value of the measured target, which is determined by the intensity sensor through each optimal loop when running the program, and \(t_{j}\) is the optimization target defined with a value corresponding to the retroreflective light intensity on the retroreflector plane. Luminous intensity function: In order to improve the primary CCCR further, the add-on ray tracing simulation tool OptisWork (Optis SAS, La Farlede, France), embedded in SolidWorks mechanical design software, was used to search suitable variable parameters to get an optimized CCCR, using  
Figure 12: The CCCR #3 reflecting surface in the posterior region is hit by a simulated laser beam (**left**) and the resulting retroreflected light intensity distributions (**right**). Figure 13: The height difference between the neighboring pins in a double-pin group. to elevate its performance and \(\mathrm{D_{i}}\) to fit the reference curve for the outlook of CCCR smoothly. The constraint of each variable parameter is determined by the curvature of the CCCR surface. The lighting performances, such as intensity distributions, illumination uniformity and optical efficiencies of CCCR, 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 (\(\mathrm{R_{I}}\)) I(\(\phi\),a,b,c) as object function, which is at the polar angle \(\Phi\) in the form:  
\[\mathrm{I(\phi,x,y,z)}\ =\ \mathrm{I_{max}}\sum_{k=1}^{k}x_{k}\mathrm{cos}^{z_{ k}}\left(\phi-\mathrm{y_{k}}\right) \tag{8}\]  
where K is the number of functions to sum and \(\mathrm{x_{k}}\), \(\mathrm{y_{k}}\), \(\mathrm{z_{k}}\) are the function coefficients that we expect. For brevity, coefficients are written as vectors x = (x\({}_{1}\), x\({}_{2}\),...,x\({}_{k}\)), y = (y\({}_{1}\),y\({}_{2}\),...,y\({}_{k}\)), z = (z\({}_{1}\),z\({}_{2}\),...,z\({}_{k}\)). The interval range of the coefficients is: a = [0,0.81], b = [-1,1], c = [0,100]. Discrete optimization algorithms will work on the finite subsets where the possible values will be: x\({}^{*}\)\(\epsilon\) {0, 0.001,0.002,...0.81}, \(\mathrm{y^{*}}\)\(\epsilon\) {1, 0.9,0.8,0.7,..., -1}, \(\mathrm{z^{*}}\)\(\epsilon\){0, 1, 2,...,100}. The components in the OptisWork optimization software have been configured to incorporate three elements: the light source, intensity sensor and CCCR. The interspace between the CCCR and the surface source had been fixed as stated by ECE standards as the interval of the intensity sensor. For the rapid finishing of the optimization, \(\mathrm{D_{i}}\) is initially set to be constant and each double-pin group was assigned a value of _di_ as a variable.