## 1 Introduction  
A reflex reflector is an optical device that allows light to be reflected in a direction that is parallel to that of the source [1; 2; 3]. The corner cube array is the typically used structure and such an array can be built up through pin grouping to generate the expected retro-reflected light [4; 5; 6]. Reflex reflectors on cars or signage can increase visibility in the dark for safety [7; 8], so they have been applied extensively in vehicle applications [9]. Due to their high tolerance to the direction of incident waves [10; 11; 12] retroreflectors have been used extensively in many applications instead of plane mirrors [13]. For instance, regular reflex reflectors [14; 15; 16], as shown in Figure 1a, can diverge the reflected energy into multiple light beams with equal emitting angle intervals [17; 18; 19], and these are currently the most commonly used retro-reflecting devices for vehicles [20; 21]. In contrast to regular reflex reflectors, SuperPin reflex reflectors not only reflect light beams but also concentrate them to amplify the light intensity of signals for observers, as shown in Figure 1b [22]. Owing to the highly effective retro-reflection ability, SuperPin retro-reflectors have been replacing regular retroreflectors in vehicle application markets [17; 21; 23]. According to regulations of the US Society of Automotive Engineers (SAE) and EU Economic Commission for Europe (ECE), reflex reflectors for vehicles need to return light to an observer located at 0.2 degrees (SAE regulations) and 0.33 degrees (ECE regulations) above the light source [23], respectively. Therefore, corner cube arrays composed of pins need to be designed and produced with different specification for the requirements of ECE and SAE reflex reflectors, respectively. In this paper, a new reflex reflector structure called SuperPin Plus is proposed for fitting both the ECE and SAE regulations, shown in Figure 1c. SuperPin Plus's principle is based on the structure of SuperPin [24], which was developed by the difference in the value of dihedral angle. The reflex reflector can switch its function from ECE to SAE or SAE to ECE just by rotating pins group 45\({}^{\circ}\) in structure, so one type of pin is enough to handle the production of ECE and SAE reflex reflectors. Flat SuperPin Plus reflex reflectors and curved SuperPin Plus reflex reflectors with the new corner cube structure are proposed and demonstrated to meet the ECE/SAE dual function requirements through experiments. By using genetic algorithms for optimization, we use the angles and the positions of the pins serving as the building elements of corner cube reflectors as the parameters to enhance the performance of the SuperPin Plus curved reflex reflector. Compared with conventional regular retro-reflectors, it is found that not only can 41% higher retro-reflection efficiency be achieved with the ECE SuperPin Plus flat reflex reflector, but the SuperPin Plus can also act as a SAE reflex reflector. It is shown that a 32% larger working area can be achieved if double pin groups are used to construct corner cubes instead of the single pin arrangement in a curved SuperPin Plus reflex reflector. Figure 1: _Cont._  
According to the standards of SAE and ECE, the coefficient of luminous intensity \(\mathbf{R_{I}}\) should be higher than the threshold values within the 20\({}^{\circ}\) angle of light incidence [23; 24; 25]. The vehicle signage performance \(\mathbf{R_{I}}\) is evaluated by the ratio of the strength of the reflected light \(\mathbf{\Phi_{RI}}\) (retro-reflected light intensity) to the amount of light that falls on the retro-reflector \(\mathbf{\Phi_{ILI}}\) (incident light illuminance), as shown in Figure 1. The minimum coefficients of luminous intensity \(\mathbf{R_{I}}\) requirement for EU ECE or US SAE standards are shown in Table 1. \(\mathbf{R_{A}}\) is the measure of retro-reflection efficiency, defined as the ratio of the flux of incident light \(\mathbf{\Phi_{1}}\) to the total flux of the reflected cone \(\mathbf{\Phi_{2}}\)[23; 18].