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Abstract
This paper proposes a passive optical brightening element design, a non-axisymmetric freeform lens (NAFL), arranged and assembled on a traditional traffic sign. NAFL is the first optical design which can effectively solve the traffic problem that direct sunlight affects the driver's inability to look directly at the traffic sign. The NAFL can converge the sunlight behind the traffic sign and diverge forward to 150 meters away. In this way, the NAFL array combinations on the traffic sign can directly rely on sunlight as image information pixels. According to the simulation, the optical efficiency of the NAFL can be as high as 81.5%. Besides, the angular tolerance is also analyzed to evaluate the working hours of the NAFL. Finally, we made the prototype and proved that such passive brightening components could effectively improve the traffic sign's visibility in harsh sunlight.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Smooth traffic can provide drivers with a high degree of road safety and enable people, goods, or information to be smoothly and quickly transferred between the two places, thereby further increasing economic development speed. In order to maintain smooth traffic, avoiding traffic accidents is one of the necessary. In addition to the driver's excellent driving skills, whether the driver can identify traffic signs will significantly affect traffic accidents.
Traffic signs provide clear information and instructions on the directions, locations, or traffic conditions. Much research on traffic signs was widely carried out to enhance pedestrians’ and drivers’ convenience and safety. Such as the improved design of systems that use traffic signs to remind passersby of traffic conditions [1], promote the development of related technologies for drivers and intelligent vehicles to recognize traffic sign information [2–11], as well as the human factor study of the direct relationship between the traffic signs and passersby [12–14]. Nevertheless, the study of the structural improvement of the traffic sign is less so far. As shown in Fig. 1, the same as the reasons that use the optical system of the sunlight or the natural ambient light developed in recent years to provide part of lighting or display, using sunlight or natural ambient light directly is convenient [15–22]. Therefore, in general, the traditional traffic signs rely on the reflection of surrounding ambient light to provide traffic information. For example, for Fig. 1, the surrounding ambient light and the specific additional projection lamp illuminate the traffic signs in daytime and night. Due to the compact size and the high luminous efficacy of LEDs, LEDs effectively provided the use of traffic sign displays and significantly reduced electrical power consumption. However, with increasing awareness of green energy, some lighting or display applications are still gradually replaced by sunlight or natural ambient light.
For increasing the clarity of the traffic signs used in the night, even used in the daytime, with the high technology developments in LED and backlight display [23–39], the additional LED light sources and the backlight modules recently also are applied in novel traffic signs. As shown in Fig. 2(a), the traffic sign’s primary graphical-text information can be presented on the emitting surface of a uniform backlight module, or by a specific arrangement of multiple LEDs, like the pixels in an image, such as the LEDs in Fig. 2(b). As shown in Fig. 3(a), the traffic sign’s information can generally be identified by the illumination of ambient light or LED display in the daytime. However, no matter what kind of traffic sign, since sun backlight often the self-protecting effect of human eyes causes pupils to shrink and the brightness of the image in the eyes to decrease, the traffic sign cannot be seen and further occur hazardous traffic accidents, as shown in Fig. 3(b). This condition is straightforward to occur on the fast road in the east-west direction in the early morning or evening, but it has rarely been solved well so far. Due to the ease of production, a method of digging holes on the traffic sign was proposed to solve this problem [40]. Besides, it directly utilizes the sun backlight behind the traffic sign to provide the information display for drivers. However, the optical elements which lengthen the viewing distance still must be needed to assemble in the holes due to the larger elevation angle of the sun backlight. Therefore, in this study, we propose an optical design of the non-axisymmetric freeform lens (NAFL). In this optical design, an oblique collimating light that represents the sun backlight enters into the NAFL, and the ray paths of the output light of NAFL can be obtained by ray-tracing method. Moreover, the shape of NAFL must be designed such that the intensity distribution of output light meets the requirements that traffic signs can still be recognized by most drivers in the event of sun backlight, as shown in Fig. 4. NAFL array combinations are assembled and treated as the pixels of the graphical-text information on the traffic sign and expected to still be recognized by drivers under strong sun backlight. That is usually when people go to work or go home from office, that is, the time that the traffic is hectic and heavy.
Fig. 3. The traffic signs, (a) are illuminated by surrounding ambient light. (b) are existed between the sun backlight and the driver, and the driver cannot identify the traffic sign due to the intense glare of the sun.
2. Method of optical design
2.1 Design goal developing
To effectively enhance road safety during traffic congestion, NAFLs are expected to be used in the east-west direction highway of Taichung city, Taiwan, at 8 am and 4 pm. At that time, most people are busy at work and school. Hence, the elevation angle of sunlight into a NAFL is set as 25.6°, which is calculated by the average elevation angle on the 15th day of every month and must be considered factor of the front’s shape design surface in NAFL [41]. In addition to the front surface, the back surface design in NAFL must also consider the location of the drivers and traffic signs. Therefore, the distributed region of the light output that emerged from a NAFL must be investigated before design.
As Fig. 5, according to the method of traffic sign assembling in the highway in Taiwan, there are generally two kinds of traffic sign, one is hanging sign, which is shown in Fig. 5(a), hangs the traffic sign in the middle of the road, and the set height is at least 4.9 meters. Besides, another one is the standing sign, which is shown in Fig. 5(b), which assembles the traffic sign at the side of the road, and set height is at least 2.1 meters. Moreover, as the top view in Fig. 6, for general highways in Taiwan, the road’s total width is 14.95 meters. Based on all drivers’ safety requirements, the traffic sign information must be received clearly by drivers 150 meters away from the traffic sign. Therefore, the smallest field of view of the output light from the hanging and the standing traffic signs least should respectively be 2.1° and 5.3°.
Similarly, as the side-views in Fig. 7, the traffic sign's output light must be received by both cars and trucks. For the driver of a car 150 meters away from the traffic sign, the observing height is 1 meter, and the most appropriate elevation angle of the line-of-sight to observe the hanging and the standing traffic signs are respectively 1.87° and 0.8°, similarly, for the driver of a truck, the observing height is 2.4 meters, and the most appropriate elevation angle of the line-of-sight to observe the hanging and the standing traffic signs are respectively 1.33° and almost zero. Thus, to synthesize the above reasons, for most drivers observing the information of traffic signs in 150 meters away, even shorter than 150 meters away, the design goals of NAFL would be set to receive the input sunlight with an elevation angle is 25.6° and transmit through the NAFL. Finally, the output sunlight is expected to be deflected toward the ground with a divergence half-angle at least 5.3°, and lower than the horizontal plane as much as possible, as shown in Fig. 8.
2.2 Optical design of NAFL
As in Fig. 9(a), a designed NAFL composed of a non-axisymmetric front surface, a front tube, a back tube, and a non-axisymmetric back surface. The sunlight behind the traffic sign is expected to be refracted to the driver’s eyes again. For both obtaining more considerable input luminous flux and enough image resolution in long-distance, and matching the existing LED traffic sign structure, the diameters of the front tube of the NAFL, which is set as 16 mm, is larger than that of the back tube, 8.2 mm. Also, the back tube of NAFL, which is provided as a pixel of the information and assemble into the traffic sign board’s hole whose thickness is 3.26 mm, and the spacing between each pixel is required to greater than 20 mm, as shown in Fig. 9(b). Thus, the non-axisymmetric front surface is a left-right symmetrical but up-down asymmetrical surface so that the skewed input sunlight can both be refracted and converged to the back surface and avoid leaking sunlight from the side surface between the front and back tubes.
Fig. 9. The NAFL which includes a non-axisymmetric front surface, a front tube, a back tube, and a non-axisymmetric back surface is (a) illuminated by skewed sunlight, and (b) is assembled on the traffic sign.
As shown in Fig. 10, the front surface of the NAFL using the freeform surface design [43–47] and has to refract and converges the input sunlight to the back surface; therefore, in the design procedure, the front surface is sampled to K small tangential planes. Each of the K parallel rays, which are treated as the input sunlight propagates to the center point ${P_i}$ (i=1,2,3,4,…….K) of the small tangential planes. Then, the K output rays, which are treated as the output sunlight refracted from the front surface are arranged according to the expecting converged directions and mapped to the input sunlight. Hence, the surface normal of the separate tangential plane between the input ray and the output ray can be obtained by the vector form of Snell’s law [48], as below
The ${n_{NAFL}}$ is the refractive index of the NAFL. The ${\bar I _i}$ and ${\bar O _i}$ (i=1,2,3,4,…….K) respective are the vectors of the input rays and the output rays; the ${\hat{N}_i}$ (i=1,2,3,4,…….K) is the unit normal vector of separate tangential plane between the input ray and the output ray. Besides, the tangential vector of separate tangential plane is calculated by the corresponding ${\hat{N}_i}$. Finally, the coordinate of an edge point of the front surface must be determined first. The coordinates of each terminal point of every small tangential plane are sequentially calculated from the edge point according to the separate tangential vector, and we can connect the separate small tangential planes into a complete object which is consisting of multiple small planes. Then the shape of the front surface can be obtained by fitting the object.
The length of the whole NAFL and the back tube are respectively 24 mm and 3.6 mm. The back surface is composed of three single conical surfaces: A, B and C surfaces, are utilized to mitigate the drop of optical transmission efficiency caused by the changes in the elevation angle of sunlight. Their shape can be designed by the sag function [49], as below
where z, r, β and k are the sag, the axial height, the curvature at the vertex and the conic constant of the aspherical surface, respectively. The surfaces of A, B, and C are designed for sunlight with incident elevation angles of 15.6°, 25.6°, and 35.6°, respectively, in order to achieve the purpose of obtaining excellent optical transmission efficiency of sunlight in a direction that changes with time, and ensure the output sunlight can reach as much as we want, that is, a large amount of output sunlight can be refracted below the horizontal plane and cover the entire road width behind the NAFL 150 meters. The curvature and conic constant of the A, B, C surfaces are listed in Table 1. The side view and the 3D view of NAFL are drawn by Rhinoceros 3D drawing software and respectively shown in Fig. 11(a) and Fig. 11(b).
Table 1. The curvature and conic constant of A, B, C surfaces.
2.3 Ray-tracing simulation of NAFL
The parallel rays present the light paths in NAFL with 25.6° elevation angle, which is treated as the oblique sunlight, is simulated by ASAP program. The light paths of the ray-tracing simulation of the NAFL is shown in Fig. 12, the material of NAFL is Polycarbonate (PC), and its refractive index is 1.59. The number of the ray is 20 million. After analyzing the ray paths by ray-tracing method, most incident rays are refracted into the NAFL and converged to the back surface directly, which avoids dissipating the converged light out the back tube of the NAFL. The refracted light is refracted again by the back surface and propagated to the drivers on the road. Only a few rays are directly reflected to air by the front surface of the NAFL owing to Fresnel loss effect, the energy loss is about 18% of the incident sunlight energy. The three-dimensional view of the ray-tracing is shown in Fig. 12(c), and the intensity distribution of the output light of the NAFL along yz plane and xz plane are analyzed. In Fig. 13, the intensity distribution results are shown by the black line and the red line. The black line illustrates the intensity distribution is only asymmetric along the single plane, that is yz plane. Moreover, the peak value of the normalized intensity appears at -25°, and the FWHM value in divergent angle (Full Width at Half Magnitude) along yz plane (FWHMyz) and xz plane (FWHMxz) are respectively 30° and 70°. The asymmetric intensity distribution along yz plane represents that most of the output light of NAFL is incident on the ground. The optical transmission efficiency, which is defined as the ratio of the output light power emerged from the back surface to the incident sunlight power, is 81.5%.
The light path simulations of the NAFL are projected by 15.6° and 35.6° elevation angles sunlight are shown in Fig. 14(a) and 14(b). When the elevation angle of the sunlight is smaller than 25.6°, the converging light from the front surface of the NAFL is moved upward, the elevation angle is more extensive than 25.6°, the converging light is moved downward so that the surface A and C of the NAFL can also refract most of the output light to the ground. Hence, the angular tolerance that the sunlight is incident on the NAFL with different direction can be extended by back surface’s design. The related angular tolerance analysis is illustrated below.
Fig. 14. Ray-tracing simulation of NAFL with 15.6° and 35.6° elevation angles sunlight, (a) elevation angle is 15.6°. (b) elevation angle is 35.6°.
3. Tolerance analysis of NAFL
3.1 Angular tolerance analysis of NAFL of different direction sunlight
Owing to varying direction of sunlight with time changing, so that the ability of light collection of NAFL will decrease. Although the NAFL is mainly designed to use in the commuting time, it is expected to extend the available time of NAFL. To comprehend the region of the available time, the parameters of the output light of NAFL irradiated by different direction sunlight must be analyzed. As in Fig. 15(a), the direction of sunlight is respectively changed along yz plane, moreover, it changed along the xz plane at 25.6° elevation angle, as shown in Fig. 15(b). With the changed direction of sunlight, the power of output light of NAFL is varied. The relative output light power and the optical transmission efficiency of the NAFL irradiated by the sunlight with the specific incident angle are analyzed to determine the reason for the varying output light power. The relative output light power is defined as the ratio of the output light power to the maximum output light power. The analyzing results of the relative output light power and the optical transmission efficiency while the sunlight is respectively turned around the y axis at 25.6° elevation angle, and turned along yz plane, are shown in Fig. 16(a) and Fig. 16(b). According to the analyzing results of the angular tolerance in Fig. 16(a), with changing azimuth angle (φ) at 25.6° elevation angle, the relative output light power and the optical transmission efficiency are both slowly decreasing while the azimuth angle is smaller than 15°, and falling to zero when the azimuth angle is larger 15°. Only a small fluctuation occurs between 50° and 90°. The half value of the relative output light power occurs at 20.5°. Moreover, in Fig. 16(b), with the sunlight turning along yz plane, the most robust output light power and the optical transmission efficiency of the NAFL appear at the elevation angle (θ) are both 14°, and the optical transmission efficiency is 82.9%. In addition, the relative output light power at 25.6°, 15.6°, and the 35.6° are respectively 0.7, 0.95, and 0.47, the optical transmission efficiency at 25.6°, 15.6°, and the 35.6° are respectively 81.5%, 82.3%, and 79.4%. The half values of the relative output light power appear at 34° and the -3.5°. Hence, the full width of the half magnitude (FWHM) value is 37.5°. For using NAFL in Taichung in one day, the time region during the range of the FWHM roughly corresponds to 3 hours (face to east during about 6:00 am to 9:00 am, and face to west from about 3:30 pm to 6:30 pm). As the elevation angle is between 14° and 41°, the light transmission efficiency slowly decreases, which obviously verifies the effectiveness of the extension of the angular tolerance caused by the multi-segment design of back surface.
Fig. 15. The NAFL is irradiated by the sunlight which is turned (a) around the y axis at 25.6° elevation angle; (b) along the yz plane.
Fig. 16. The relative output light power and the optical transmission efficiency of the NAFL irradiated by the sunlight which is turned along (a) the yz plane; (b) around the y axis at 25.6° elevation angle.
3.2 Rotational tolerance analysis of assembling NAFL
The angular misalignment that the NAFL assembled in the traffic sign may occur in rotating around the optical axis and further causes the optical performance’s alteration. Hence, we also analyze the angular tolerance of NAFL in rotating around the optical axis. As in Fig. 17(a), the relative output light power and the optical transmission efficiency of NAFL are also analyzed with varying rotating angles around the z-axis while the elevation angle of sunlight is 25.6°. The analyzing results are shown in Fig. 17(b).
Fig. 17. The rotational tolerance analysis of assembling NAFL that the elevation angle of sunlight is 25.6° on the yz plane, (a) NAFL is assembled on the traffic sign board and rotated around the z axis, the corresponding relative output light power and optical transmission efficiency with varying rotating angle.
4. Intensity measuring of the NAFL and practical applications
The prototype of the NAFL is fabricated by plastic injection molding technology, is shown in Fig. 18(a). In real applications, we fabricate many NAFLs and insert them into pre-designed sign holes, which is shown as Fig. 18(b). To comprehend the luminous intensity of the NAFL with the moving sunlight during the day, a NAFL is inserted and assembled at a blackboard that faces to the sun. Besides, when using NAFL in the morning of the day (between 6 am and 12 pm), the luminous intensity of the measuring angle which rotates down 1.87° from the optical axis along the tangent plane, that is, the line-of-sight direction between the car drivers and the NAFL of the traffic sign at 150 meters, is measured by a luminance meter and the projected area of the output surface of the NAFL. As Table 2, the luminous intensity values at Taichung city, Taiwan on June 15, 2020 are also simulated. In this simulation, daylight with a solar irradiance of 1000 watts/m2 is used as the simulated incident sunlight. According to the simulation results of the luminous intensity, between 6 am and 12 pm, the luminous intensity achieves the highest value, 17.2 cd, at 6 am (elevation angle is 9.5°), and gradually drops below 1 cd when the time exceeds 9 am (elevation angle is 49.2°). Therefore, the NAFL can provide an average luminous intensity of about 6.5 cd to car drivers on sunny days. Moreover, In Fig. 19, the simulation results of luminous intensity roughly match the corresponding experimental results. Like Fig. 13, we also have provided the simulation results of the output light intensity distribution at different times, as shown in Fig. 20. The simulation luminous intensity could be determined by the output sunlight power of Fig. 16(b) and the normalized intensity of Fig. 20.
Fig. 18. Fabrication of the sign with the NAFLs, (a) prototype of NAFL, (b) many NAFLs are assembled on the sign.
Fig. 19. The comparison of the simulation results and the experimental results of NAFL’s luminous light at different time.
Table 2. The luminous intensity of a NAFL at Taichung city, Taiwan on June 15, 2020.
As time goes by, the maximum simulation luminous intensity at 6 am, depends on the factors that the output sunlight power in Fig. 16(b) is significantly higher, and the normalized light intensity in Fig. 20 is slightly lower. When it’s 7 am, although the normalized intensity is slightly increased, excessive reduction of output sunlight power causes the decreasing of the simulation luminous intensity. When the time exceeds 7 am, the sharp decline of output sunlight power in Fig. 16(b) dominates the downward trend of simulation luminous intensity. Finally, the simulation luminous intensity is reduced to zero. In Table 2, slight differences between the simulation result and the experimental result might be caused by the manufacturing error of NAFL, the experimental setup error or the environmental factors, etc., such as the stray light in actual environment. A general sign with the multiple NAFLs is tested at 2 and 150 meters, are shown in Fig. 21(a) and Fig. 21(b). Whether 2 meters or 150 meters, the information can be recognized by the NAFLs even we face the intense sun backlight. Currently, the speed limit sign with multiple NAFLs had been tried and tested on the public roads and the output terminal of a tunnel in Taiwan, as shown in Fig. 22(a) and Fig. 22(b), the traffic sign with NAFLs can provide the drivers’ safety and the convenience of the early recognition of the information but no use any electric power, although under the trouble of facing to strong sun backlight.
Fig. 22. The speed limit sign with multiple NAFLs is used on (a) the general road, (b) the output terminal of a tunnel.
5. Conclusion
In this paper, a NAFL composed of a front surface, a front tube, a back tube, and a back surface is designed to transport the oblique incident sunlight with 25.6° elevation angle to the drivers 150 meters away. To solve the visual disability of the traffic signs induced by the sun backlight, NAFL array combinations are assembled on a traffic sign and treated as the pixels of the graphical-text information in the east-west direction highway of Taichung city, Taiwan at 8 am and 4 pm. To evaluate the performance of NAFL, the light paths and the output light intensity distribution is simulated by ray-tracing method and ASAP program. According to the simulation results, the NAFL’s optical transmission efficiency is 81.5%. An asymmetric intensity distribution only exists along the yz plane and contains a peak value at -25°. Besides, the FWHMyz value and the FWHMxz value are respectively 30° and 70°.
The direction of sunlight projecting to the NAFL is analyzed to comprehend the available time extension of the traffic sign with NAFLs. Angular tolerance of sunlight’s incident angle is also determined by simulations. According to the simulation results, at 25.6° elevation angle, the relative output light power and the optical transmission efficiency both slowly decrease within 15° azimuth angle, and then sharply fall to zero beyond 15° azimuth angle except for the small fluctuation between 50° and 90°, the half value of the relative output light power appears at 20.5° azimuth angle. Angular tolerance of the sunlight’s elevation angle is also assessed by simulation results. The peak value of the relative output light power and the optical transmission efficiency both appear at 14° elevation angle, and the corresponding optical transmission efficiency is 82.9%. Besides, the FWHM value of the relative output light power is 37.5° and roughly suitable for applying in 3 hours of one day, in Taichung city. (face to east during about 6:00 am to 9:00 am, and face to west from about 3:30 pm to 6:30 pm). That verifies the effectiveness of the using time extension of the NAFL by utilizing the multi-segment surface design of the back surface.
The prototype of the NAFL is realized and installed at 150 meters, and tested in the morning of one day. According to the experimental results, the NAFL can provide an average luminous intensity of about 8.3 cd to car’s drivers at 150 meters on sunny days. Besides, a general sign with multiple NAFLs can be recognized at 2 meters and 150 meters away even we face the intense sun backlight. The speed limit sign with multiple NAFLs also can be used well on the ordinary roads and the tunnels output terminal in Taiwan during the day without any electrical power and circuits. Based on the performances and the advantages of the NAFL, we believe that the design of NAFL will help both the application of green energy and the improvement of traffic safety.
Funding
Ministry of Science and Technology, Taiwan (MOST 109-2221-E-035-078).
Acknowledgements
In this article, the authors would like to thank Mr. Lien-Hsiung Hu for his guidance on knowledge and regulations related to traffic signs. Moreover, this work was supported by the Ministry of Science and Technology, Taiwan, Project MOST 109-2221-E-035-078.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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