Optical Design of an LED Motorcycle Headlamp with Compound Reflectors and a Toric Lens

Home , Nonimaging optics, Parabolic reflector

E102 Vol. 54, No. 28 / October 1 2015 / Applied Optics Research Article

Optical design of an LED motorcycle headlamp with compound reflectors and a toric lens

1 2, 1 1 WEN-SHING SUN, CHUEN-LIN TIEN, *WEI-CHEN LO, AND PU-YI CHU 1Department of Optics and Photonics, National Central University, Chung-Li 32001, Taiwan 2Department of Electrical Engineering, Feng Chia University, Taichung 40724, Taiwan *Corresponding author: [email protected]

Received 31 March 2015; revised 16 July 2015; accepted 16 July 2015; posted 28 July 2015 (Doc. ID 236954); published 21 August 2015

An optical design for a new white LED motorcycle headlamp is presented. The motorcycle headlamp designed in this study comprises a white LED module, an elliptical reflector, a parabolic reflector, and a toric lens. The light emitted from the white LED module is located at the first focal point of the elliptical reflector and focuses on the second focal point. The second focal point of the elliptical reflector and the focal point of the parabolic reflector are confocal. We use nonsequential rays to improve the optical efficiency of the compound reflectors. The toric spherical lens allows the device to meet the Economic Commission of Europe, regulation no. 113 (ECE R113). Furthermore, good uniformity is obtained by using aspherical surface optimization of the same toric lens. The reflectivity of the reflector is 95%, and the transmittance of each lens surface is 98%. The average deviation of the high beam is 14.17%, and the optical efficiency is 66.45%. © 2015 Optical Society of America

OCIS codes: (080.4228) Nonspherical mirror surfaces; (080.4295) Nonimaging optical systems; (220.2945) Illumination design; (220.4298) Nonimaging optics.

http://dx.doi.org/10.1364/AO.54.00E102

1. INTRODUCTION and the other a paraboloid collimating reflector, an off-axis A motorcycle headlamp usually consists of low- and high-beam paraboloid reflector, a baffle, and an imaging lens. The system efficiency of the composite low-beam module reached 58% [8]. lights. Various regulations include certain restrictions for illu- et al. mination requirements. In recent years, with the development Hsieh proposed an LED vehicle projector headlamp sys- of nonimaging optics, some LED headlamp optical design tem, which contained several LED headlamp modules, each of methods based on nonimaging optics have been suggested. which included four components: focused LEDs, asymmetric Herkommer [1] reported on free-form systems as applied to metal-based plates, free-form surfaces, and condenser lenses [9]. imaging and illumination systems. Cvetkovic et al. created a A number of researchers have studied light source modeling to et al. headlamp with one refractive and one reflective free-form sur- simulate various lighting systems. Cassarly measured the face, which produced light with good uniformity and high in- spatial luminance distributions over a range of view angles, tensity [2]. A vehicle headlamp design based on fiber optics and which is an important consideration for lamps in elliptical re- et al. LEDs has also been presented, the intention being to reduce flectors and LEDs [10]. Jenkins rendered the distributive lamp size and heat-dissipation problems. An optical efficiency light for a low-beam headlight design. The challenge here was of 49.4% was obtained for the low beam design [3]. In 2011, to design an efficient lamp package that angularly distributed an LED-based motorcycle headlamp with two horizontal reflec- the flux to meet legal and customer requirements [11]. Zerhau- tors and a light pipe was designed, which had an optical effi- Dreihoefer et al. presented the light source modeling for auto- ciency of about 80% [4]. Chen et al. presented a high-efficiency motive lighting devices and, in the process of calculating and LED headlamp free-form lens design. The free-form lens was simulating automotive lighting devices, used different light separated into low- and high-beam lenses, and the optical effi- source modeling techniques [12]. In this work, we use nonse- ciencies of both lenses were more than 88% [5]. Zhu et al. used quential (NS) rays to improve the optical efficiency of the com- 48 LEDs to build an array with a rectangular beam region pound reflectors. By using a toric lens, we could meet the divided into multiple blocks, each illuminated by an LED. Economic Commission of Europe, regulation no. 113 (ECE In theory, the optical efficiency of the device would exceed R113) and obtain good uniformity. The optical simulation 85% [6]. In 2013, Ge et al. proposed two low-beam systems showed the efficiency of the high beam to be 66.45%, average for an LED-based headlamp architecture, one of which com- deviation 14.17%; the optical efficiency of the low beam was prised an elliptical reflector, a baffle, and a faceted reflector [7], 66.41%, and the average deviation was 13.96%.

2. DESIGN METHOD A. Requirements for a High Beam The motorcycle headlamp was designed to conform to ECE R113. The illumination requirements for a high beam projected onto a measuring screen 25 m away from the headlamp are illustrated in Fig. 1. The irradiated area is 4500 mm × 1000 mm. The height of the HV point is equal to the height of the motorcycle headlamp. The illumination in region B should be greater than 3 lux, while that in region A should be greater than 12 lux. Fig. 2. Requirements for low beam light irradiating the measuring B. Requirements for a Low Beam screen. The illumination requirements for a low beam projected on a measuring screen are shown in Fig. 2. Point HV indicates the height between the headlamp and the road. Point 50 V is located 375 mm below point HV. The illumination in region A should be greater than 1.5 lux, and, to avoid glare, the illumination in region B should be less than 0.7 lux. The illumination at point 50 V should be greater than 3 lux. There should be a clear cut-off line below the H-H plane of 250 mm. C. Candle Power Distribution Curve A candle power distribution curve shows the normalized intensity of a light source at each degree of the chip emitting surface as shown in Fig. 3. The normal direction is at 0 deg, and the radial direction is the normalized intensity. The optical efficiency can be calculated by analyzing the candle power distribution curve. The angular distribution of the light emission of Fig. 3. the white LED is from −90° to 90°. The yellow region is the Optical efficiency is 78.48%, and the light distribution of the white LED is from −60° to 60°. design region having a light distribution from −60° to 60°, so the optical efficiency of the design requirement is more than 78.48%. 3. MOTORCYCLE HEADLAMP DESIGN D. Average Deviation A. Spread Angles of the Light Source Projected onto The average deviation is calculated from the ratio of the stan- the Measuring Screen dard deviation to the average as given by Eq. (1). By computing The distance from the headlamp to the measuring screen the average deviation for the entire measuring screen, we could is 25 m. The size of the measuring screen is 4500 mm × completely determine the uniformity of the light pattern on the 1000 mm. The relationship of the spread angle of the light measuring screen. The smaller the average deviation, the better source on the measuring screen is shown in Fig. 4. The spread the uniformity: angle is 10.28° in the horizontal direction and 2.29° in the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP 1 N X − X 2 vertical direction, indicating the angles of the light source σ N i1 i ; (1) projected on the measuring screen. Average Deviation X X B. Luminous Flux Calculation X σ N where is the average, is the standard deviation, and is the It is difficult to design the high beam for an irregular illumi- number of sampling points. nation distribution, as shown in Fig. 1. The maximum illumination requirement is 12 lux. In order to simplify the design, consider the high beam illuminating a measuring screen of 4500 mm × 1000 mm to be 12 lux. The total luminous flux is 54 lm. The height is defined by the size of the motorcycle; we set the height of the motorcycle headlamp (HV) to be 750 mm from the road. The design calls for the headlamp to be 25 m from the measuring screen. The height of 1000 mm of projected illumination is 750 mm in the vertical direction over the road and 250 mm below, as shown in Fig. 5. The vertical angle of the high beam is 2.29°, and the minimum distance irradiating the road is 18.76 m. Fig. 1. Illumination requirements for a high beam projected onto a The illumination requirements for the low beam are shown measuring screen in order to meet ECE R113. in Fig. 2. The maximum illumination of the low beam on the E104 Vol. 54, No. 28 / October 1 2015 / Applied Optics Research Article

Fig. 7. Picture of the Osram LW-W5SN LED.

Fig. 4. Spread angle of the light source projected onto the measuring screen.

Fig. 5. Lateral view of the high-beam irradiation on the road.

Fig. 8. Light distribution curve of Osram LW-W5SN LED. measuring screen is 3 lux in an area 4500 mm × 1000 mm. The total luminous flux needed is 13.5 lm. For the low-beam design, the angle of the high beam is rotated 0.86° downward to lighting would preferably be more than 20 lux. In order to es- the point 50 V located 375 mm below the point HV. This is timate the reflectivity and absorption of the material, we set the sufficient to meet the ECE-113 regulations for a low-beam system efficiency at close to 65%. The measurement surface light. The illumination projected onto the measuring screen area is 4.5 m × 1m, and the selected light flux is 138 lm at is 375 mm over the road in the vertical direction and the least. For this design, we select an Osram LW-W5SN as 625 mm below the ground as shown in Fig. 6. The minimum the light source [13], as shown in Fig. 7. The chip size is irradiation distance on the road is 13.63 m. 1mm× 1mm. The Osram LW-W5SN LED light distribution C. White LED Specification curve, as shown in Fig. 8, is a Lambertian source. The input The design requirement of the high beam is greater than 12 lux luminous flux is 146 lm. The white light spectrum of the for an average illuminance, which means that the design meets Osram LW-W5SN LED is illustrated in Fig. 9 as the solid line, the requirements of ECE R113. However, when riding a mo- and the dashed lines represent the relative spectral response of torcycle on the road at night, there can sometimes be no lights, the human eye [14]. and, at speeds of 60 km∕h or more, motorcycle lighting of only 12 lux is not sufficient. Pets, wildlife, or people can rush out onto the road beyond the 25 m range, and, to increase motor- cycling safety, more illumination is needed in order for riders to see objects and allow for earlier reaction times. Motorcycle

Fig. 6. Lateral view of the low-beam irradiation on the road. Fig. 9. Spectrum of the Osram LW-W5SN LED. Research Article Vol. 54, No. 28 / October 1 2015 / Applied Optics E105

D. Reflectors In this paper, we discuss a motorcycle headlamp design that uses two reflectors, one of which is a parabolic reflector, the other an elliptical reflector. The distances from the focus to the vertex of the reflectors can be expressed as Eqs. (2) and (3). The geometry is shown in Fig. 10 [15]. If we set d R∕ d d 1 2, then 2 and 3 are given by R pffiffiffiffiffiffiffi d 1 −K ; (2) 2 K 1

R pffiffiffiffiffiffiffi d 1 − −K ; (3) 3 K 1 where R is the radius of curvature, and K is the conic constant. E. NS Ray Analysis The motorcycle headlamp comprises a white LED module, an elliptical reflector, a parabolic reflector, and a toric lens. The light beams become parallel and irradiate the measuring screen through the toric lenses, as shown in Fig. 11. For the parabolic Fig. 11. Compound reflector system. reflector, as designed, the luminous flux is 135.62 lm, and the optical efficiency is 92.89%. The distribution of the light emitted is from −47.26° to 90°, as shown in Fig. 12. In the angle serves as a merit function for the optimization. The optimiza- range of 60° for the white LED light source, light use effi- tion technique is based on the damped least-squares (DLS) ciency of 78.48% can be achieved. For the nine point positions method. We use the toric lens arranged in front of a compound of the white LED chip, NS ray tracing is used to trace five rays reflector to increase the horizontal beam width. The material of in the directions of 0°, 60° (up), 60° (down), 60° (left), and 60° the toric lens is polycarbonate (PC). After removing the toric (right) for each point, for a total of 45 rays, as shown in Fig. 13. lens, the white LED light passed through the compound Figure 14 shows a diagram of ray tracing on the compound reflectors for the 45 NS rays. The energy loss from the up direction of −47.26° (red line) to the up direction of the −90° range without any light entering the parabolic reflector can be clearly seen, as indicated in cyan-blue in Fig. 12. After rotating the assembly 15.86° clockwise, NS ray tracing is carried out on the 45 rays, as shown in Fig. 15. Energy loss is evident from the up direction of −63.11° (red line) to the up direction of −90°, as shown in Fig. 16 (cyan-blue part), and the light usage increased from 92.89% to 98.43%. F. Toric Lens Design We use the LightTools optical design software to do the optimization in this study. The parameters of the toric lens are used as the variables. The average deviation of the measuring screen

Fig. 12. Optical efficiency of 92.89%, with light distribution from −47.26° to 90°.

Fig. 10. Distances from the focus to the vertex of the reflectors. (a) Parabolic reflector (K −1). (b) Elliptical reflector (−1

Fig. 17. Illuminance distribution projected on the measuring screen from the white LED light source after passing through the compound reflectors without the toric lens. Fig. 14. Loss of rays from up to 60°.

reflectors to obtain the illuminance distribution on the measuring screen 25 m in front, as shown in Fig. 17. According to ECE R113, the width of the illuminance distribution in the horizontal and vertical directions is not the same. The toric lens design is that of a cylindrical lens. We chose the first surface as the plane, so the second surface as cylindrical in the vertical and horizontal directions are the plane and the concave surfaces, respectively. The concave curvature radius of the second surface is 320 mm. The illuminance distribution on the measuring screen is shown in Fig. 18. The illuminance of the center por- tion is too high. The average deviation is 92%. Figure 19 indicates the uniformity optimization of the illuminance distribution on the measuring screen using the aspheric surface coefficients of the second concave surface of the toric lens in the horizontal direction. The uniformity has improved significantly. We add the first plane surface and the second concave surface of the toric lens to set the aspherical coefficients in the horizontal direction as variables with simultaneously optimized the uniformity on the measuring screen, as shown in Fig. 20. Fig. 15. Turning down the white LED 15.85°. We simultaneously chose the aspheric coefficients as the variables for the first and the second surfaces of the toric lens in the

Fig. 16. Optical efficiency of 98.43% and light distribution from Fig. 18. Illuminance distribution on the measuring screen with an −63.11° to 90°. average deviation of 92% at the initial design. Research Article Vol. 54, No. 28 / October 1 2015 / Applied Optics E107

Fig. 19. Illuminance distribution on the measuring screen after the second aspherical surface optimization of the toric lens in the horizontal direction. Fig. 22. Size of the motorcycle headlamp.

LED light is designed as 9.5 cm in length, 16.6 cm in width, and 16.6 cm in height, as shown in Fig. 22.

4. DESIGN RESULTS We assume the reflectivity of the reflector to be 95%, and the transmittance of each surface of the toric lens as 98%. The illuminance distribution of the high beam on the measuring screen is shown in Fig. 23. The average illuminance is 21.56 lux, the optical efficiency 66.45%, and the average deviation 14.17%. The low beam is obtained by rotating Fig. 20. Illuminance distribution on the measuring screen after the the high-beam lamp downward 0.86 deg. The illuminance dis- first and the second aspheric surfaces optimization of the toric lens in tribution of the low beam on the measuring screen is shown in the horizontal direction. Fig. 24. The illumination above the HV line is less than 0.7 lux. The average illuminance is 21.55 lux, the optical efficiency 66.43%, and the average deviation 13.96%. Based on the horizontal and vertical directions. The average deviation of the low-beam ECE R113 regulation, the illumination above the measuring screen can be optimized by the DLS method. The HV line should be less than 0.7 lux. The color blue represents result is shown in Fig. 21. The average illuminance is 30 lux, the lowest illumination, as shown in Fig. 24. In the design the optical efficiency is 92.49%, and the average deviation is range of 0–2 lux, it is difficult to judge if the specifications 14.78%. The size of the motorcycle lamps using a white are satisfied. If we choose the lowest illumination range of 0–0.7 lux, it is easy to see that the illumination requirement

Fig. 23. Illuminance distribution of the high beam on the measur- Fig. 21. Illuminance distribution on the measuring screen with a ing screen. The reflectivity of the reflector is 95%, and the transmit- toric aspherical lens. tance of each surface of the toric lens is 98%. E108 Vol. 54, No. 28 / October 1 2015 / Applied Optics Research Article

the headlamp was rotated downward 0.86° for the low-beam light. In the high-beam design, the main consideration was to meet the ECE R113 regulations. The average deviation of the high beam is 14.17%, and the optical efficiency is 66.45%. The average deviation of the low beam is 13.96%, and the optical efficiency is 66.41%.

Funding. Ministry of Science and Technology, Taiwan (MOST) (MOST 103-2221-E-008-052, MOST 103-2622- E-035-023-CC3).

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