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Design method of a light emitting diode front fog lamp based on a freeform reflector
Optics & Laser Technology 72 (2015) 125–133
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Design method of a light emitting diode front fog lamp based on a freeform reflector Heng Wu a, Xianmin Zhang a, Peng Ge b,n a Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China b Engineering Research Center for Optoelectronics of Guangdong Province, School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
art ic l e i nf o
a b s t r a c t
Available online 1 May 2015
We propose a method for the design of a light emitting diode front fog lamp based on a freeform reflector. The source–target mapping is used to establish the relationship between the solid angle of the source and the target plane. The reflector is then constructed based on the non-imaging optics theory and Snell's law. A feedback function is deduced from the deviation in the simulated light pattern based on the sampling method. The reflector is then regenerated with feedback modifications and the variance is minimized after several feedbacks. A reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm. Simulation results indicate that the light performance can well meet the standard of the front fog lamps in ECE R19 Revision 7. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Nonimaging optics Light-emitting diodes Freeform surface
1. Introduction With rapid development of semiconductor lighting technologies, light-emitting diodes (LEDs) are gradually replacing traditional light sources because of their numerous advantages, and have been widely used in indoor and outdoor lighting, architectural lighting, and so on [1]. However, traditional luminaires cannot work well with LEDs in most cases due to the LED's Lambertian emission character. Hence, a proper primary or secondary optical design is usually needed to redistribute the spatial energy of the LED so that all lighting advantages of LEDs can be put into practice for the high-quality illumination [2–6]. LEDs have been widely used in automobile front headlamps, especially in low-beam and high-beam headlamps [7–16]. However, there are few literatures reported on high-power LED front fog lamps with a small and compact size. Although Chinniah, Jeyachandrabose et al. proposed a method on the LED fog lamp, six LEDs were used and each LED together with a reflector to form a modular element [17]. Hamm et al. researched on the LED fog lamps too, but not mainly on the optical design [18]. Though some LED fog lamps can be searched from the web, they have either a big size or are energy consumption. So in this paper we will focus
n
Corresponding author. E-mail address: [email protected] (P. Ge).
http://dx.doi.org/10.1016/j.optlastec.2015.04.002 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
on the design of the freeform front fog lamps based on the highpower LED source with a small and compact size. In the design of the freeform LED lighting systems, the feedback method has been widely used to optimize the optical performance for the freeform surface. Yi Luo et.al. did a deep research on the freeform lens design with feedback method [19]. In their research, the feedback function was originated from the difference between the simulated illuminance and desired illuminance. This method works very well in the uniform illumination. However, when it comes to the special nonuniform illumination with a reflector, such as low-beam lamps and fog lamps, different methods need to be employed. We present a light emitting diode front fog lamp based on a freeform reflector by optimization in this paper. A new feedback method is shown in details to optimize the optical performance for the reflector based on the sampling method. Firstly, the placement between the LED source and the reflector is determined. Then the source–target mapping is established and a reflector is constructed based on non-imaging optics theory and Snell's law by numerical calculation [20]. With the feedback function, the reflector is regenerated and the deviation could be minimized after several feedbacks. As an example, a reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm and results indicate that the light performance can attain the requirements of the front fog lamps. In addition, light efficiency can be improved from 66.17% to 77.86%.
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This paper is organized as follows: Section 2 will quickly mention the ECE regulation for vehicle front lamps. The detailed design principles are given in Section 3. Simulation results are given in Section 4. Finally the conclusions are drawn in Section 5.
2. ECE regulation no. 19 revision 7 for vehicle front fog lamps The ECE regulation R19 revision 7 is applied to front fog lamps, which contains two distinct classes. The first one is Class “B” which is used for the original front fog lamp. For this class, only light sources as specified in regulation no. 37 are allowed. The second one is Class “F3” which is designed to increase photometric performance. Most importantly, LED sources can be used in Class “F3” [21]. As shown in Fig. 1, in the case of Class F3, the beam pattern should have a wide horizontal spread, which is over a width of more than 5° on both sides of the line v. A symmetrical and substantially horizontal cut-off that is 1° below the line h shall be also created. Moreover, the beam pattern should be substantially uniform between lines 1 and 5. Intensity discontinuities between the lines 6 and 9 are not permitted. Variations in homogeneity detrimental to satisfactory visibility in the zone above the line 5 from 10° left to 10° right are not allowed either. In addition, the luminous intensity in the specified points, lines and regions shall be measured strictly at the measuring screen 25 m front the fog lamp [21]. Fig. 1. Light distribution of Class F3 front fog lamp.
3. Design principles
reflector 3.1. Relationship between the LED source and the reflector
3.2. Establishment of the source–target mapping In this paper, the light is supposed to be reflected onto the target plane to form a rectangular illumination area with a length L and width W. As both the target plane and LED source are of axial symmetry, just a half of them are considered. As shown in Fig. 5, the energy distribution of the light source is divided into M, N grids
LED source Fig. 2. LED's central axis is perpendicular to the optical axis.
reflector
LED source
In the design process, there are two types of placement for the LED source and the reflector: (1) The LED's center axis is perpendicular to the optical axis, as shown in Fig. 2; (2) the LED's center axis is parallel to the optical axis, as shown in Fig. 3. Since the LED source has a Lambertian intensity distribution, the intensity in the center is very strong and it weakens toward both sides gradually. As a result, when the parallel placement is chosen, the glare effect can be generated easily, which gives bad influence on the illumination, and most often this placement is used to produce round and oval light distribution. Against that, the vertical placement can be a good way to control the angle of the light rays for desired light distribution, and to effectively suppress the glare effects. Meanwhile, when the vertical placement is adopted, the volume of the reflector is nearly half of that with the parallel placement, which makes the arrangement for the LED modules and the design of reflectors more flexible. Therefore, the vertical placement is utilized in this design. When the vertical placement is taken, the light pattern is formed by the reflected rays, which deliver the energy emitted from the LED source onto the target plane and produce the required light distribution. Nonetheless, there are some rays which are not reflected because their emitting angle is bigger than the maximum angle that the reflector can control, as shown in Fig. 4. Actually, these rays are not stray lights and do not disturb the lighting performance when Fig. 2 is taken into consideration. In contrast, they can provide some illuminance on the ground, which is helpful for the drivers to see the ground condition.
Fig. 3. LED's central axis is parallel to the optical axis.
O
x
θmax
Target plane
z
Out rays
Reflector
Ground Fig. 4. Schematic diagram of the reflected lighting system.
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
Z
y
source-to-target O
A
° A
° A
βj
X
P2,3
Ă
P2,2
Tangent plane
Normal vector
t(yj) Y
P3,1
° A
αi
x
Ă
P3,3
P3,2
Initial line
m-1 t(xM)
° A
1
1
° t(xi) A ° A
127
P2,1
P1,2
t(yN)
P1,3
Ă
(t(xM),t(yN))
P1,1 Fig. 5. Schematic diagram for source–target mapping.
Out rays Incident rays
equally, which is specified by coordinates (αi , βj )as follows [22]:
αmax − αmin ⎧ α = αmin + ·i ⎪ ⎪ i M ⎨ βmax − βmin ⎪β = β ·j ⎪ min + ⎩ i N
LED source
(i = 0, 1, …, M) (j = 0, 1, …, N)
Fig. 6. Schematic of generation of points on the freeform reflector.
(1)
where αmin and αmax are the minimum and maximum zenith angles of the source (i.e., the angle against the z axis), while βmin and βmax are the minimum and maximum azimuth angles of the source (i.e., the angle against the x axis), respectively. Correspondingly, half of the length L/2 and the width W of the target plane are divided into M and N parts uniformly along the x-axis and y-axis, respectively, which are specified by (t (xi ), t (yj )) in the Cartesian coordinate system as follows:
⎧ L/2 ⎪ ⎪t (xi ) = M ·i ⎨ W ⎪ t (y ) = ·j ⎪ ⎩ i N
(i = 0, 1, …, M) (j = 0, 1, …, N)
(2)
The mapping relationship is shown in Fig. 5 and the relationship between the source and the target plane can be represented as follows:
Source: (αi , βj ) ↓ Freeform: (f (xi ), f (yj ), f (zi )) ↓ Target: (t (xi ), t (yj ), d)
(3)
where d is the distance between the source and the target plane, and f (xi ), f (yj ) and f (zi ) are the coordinates on the freeform reflector. 3.3. Calculating the freeform reflector and simulating The calculation on the reflector contour mainly in cludes three steps: determine a starting point, calculate the initial line and construct the entire freeform surface. With Eqs. (1)–(3), the unit vectors of incident and reflected rays can be written as Eqs. (4) and (5), respectively: →
In = (sin αi ⋅cos βj , sin αi ⋅sin βj , cos αi )
⎯⎯⎯⎯→ Out =
(4)
(t (xi ) − f (xi ), t (yj ) − f (yj ) , d − f (zi )) (t (xi ) − f (xi ))2 + (t (yj ) − f (yj ))2 + (d − f (zi ))2
(5)
Now that the unit vectors of incident and reflected rays are ⎯→ ⎯ known, the normal vector N on the point can be obtained by Snell's law. In the totally reflective case, Snell's law can be expressed
as follows [20]:
⎯⎯⎯⎯→ ⎯→ ⎯ ⎤ 21 → ⎯⎯⎯⎯→ ⎯→ ⎯ ⎡ ⎣⎢2 − 2⋅( Out ⋅ In ) ⎦⎥ ⋅N = Out − In
(6)
With the normal vectors obtained, the tangent plane on the point can be obtained, and the coordinate of the next point can be calculated by computing the intersection of the next incident ray and the tangent plane. The rest points may be deduced by analogy and so the starting line is calculated. Then the entire freeform surface can be obtained by taking each point on the starting line as the new starting point in the same way, as shown in Fig. 6. Detailed calculation steps: 1. Determining a starting point. 2. Calculating the tangent plane. The normal vector of the starting point is obtained by Snell's law with the unit vectors of first incident and reflected rays. Then the tangent plane is determined and the second point is calculated by computing the intersection of the second incident ray and the tangent plane. 3. Figuring out the initial line. The second tangent plane is gained so as the step 2 does. Then the third point is determined through calculating the intersection of the third incident ray and the previous tangent plane. Similarly, each of the next point is calculated and thereby the initial line is generated. 4. Constructing the freeform surface. Taking each point on the initial line as the new starting point and the coordinates of all points on the free-form surface are calculated according to steps 1–3. The entity for the smooth freeform surface is constructed with the points which are acquired by the methods above by the mechanical software. Then the performance is simulated by the Monte Carlo ray tracing method. The simulation result is shown in Fig. 7. Obviously, the light pattern is basically consistent with expectations in the horizontal direction. However, a bending occurs in the vertical direction and some divergence appears in the bottom. The light deviations are caused mainly by the mapping presented in Fig. 5, which is detailed explained in references [23] and [24]. As Fournier said, in order to construct a smooth continuous ⎯→ ⎯ surface, a field of surface normal N must satisfy the integrability condition which is expressed as Eq. (7) [23], →
→
N · (∇ × N ) = 0
(7)
Deviations in Fig. 7 mean that the mapping shown in Fig. 5 is not an integrable mapping, which does not satisfy the integrability
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Fig. 9. The initial curve and the feedback curve. (For interpretation of the references to color in this figure , the reader is referred to the web version of this article.) Fig. 7. The initial light pattern on the target plane.
the symmetry with the initial function along the abscissa axis, as the blue line shown in Fig. 9. As the initial sampling point is not unique, many initial functions and feedback functions may be created by this way. Nevertheless, the most suitable initial function must be the one that can approximate the bending trend of the light pattern best, which mainly decided by the selection of sampling points. The initial function and the feedback function are written as Eqs. (8) and (9), respectively:
Fig. 8. Taking sampling points from the target plane.
condition. Yet, establishing a ray mapping that exactly fulfills Eq. (7) is not a straightforward task. So special measurement must be taken to find a mapping that leads to a continuously optical surface. 3.4. Design of feedback method In this section we will find out a feedback function to optimize the design for the freeform surface, which can reduce the light deviations caused by the mapping in Section 3.2. To be simple, we just take modifications for the vertical direction as an example. The Cartesian coordinate system is first established as shown in Fig. 8 and an initial sampling point is determined. Actually, the initial sampling point can be fixed at any point on the z axis within the light pattern. Nonetheless, as the convenience for calculations and comparisons is concerned, the point is chosen from the light pattern where a high contrast exists. Then the rest sampling points are taken at the same interval along the bending direction and the abscissa and ordinate values are recorded, respectively. In this design, the sampling size is set as 30. Much more attentions should be paid to the continuity when the sampling points are produced. Then the coordinate values are fitted into a curve which reflects the bending trend of the light pattern in the vertical direction and is defined as the initial function in mathematics, as the red line shown in Fig. 9. The feedback function is derived by
yo = fo (t (xi ))
(8)
ye = fe (t (xi )) = − Afo (t (xi )) + C
(9)
where A (A40) and C are constants which control the shape and the location of the function, respectively. When the feedback function is figured out, the coordinates of the target plane is re-divided and the new coordinates are written as Eq. (10): ⎧ L /2 ·i (i = 0, 1, …, M) ⎪ t (xi )′ = ⎪ M ⎨ W − fe (t (xi )) ⎪ t (y )′ = fe (t (xi )) + ·j ⎪ ⎩ j N
(j = 0, 1, …, N)
(10)
Then a new mapping is set up and all points on the reflector are re-calculated with the re-divided coordinates. Fig. 10 shows the final light distribution after several feedbacks. As it can be seen, the distortions in the vertical direction and the bottom are decreased dramatically. In addition, owing to the continuous feedback function, the light pattern is uniformly bended along the modified feedback curve. Theoretically, as the variation trend of the feedback curve is opposite to the initial one, when a reflector is established based on the re-divided coordinates, the new light pattern could be changed to the opposite direction correspondingly. As a result, the distortion caused by the mapping can be eliminated. But in practice, the blue line in Fig. 9 is not the final curve yet, which is just a variation tendency the feedback curve needed to be. If we just take the feedback function into the calculation without any modifications, the lighting performance may still be far away from the desired. The main reason is that the initial function acquired is based on sampling points, which are not completely accurate and certain sampling errors appears inevitably. Thereby the parameters A and C in Eq. (9) are extremely necessary and are ought to be modified
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
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35 mm
36 mm 7 mm LED
θmax
25m
x
Target plane
z
Reflector 500 mm
Ground
Fig. 11. Schematic diagram of the lighting system for the front fog lamp (not to scale).
Fig. 10. Final illumination distribution on the target plane.
so as to change the shape and the location of the function according to the later simulation results. To evaluate the transmittability on the reflector, the light control efficiency (LCE) is defined as the ratio between the energy projected to the illuminated areas and the total energy emitted from the LED source, which is denoted as Eq. (11):
η=
Φtarget Φsource
(11)
where in Φtarget and Φsource are the luminous flux on the illuminated areas and the total luminous flux from the LED source, respectively. The LCE is different from the light output efficiency, which includes all the rays emitted from the optical system. Generally speaking, the output efficiency of the optical system is higher than the LCE.
4. Simulation results In order to verify the proposed method, a reflector for the LED front fog lamp is designed to form a 12 m long and 2.5 m wide rectangular radiation pattern on the target plane 25 m front of the lamp [21]. The front fog reflector is set at the height of 500 mm over the ground, the size of which is 35 mm high, 36 mm long and 50 mm wide. Fig. 11 shows the model of the reflector and target plane in details and the drawing is not to scale. The LED source is LE UW D1W1 01, OSTAR Headlamp, 1 chip, whose emitting surface is 2.8 mm 2.5 mm. Fig. 12 shows the model of the final reflector, which has a continuous surface and a small size, making it eligible for injection molding and production. Once the reflector module is constructed, the Monte Carlo ray tracing method is employed for simulation. After the simulation, measurements are taken on the target plane and feedback methods are carried out according to the results until the desired lighting performance is achieved. Moreover, the proposed feedback concepts can also be applied to other areas such as the mechanical design and image acquisition. For example, in the vision detection system, a feature of the image is first constructed and then the desired image can be acquired through feedbacks and feature comparisons. The lighting performance before and after feedback method are shown in Fig. 13 for comparison. It is clear that the light pattern of the initial design is far from the prescribed one, while the results of the final designs are much better after several feedback modifications. That is to say, when a clear cut-off line and a wide light
distribution in the horizontal direction are created, the feedback modifications will come to an end and then the calculations are terminated. It only takes about 2 s to acquire the numerical results which stand for the contour of the freeform reflector with feedback modification. Compared with previous methods about the freeform construction and the headlamp design, such as references [2,8,12] introduced, our method can achieve good results in much more simply and quickly. In reference [2], it took about 20 s to obtain the contour of the freeform surface, while as reference [8] presented, it cost lots of time to optimize all the parameters so as to get the final results. The optical system is rather complex in reference [12]. Moreover, our method mainly focuses on the long distance (25 m or more) nonuniform illumination for the LED source, while the distance for general uniform illuminations is about 10 m [19,22]. Fig. 13(a)–(c) shows the results of the initial designs, after one time and two times feedback modification, respectively, while Fig. 13(d) shows the final light pattern after five times of feedback modification. As shown in Fig. 13(d), though the light pattern in the vertical direction is satisfied, certain divergences appear in both the vertical and horizontal direction. But when taken the illumination requirements of the front fog lamp into account, where a clear cut-off line and a wide light distribution in the horizontal and vertical direction are needed, the effects of the divergence is actually helpful. The comparisons of the initial curve and the feedback curves are shown in Fig. 14, which are corresponding to Fig. 13(a–d), respectively. It shows that some more modifications are needed so as to obtain the required light distribution. In this design, we mainly focus on the distortion correction in the vertical direction, and if the modifications are needed in the horizontal direction, the same method can be applied. Fig. 15 shows the ultimate light distribution of the front fog lamp and the results are generated by three reflectors lain in a line. The dimension (length, width and height) of each reflector is 36 mm 50 m 35 mm and the luminous flux is 200 lm for each LED. It can be seen from that a clear cut-off line is produced on the target plane. According to the ECE regulations R19 revision 7, the light pattern can fully satisfy the lighting requirements of Class F3 front fog lamp. Some measurements are also done on the prescribed area and the test data in each region is shown in Table 1. From Table 1 we can know that the test data in each region is within the limitation of ECE regulations. Furthermore, the energy which is reflected onto whether the road or the target plane is sufficient, which can well fulfill the lighting requirements for front fog lamps. The variation of the LCE during feedbacks is shown in Fig. 16, where the LCE is improved from 66.17% to 77.86%. It shows that the proposed feedback method could effectively improve the LCE. That is mainly because the LCE has a significant relation with the locations of the sampling points, which can change the size of the
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Fig. 12. Geometry of the final optical reflector model.
Fig. 13. The lighting performance before and after feedback method (a) Initial; (b) After one feedback; (c) After two feedbacks; and ( d) the final light pattern.
reflector. When the reflector size changes, the energy that the reflector collects varies correspondingly. However, as the sampling method cannot change the reflector size dramatically, the LCE is just improved on a small scale. In addition, the sampling size determines the accuracy of the feedback function. Theoretically, the larger the sampling size, the more accurate the feedback function.
The tolerance of a freeform surface is an important issue in the optical design. In this design, the tolerance analysis is mainly concentrated on the source translation. For simplicity, the coordinate system is established as shown in Fig. 17. Fig. 18 shows the influence of LED's position to the light distribution. In Fig. 18(a) and (b), the LED source is translated along þz, þx, þy and y directions for
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
0.2 mm, respectively. Both of the two light distributions can still meet the requirements of the ECE regulations R19 revision 7. It indicates that the light distribution is not sensitive to the z axis, x axis and z axis displacements of the source. However, the maximum
131
illumination value decreases from 18 lx to 14 lx and the light pattern extends below the horizontal line when the source is translated from the y axis to the y axis. Anyway, the positioning errors of LEDs have small impacts on the illumination. Fig. 19 shows the illumination distribution on the target plane when the LED source is rotated round the z axis, x axis, y axis and vector (1, 1, 1) for 0.2°, respectively. It demonstrates that the source rotations have a large influence on the illumination. As shown in Fig. 19(a) and (b), when the source is rotated round x axis and z axis for 0.2°, respectively, the illumination along the x axis and y axis deteriorate, especially on the right part of the light pattern. Although the cut-off line is still clear, it inclines a little from the horizontal line. Nonetheless, the light distribution does not vary and can fulfill the requirements of the ECE regulations
Fig. 14. The comparisons of the initial curve and the feedback curves.
Fig. 16. Variation of the LCE during feedbacks and the final.
Fig. 15. The ultimate illumination distribution on the target plane.
Fig. 17. Establishment of the coordinate system for the reflectors.
Table 1 Simulation results of the LED front fog lamp based on ECE R19 Rev7. Designated lines or zones Vertical position above h þ below h
Horizontal position left of v: right of v: þ
Luminous intensity (in cd)
To comply
Simulated results (in cd)
o ¼ 60
All points
o ¼ 20.06
All All All All All All All
points points points points points points points
o ¼ 9.54 o ¼ 21.93 o ¼ 68.61 o ¼ 125.92 o ¼ 218.48 4 ¼4882 o ¼ 1849.04
One or more points One or more points Whole zone
4 ¼2063.87
Point 1, 2 Point 3, 4 Point 5, 6 Point 7, 10 Point 8, 9 Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7
þ60° þ40° þ30° þ20° þ20° þ8° þ4° þ2° þ1° 0° 2.5° 6.0°
745° 730° 760° 740° 715° 26° to 26° to 26° to 26° to 10° to 10° to 10° to
Line 8L and R
1.5° to 3.5°
22° and þ 22°
o ¼ 90 o ¼ 105 o ¼ 170 o ¼ 250 o ¼ 340 4 ¼ 2700 o ¼ 50% of max on line 6 4 ¼ 800
Line 9L and R
1.5° to 4.5°
35° and þ 35°
4 ¼ 320
Zone D
1.5° to 3.5°
10° to þ 10°
o ¼ 8400
þ26° þ26° þ26° þ26° þ 10° þ 10° þ 10°
4 ¼509.29 o ¼ 7832
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H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
Fig. 18. Influences of LED's positions to the light distribution: (a) the LED source is translated along þ z, þ x, þ y directions and (b) þz, þx, y directions for 0.2 mm, respectively.
Fig. 19. Influences of LED’s rotations to the light distribution: the LED source is rotated round the (a) z axis, (b) x axis, (c) y axis and (d) vector (1, 1, 1) for 0.2°, respectively.
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
when the source is rotated round the y axis as shown in Fig. 19(c). That is because the LED source is of central symmetry. In Fig. 19(d), the deterioration caused by rotation round vector (1, 1, 1) is worse than that by rotation round the x axis and z axis. Moreover, the light distribution in Fig. 19(a), (b) and (d) can no longer satisfy the requirements of the ECE regulations R19 revision 7. It can be seen from Fig. 19 that the rotation errors can greatly affect the illumination. In short, in order to get better performances, both the positioning error (not more than 0.2 mm) and the rotation error (not more than 0.1°) of LEDs should be strictly controlled. Since the vertical placement is adopted, the volume of the reflector decreases nearly 50%, which brings a great flexibility for front fog lamps design.
5. Conclusions A design method for the light emitting diode front fog lamp based on a freeform reflector is proposed. The placement between the LED source and the reflector is first determined, and the source–target mapping is established. Then, a reflector is constructed and the Monte Carlo ray tracing method is employed for simulation. A feedback function is deduced based on the simulation results and the sampling method. The reflector is regenerated with the feedback function and the deviation could be minimized after several feedbacks. A reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm and results demonstrate that the lighting performance can well accomplish the requirements of ECE regulations R19 revision 7. The LCE is improved from 66.17% to 77.86%. Moreover, this method can be used not only for automobile front fog lamps, but also for motorcycle headlamps, bike lights and reflectors where long distance illumination is needed.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant nos. 91223201, 50825504), the Natural Science Foundation of Guangdong Province (Grant no. S2013030013355), the NSFC United Foundation of Guangdong Province (Grant no. U0934004), and the Fundamental Research Funds for the Central Universities (2012ZP0004, 2013ZM0092).
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Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Design method of a light emitting diode front fog lamp based on a freeform reflector Heng Wu a, Xianmin Zhang a, Peng Ge b,n a Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China b Engineering Research Center for Optoelectronics of Guangdong Province, School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
art ic l e i nf o
a b s t r a c t
Available online 1 May 2015
We propose a method for the design of a light emitting diode front fog lamp based on a freeform reflector. The source–target mapping is used to establish the relationship between the solid angle of the source and the target plane. The reflector is then constructed based on the non-imaging optics theory and Snell's law. A feedback function is deduced from the deviation in the simulated light pattern based on the sampling method. The reflector is then regenerated with feedback modifications and the variance is minimized after several feedbacks. A reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm. Simulation results indicate that the light performance can well meet the standard of the front fog lamps in ECE R19 Revision 7. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Nonimaging optics Light-emitting diodes Freeform surface
1. Introduction With rapid development of semiconductor lighting technologies, light-emitting diodes (LEDs) are gradually replacing traditional light sources because of their numerous advantages, and have been widely used in indoor and outdoor lighting, architectural lighting, and so on [1]. However, traditional luminaires cannot work well with LEDs in most cases due to the LED's Lambertian emission character. Hence, a proper primary or secondary optical design is usually needed to redistribute the spatial energy of the LED so that all lighting advantages of LEDs can be put into practice for the high-quality illumination [2–6]. LEDs have been widely used in automobile front headlamps, especially in low-beam and high-beam headlamps [7–16]. However, there are few literatures reported on high-power LED front fog lamps with a small and compact size. Although Chinniah, Jeyachandrabose et al. proposed a method on the LED fog lamp, six LEDs were used and each LED together with a reflector to form a modular element [17]. Hamm et al. researched on the LED fog lamps too, but not mainly on the optical design [18]. Though some LED fog lamps can be searched from the web, they have either a big size or are energy consumption. So in this paper we will focus
n
Corresponding author. E-mail address: [email protected] (P. Ge).
http://dx.doi.org/10.1016/j.optlastec.2015.04.002 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
on the design of the freeform front fog lamps based on the highpower LED source with a small and compact size. In the design of the freeform LED lighting systems, the feedback method has been widely used to optimize the optical performance for the freeform surface. Yi Luo et.al. did a deep research on the freeform lens design with feedback method [19]. In their research, the feedback function was originated from the difference between the simulated illuminance and desired illuminance. This method works very well in the uniform illumination. However, when it comes to the special nonuniform illumination with a reflector, such as low-beam lamps and fog lamps, different methods need to be employed. We present a light emitting diode front fog lamp based on a freeform reflector by optimization in this paper. A new feedback method is shown in details to optimize the optical performance for the reflector based on the sampling method. Firstly, the placement between the LED source and the reflector is determined. Then the source–target mapping is established and a reflector is constructed based on non-imaging optics theory and Snell's law by numerical calculation [20]. With the feedback function, the reflector is regenerated and the deviation could be minimized after several feedbacks. As an example, a reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm and results indicate that the light performance can attain the requirements of the front fog lamps. In addition, light efficiency can be improved from 66.17% to 77.86%.
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This paper is organized as follows: Section 2 will quickly mention the ECE regulation for vehicle front lamps. The detailed design principles are given in Section 3. Simulation results are given in Section 4. Finally the conclusions are drawn in Section 5.
2. ECE regulation no. 19 revision 7 for vehicle front fog lamps The ECE regulation R19 revision 7 is applied to front fog lamps, which contains two distinct classes. The first one is Class “B” which is used for the original front fog lamp. For this class, only light sources as specified in regulation no. 37 are allowed. The second one is Class “F3” which is designed to increase photometric performance. Most importantly, LED sources can be used in Class “F3” [21]. As shown in Fig. 1, in the case of Class F3, the beam pattern should have a wide horizontal spread, which is over a width of more than 5° on both sides of the line v. A symmetrical and substantially horizontal cut-off that is 1° below the line h shall be also created. Moreover, the beam pattern should be substantially uniform between lines 1 and 5. Intensity discontinuities between the lines 6 and 9 are not permitted. Variations in homogeneity detrimental to satisfactory visibility in the zone above the line 5 from 10° left to 10° right are not allowed either. In addition, the luminous intensity in the specified points, lines and regions shall be measured strictly at the measuring screen 25 m front the fog lamp [21]. Fig. 1. Light distribution of Class F3 front fog lamp.
3. Design principles
reflector 3.1. Relationship between the LED source and the reflector
3.2. Establishment of the source–target mapping In this paper, the light is supposed to be reflected onto the target plane to form a rectangular illumination area with a length L and width W. As both the target plane and LED source are of axial symmetry, just a half of them are considered. As shown in Fig. 5, the energy distribution of the light source is divided into M, N grids
LED source Fig. 2. LED's central axis is perpendicular to the optical axis.
reflector
LED source
In the design process, there are two types of placement for the LED source and the reflector: (1) The LED's center axis is perpendicular to the optical axis, as shown in Fig. 2; (2) the LED's center axis is parallel to the optical axis, as shown in Fig. 3. Since the LED source has a Lambertian intensity distribution, the intensity in the center is very strong and it weakens toward both sides gradually. As a result, when the parallel placement is chosen, the glare effect can be generated easily, which gives bad influence on the illumination, and most often this placement is used to produce round and oval light distribution. Against that, the vertical placement can be a good way to control the angle of the light rays for desired light distribution, and to effectively suppress the glare effects. Meanwhile, when the vertical placement is adopted, the volume of the reflector is nearly half of that with the parallel placement, which makes the arrangement for the LED modules and the design of reflectors more flexible. Therefore, the vertical placement is utilized in this design. When the vertical placement is taken, the light pattern is formed by the reflected rays, which deliver the energy emitted from the LED source onto the target plane and produce the required light distribution. Nonetheless, there are some rays which are not reflected because their emitting angle is bigger than the maximum angle that the reflector can control, as shown in Fig. 4. Actually, these rays are not stray lights and do not disturb the lighting performance when Fig. 2 is taken into consideration. In contrast, they can provide some illuminance on the ground, which is helpful for the drivers to see the ground condition.
Fig. 3. LED's central axis is parallel to the optical axis.
O
x
θmax
Target plane
z
Out rays
Reflector
Ground Fig. 4. Schematic diagram of the reflected lighting system.
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
Z
y
source-to-target O
A
° A
° A
βj
X
P2,3
Ă
P2,2
Tangent plane
Normal vector
t(yj) Y
P3,1
° A
αi
x
Ă
P3,3
P3,2
Initial line
m-1 t(xM)
° A
1
1
° t(xi) A ° A
127
P2,1
P1,2
t(yN)
P1,3
Ă
(t(xM),t(yN))
P1,1 Fig. 5. Schematic diagram for source–target mapping.
Out rays Incident rays
equally, which is specified by coordinates (αi , βj )as follows [22]:
αmax − αmin ⎧ α = αmin + ·i ⎪ ⎪ i M ⎨ βmax − βmin ⎪β = β ·j ⎪ min + ⎩ i N
LED source
(i = 0, 1, …, M) (j = 0, 1, …, N)
Fig. 6. Schematic of generation of points on the freeform reflector.
(1)
where αmin and αmax are the minimum and maximum zenith angles of the source (i.e., the angle against the z axis), while βmin and βmax are the minimum and maximum azimuth angles of the source (i.e., the angle against the x axis), respectively. Correspondingly, half of the length L/2 and the width W of the target plane are divided into M and N parts uniformly along the x-axis and y-axis, respectively, which are specified by (t (xi ), t (yj )) in the Cartesian coordinate system as follows:
⎧ L/2 ⎪ ⎪t (xi ) = M ·i ⎨ W ⎪ t (y ) = ·j ⎪ ⎩ i N
(i = 0, 1, …, M) (j = 0, 1, …, N)
(2)
The mapping relationship is shown in Fig. 5 and the relationship between the source and the target plane can be represented as follows:
Source: (αi , βj ) ↓ Freeform: (f (xi ), f (yj ), f (zi )) ↓ Target: (t (xi ), t (yj ), d)
(3)
where d is the distance between the source and the target plane, and f (xi ), f (yj ) and f (zi ) are the coordinates on the freeform reflector. 3.3. Calculating the freeform reflector and simulating The calculation on the reflector contour mainly in cludes three steps: determine a starting point, calculate the initial line and construct the entire freeform surface. With Eqs. (1)–(3), the unit vectors of incident and reflected rays can be written as Eqs. (4) and (5), respectively: →
In = (sin αi ⋅cos βj , sin αi ⋅sin βj , cos αi )
⎯⎯⎯⎯→ Out =
(4)
(t (xi ) − f (xi ), t (yj ) − f (yj ) , d − f (zi )) (t (xi ) − f (xi ))2 + (t (yj ) − f (yj ))2 + (d − f (zi ))2
(5)
Now that the unit vectors of incident and reflected rays are ⎯→ ⎯ known, the normal vector N on the point can be obtained by Snell's law. In the totally reflective case, Snell's law can be expressed
as follows [20]:
⎯⎯⎯⎯→ ⎯→ ⎯ ⎤ 21 → ⎯⎯⎯⎯→ ⎯→ ⎯ ⎡ ⎣⎢2 − 2⋅( Out ⋅ In ) ⎦⎥ ⋅N = Out − In
(6)
With the normal vectors obtained, the tangent plane on the point can be obtained, and the coordinate of the next point can be calculated by computing the intersection of the next incident ray and the tangent plane. The rest points may be deduced by analogy and so the starting line is calculated. Then the entire freeform surface can be obtained by taking each point on the starting line as the new starting point in the same way, as shown in Fig. 6. Detailed calculation steps: 1. Determining a starting point. 2. Calculating the tangent plane. The normal vector of the starting point is obtained by Snell's law with the unit vectors of first incident and reflected rays. Then the tangent plane is determined and the second point is calculated by computing the intersection of the second incident ray and the tangent plane. 3. Figuring out the initial line. The second tangent plane is gained so as the step 2 does. Then the third point is determined through calculating the intersection of the third incident ray and the previous tangent plane. Similarly, each of the next point is calculated and thereby the initial line is generated. 4. Constructing the freeform surface. Taking each point on the initial line as the new starting point and the coordinates of all points on the free-form surface are calculated according to steps 1–3. The entity for the smooth freeform surface is constructed with the points which are acquired by the methods above by the mechanical software. Then the performance is simulated by the Monte Carlo ray tracing method. The simulation result is shown in Fig. 7. Obviously, the light pattern is basically consistent with expectations in the horizontal direction. However, a bending occurs in the vertical direction and some divergence appears in the bottom. The light deviations are caused mainly by the mapping presented in Fig. 5, which is detailed explained in references [23] and [24]. As Fournier said, in order to construct a smooth continuous ⎯→ ⎯ surface, a field of surface normal N must satisfy the integrability condition which is expressed as Eq. (7) [23], →
→
N · (∇ × N ) = 0
(7)
Deviations in Fig. 7 mean that the mapping shown in Fig. 5 is not an integrable mapping, which does not satisfy the integrability
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Fig. 9. The initial curve and the feedback curve. (For interpretation of the references to color in this figure , the reader is referred to the web version of this article.) Fig. 7. The initial light pattern on the target plane.
the symmetry with the initial function along the abscissa axis, as the blue line shown in Fig. 9. As the initial sampling point is not unique, many initial functions and feedback functions may be created by this way. Nevertheless, the most suitable initial function must be the one that can approximate the bending trend of the light pattern best, which mainly decided by the selection of sampling points. The initial function and the feedback function are written as Eqs. (8) and (9), respectively:
Fig. 8. Taking sampling points from the target plane.
condition. Yet, establishing a ray mapping that exactly fulfills Eq. (7) is not a straightforward task. So special measurement must be taken to find a mapping that leads to a continuously optical surface. 3.4. Design of feedback method In this section we will find out a feedback function to optimize the design for the freeform surface, which can reduce the light deviations caused by the mapping in Section 3.2. To be simple, we just take modifications for the vertical direction as an example. The Cartesian coordinate system is first established as shown in Fig. 8 and an initial sampling point is determined. Actually, the initial sampling point can be fixed at any point on the z axis within the light pattern. Nonetheless, as the convenience for calculations and comparisons is concerned, the point is chosen from the light pattern where a high contrast exists. Then the rest sampling points are taken at the same interval along the bending direction and the abscissa and ordinate values are recorded, respectively. In this design, the sampling size is set as 30. Much more attentions should be paid to the continuity when the sampling points are produced. Then the coordinate values are fitted into a curve which reflects the bending trend of the light pattern in the vertical direction and is defined as the initial function in mathematics, as the red line shown in Fig. 9. The feedback function is derived by
yo = fo (t (xi ))
(8)
ye = fe (t (xi )) = − Afo (t (xi )) + C
(9)
where A (A40) and C are constants which control the shape and the location of the function, respectively. When the feedback function is figured out, the coordinates of the target plane is re-divided and the new coordinates are written as Eq. (10): ⎧ L /2 ·i (i = 0, 1, …, M) ⎪ t (xi )′ = ⎪ M ⎨ W − fe (t (xi )) ⎪ t (y )′ = fe (t (xi )) + ·j ⎪ ⎩ j N
(j = 0, 1, …, N)
(10)
Then a new mapping is set up and all points on the reflector are re-calculated with the re-divided coordinates. Fig. 10 shows the final light distribution after several feedbacks. As it can be seen, the distortions in the vertical direction and the bottom are decreased dramatically. In addition, owing to the continuous feedback function, the light pattern is uniformly bended along the modified feedback curve. Theoretically, as the variation trend of the feedback curve is opposite to the initial one, when a reflector is established based on the re-divided coordinates, the new light pattern could be changed to the opposite direction correspondingly. As a result, the distortion caused by the mapping can be eliminated. But in practice, the blue line in Fig. 9 is not the final curve yet, which is just a variation tendency the feedback curve needed to be. If we just take the feedback function into the calculation without any modifications, the lighting performance may still be far away from the desired. The main reason is that the initial function acquired is based on sampling points, which are not completely accurate and certain sampling errors appears inevitably. Thereby the parameters A and C in Eq. (9) are extremely necessary and are ought to be modified
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
129
35 mm
36 mm 7 mm LED
θmax
25m
x
Target plane
z
Reflector 500 mm
Ground
Fig. 11. Schematic diagram of the lighting system for the front fog lamp (not to scale).
Fig. 10. Final illumination distribution on the target plane.
so as to change the shape and the location of the function according to the later simulation results. To evaluate the transmittability on the reflector, the light control efficiency (LCE) is defined as the ratio between the energy projected to the illuminated areas and the total energy emitted from the LED source, which is denoted as Eq. (11):
η=
Φtarget Φsource
(11)
where in Φtarget and Φsource are the luminous flux on the illuminated areas and the total luminous flux from the LED source, respectively. The LCE is different from the light output efficiency, which includes all the rays emitted from the optical system. Generally speaking, the output efficiency of the optical system is higher than the LCE.
4. Simulation results In order to verify the proposed method, a reflector for the LED front fog lamp is designed to form a 12 m long and 2.5 m wide rectangular radiation pattern on the target plane 25 m front of the lamp [21]. The front fog reflector is set at the height of 500 mm over the ground, the size of which is 35 mm high, 36 mm long and 50 mm wide. Fig. 11 shows the model of the reflector and target plane in details and the drawing is not to scale. The LED source is LE UW D1W1 01, OSTAR Headlamp, 1 chip, whose emitting surface is 2.8 mm 2.5 mm. Fig. 12 shows the model of the final reflector, which has a continuous surface and a small size, making it eligible for injection molding and production. Once the reflector module is constructed, the Monte Carlo ray tracing method is employed for simulation. After the simulation, measurements are taken on the target plane and feedback methods are carried out according to the results until the desired lighting performance is achieved. Moreover, the proposed feedback concepts can also be applied to other areas such as the mechanical design and image acquisition. For example, in the vision detection system, a feature of the image is first constructed and then the desired image can be acquired through feedbacks and feature comparisons. The lighting performance before and after feedback method are shown in Fig. 13 for comparison. It is clear that the light pattern of the initial design is far from the prescribed one, while the results of the final designs are much better after several feedback modifications. That is to say, when a clear cut-off line and a wide light
distribution in the horizontal direction are created, the feedback modifications will come to an end and then the calculations are terminated. It only takes about 2 s to acquire the numerical results which stand for the contour of the freeform reflector with feedback modification. Compared with previous methods about the freeform construction and the headlamp design, such as references [2,8,12] introduced, our method can achieve good results in much more simply and quickly. In reference [2], it took about 20 s to obtain the contour of the freeform surface, while as reference [8] presented, it cost lots of time to optimize all the parameters so as to get the final results. The optical system is rather complex in reference [12]. Moreover, our method mainly focuses on the long distance (25 m or more) nonuniform illumination for the LED source, while the distance for general uniform illuminations is about 10 m [19,22]. Fig. 13(a)–(c) shows the results of the initial designs, after one time and two times feedback modification, respectively, while Fig. 13(d) shows the final light pattern after five times of feedback modification. As shown in Fig. 13(d), though the light pattern in the vertical direction is satisfied, certain divergences appear in both the vertical and horizontal direction. But when taken the illumination requirements of the front fog lamp into account, where a clear cut-off line and a wide light distribution in the horizontal and vertical direction are needed, the effects of the divergence is actually helpful. The comparisons of the initial curve and the feedback curves are shown in Fig. 14, which are corresponding to Fig. 13(a–d), respectively. It shows that some more modifications are needed so as to obtain the required light distribution. In this design, we mainly focus on the distortion correction in the vertical direction, and if the modifications are needed in the horizontal direction, the same method can be applied. Fig. 15 shows the ultimate light distribution of the front fog lamp and the results are generated by three reflectors lain in a line. The dimension (length, width and height) of each reflector is 36 mm 50 m 35 mm and the luminous flux is 200 lm for each LED. It can be seen from that a clear cut-off line is produced on the target plane. According to the ECE regulations R19 revision 7, the light pattern can fully satisfy the lighting requirements of Class F3 front fog lamp. Some measurements are also done on the prescribed area and the test data in each region is shown in Table 1. From Table 1 we can know that the test data in each region is within the limitation of ECE regulations. Furthermore, the energy which is reflected onto whether the road or the target plane is sufficient, which can well fulfill the lighting requirements for front fog lamps. The variation of the LCE during feedbacks is shown in Fig. 16, where the LCE is improved from 66.17% to 77.86%. It shows that the proposed feedback method could effectively improve the LCE. That is mainly because the LCE has a significant relation with the locations of the sampling points, which can change the size of the
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H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
Fig. 12. Geometry of the final optical reflector model.
Fig. 13. The lighting performance before and after feedback method (a) Initial; (b) After one feedback; (c) After two feedbacks; and ( d) the final light pattern.
reflector. When the reflector size changes, the energy that the reflector collects varies correspondingly. However, as the sampling method cannot change the reflector size dramatically, the LCE is just improved on a small scale. In addition, the sampling size determines the accuracy of the feedback function. Theoretically, the larger the sampling size, the more accurate the feedback function.
The tolerance of a freeform surface is an important issue in the optical design. In this design, the tolerance analysis is mainly concentrated on the source translation. For simplicity, the coordinate system is established as shown in Fig. 17. Fig. 18 shows the influence of LED's position to the light distribution. In Fig. 18(a) and (b), the LED source is translated along þz, þx, þy and y directions for
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
0.2 mm, respectively. Both of the two light distributions can still meet the requirements of the ECE regulations R19 revision 7. It indicates that the light distribution is not sensitive to the z axis, x axis and z axis displacements of the source. However, the maximum
131
illumination value decreases from 18 lx to 14 lx and the light pattern extends below the horizontal line when the source is translated from the y axis to the y axis. Anyway, the positioning errors of LEDs have small impacts on the illumination. Fig. 19 shows the illumination distribution on the target plane when the LED source is rotated round the z axis, x axis, y axis and vector (1, 1, 1) for 0.2°, respectively. It demonstrates that the source rotations have a large influence on the illumination. As shown in Fig. 19(a) and (b), when the source is rotated round x axis and z axis for 0.2°, respectively, the illumination along the x axis and y axis deteriorate, especially on the right part of the light pattern. Although the cut-off line is still clear, it inclines a little from the horizontal line. Nonetheless, the light distribution does not vary and can fulfill the requirements of the ECE regulations
Fig. 14. The comparisons of the initial curve and the feedback curves.
Fig. 16. Variation of the LCE during feedbacks and the final.
Fig. 15. The ultimate illumination distribution on the target plane.
Fig. 17. Establishment of the coordinate system for the reflectors.
Table 1 Simulation results of the LED front fog lamp based on ECE R19 Rev7. Designated lines or zones Vertical position above h þ below h
Horizontal position left of v: right of v: þ
Luminous intensity (in cd)
To comply
Simulated results (in cd)
o ¼ 60
All points
o ¼ 20.06
All All All All All All All
points points points points points points points
o ¼ 9.54 o ¼ 21.93 o ¼ 68.61 o ¼ 125.92 o ¼ 218.48 4 ¼4882 o ¼ 1849.04
One or more points One or more points Whole zone
4 ¼2063.87
Point 1, 2 Point 3, 4 Point 5, 6 Point 7, 10 Point 8, 9 Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7
þ60° þ40° þ30° þ20° þ20° þ8° þ4° þ2° þ1° 0° 2.5° 6.0°
745° 730° 760° 740° 715° 26° to 26° to 26° to 26° to 10° to 10° to 10° to
Line 8L and R
1.5° to 3.5°
22° and þ 22°
o ¼ 90 o ¼ 105 o ¼ 170 o ¼ 250 o ¼ 340 4 ¼ 2700 o ¼ 50% of max on line 6 4 ¼ 800
Line 9L and R
1.5° to 4.5°
35° and þ 35°
4 ¼ 320
Zone D
1.5° to 3.5°
10° to þ 10°
o ¼ 8400
þ26° þ26° þ26° þ26° þ 10° þ 10° þ 10°
4 ¼509.29 o ¼ 7832
132
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
Fig. 18. Influences of LED's positions to the light distribution: (a) the LED source is translated along þ z, þ x, þ y directions and (b) þz, þx, y directions for 0.2 mm, respectively.
Fig. 19. Influences of LED’s rotations to the light distribution: the LED source is rotated round the (a) z axis, (b) x axis, (c) y axis and (d) vector (1, 1, 1) for 0.2°, respectively.
H. Wu et al. / Optics & Laser Technology 72 (2015) 125–133
when the source is rotated round the y axis as shown in Fig. 19(c). That is because the LED source is of central symmetry. In Fig. 19(d), the deterioration caused by rotation round vector (1, 1, 1) is worse than that by rotation round the x axis and z axis. Moreover, the light distribution in Fig. 19(a), (b) and (d) can no longer satisfy the requirements of the ECE regulations R19 revision 7. It can be seen from Fig. 19 that the rotation errors can greatly affect the illumination. In short, in order to get better performances, both the positioning error (not more than 0.2 mm) and the rotation error (not more than 0.1°) of LEDs should be strictly controlled. Since the vertical placement is adopted, the volume of the reflector decreases nearly 50%, which brings a great flexibility for front fog lamps design.
5. Conclusions A design method for the light emitting diode front fog lamp based on a freeform reflector is proposed. The placement between the LED source and the reflector is first determined, and the source–target mapping is established. Then, a reflector is constructed and the Monte Carlo ray tracing method is employed for simulation. A feedback function is deduced based on the simulation results and the sampling method. The reflector is regenerated with the feedback function and the deviation could be minimized after several feedbacks. A reflector for the automobile front fog lamp is designed for the OSTAR Headlamp LED source whose emitting surface is 2.8 mm 2.5 mm and results demonstrate that the lighting performance can well accomplish the requirements of ECE regulations R19 revision 7. The LCE is improved from 66.17% to 77.86%. Moreover, this method can be used not only for automobile front fog lamps, but also for motorcycle headlamps, bike lights and reflectors where long distance illumination is needed.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant nos. 91223201, 50825504), the Natural Science Foundation of Guangdong Province (Grant no. S2013030013355), the NSFC United Foundation of Guangdong Province (Grant no. U0934004), and the Fundamental Research Funds for the Central Universities (2012ZP0004, 2013ZM0092).
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