Optik 126 (2015) 4534–4538
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Reflector designed for light-emitting-diode lighting source in three-dimensional space Guangzhen Wang a,∗ , Yu Hou b , Lichun Hu a , Wanwei Tang a , Jian Gao a , Lili Wang c a
Foundation Department, Tangshan College, Tangshan, Hebei 063000, China Physics Department, Tangshan Normal University, Tangshan, Hebei 063000, China State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences, Shanxi 710119, China b c
a r t i c l e
i n f o
Article history: Received 28 July 2014 Accepted 18 August 2015 220.4298 220.2945 080.1753
a b s t r a c t Reflectors used for light-emitting-diode (LED) light source are designed in three-dimensional space to produce uniform illuminance effect. Reflector’s surfaces are calculated by the source-target mapping method in Geometrical Optics. Ignoring scattering and absorption loss of the material, reflectors’ performances are investigated. The simulation results show that the light efficiency which is the ratio of light flux in the target surface to that from LED light source can reach above 95%. And the illuminance uniformity which is the ratio of minimum illuminance (min E) to average illuminance (ave E) also can reach above 95%. Finally, the array of reflectors is investigated and the result shows it still has good performance. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction LED is the very important light source in modern lighting because of its excellent performances. It is widely used in LCD backlight display [1], projection [2,3] and other indoor or outdoor lighting applications. But if LED lighting wants to replace general lighting absolutely, it must overcome many difficulties. Secondary optical design about LED lighting source plays a very important role in modern lighting. Especially, the enhancement of LED chip efficiency [4] and illuminance uniformity must rely on secondary optical design [5,6]. Reflection (e.g., reflectors) and refraction (e.g., lens) components are used to produce desired lighting effect and the design method belongs to inverse problems [7]. It is critical to find the shape of reflector’s surface which reflects light rays from LED source to the desired locations. The design methods of reflectors include no-imaging optics [8], edge-ray theory [9], simultaneous multi-surface method [10], optimization method [11], and so on. But these methods either are used in two-dimension design or have complex design progress and reduce the efficiency of design. Reflector designed in two-dimensional space is about designing only an appropriate curve which simplifies design process but is not very accurate. It is expected to find simple and quick design method in 3D space. In this paper, reflectors are
∗ Corresponding author. Tel.: +8603152312660. E-mail address:
[email protected] (G. Wang). http://dx.doi.org/10.1016/j.ijleo.2015.08.069 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
designed and investigated with the 1 mm × 1 mm LED chip to produce desired illuminance distribution and high light efficiency. Compared with the traditional design methods, this process is very simple and quick and it does not need long-time optimization.
2. Design process Fig. 1 shows the whole design process of the reflectors which includes four parts. Because most LED lamps are lambertian type, lambertian LED source is used as an example here. The emitting angle of LED source is 180 degrees. The wavelength of light is 550 nm. First, theoretic modeling based on Geometry optics and nonimaging optics is established. Second, the coordinates of reflector surface are calculated. Third, reflector entity is established in 3D modeling software using the calculated surface. Finally, the entire optical system is set up to be simulated and analyzed. The theoretic modeling is shown in Fig. 2, in which LED is viewed as a point source at the origin position. The flux from LED can be divided into many parts and every part is within a solid angle d. Fig. 3 describes the calculation process of the reflector’s surface. Fig. 3(a) is for diverging-type reflectors and Fig. 3(b) is for converging-type reflectors. In Fig. 3, if the incident light rays come to the positive direction, the reflector is called diverging-type reflector. If the incident rays come to the negative direction, reflector is called converging-type reflector. Any ray ៝i from LED source
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Fig. 1. (Color online) Four parts of reflector design process. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
incidents at one point on the reflector surface. If the unite vector of reflected ray o៝ at this point is known, the norm vector N(m, n) at this point is calculated by law of reflection: O = i − 2(i• N)N
(1)
A tangent plane D exists at this point which is perpendicular to the norm vector N. Another very adjacent incident ray and tangent plane D determine another adjacent point on the reflector surface. The reflected ray vector o៝ is obtained using point coordinate on the illuminated plane subtracting its corresponding point on the reflector surface. Fig. 3 describes four adjacent points forming a small area and a solid angle d to LED. Light flux in this area should be equal to that in ds on the illuminated surface:
Id˝ = Eds d˝ = sin dd
(2)
where, parameter I is the luminous intensity in this solid angle, parameters and are the elements of solid angle d. And E is the illuminance in the illuminated plane. By using the method of separation of variables, the relationship between coordinate on the reflector’s surface and that on the illuminated surface (R,ω) is:
⎧ ⎪ ⎨
ωm+1 =
⎪ ⎩ R2
n+1
I0 (m+1 − m )
ER02 I0 (cos 2 − cos 2n+1 ) + Rn2 = E
(3)
The letter m and n shows the sequence number of the points. And ω is the element of ds in Eq. (2). Use aforementioned process, all the coordinates of points on the reflector surface can be calculated.
Fig. 3. (Color online) The calculation process of the reflector’s surface. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
3. Reflector entity and simulation 3.1. Constant distance from LED source All the coordinates of points on the reflector surface are calculated in the method in part 2. These data are imported into the 3D software and then combined into surface and 3D entity. The number of calculated points on the surface is 160,000. A reflector entity designed is shown in Fig. 4. Reflector in Fig. 4 can illuminate a circular area with radius of 1 m. The output angle (Eq. (4)) is defined by the ratio of radius R of illuminated area and d which is the distance between LED source and the illuminated area. ˛ = arctan
R d
(4)
From Eq. (4), if d is set a constant, the reflector shape and size only can be influenced by parameter R.
Fig. 2. (Color online) Radiation model of LED. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Fig. 4. (Color online) Reflector entity of (a) top view, (b) isometric view and (c) right view. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
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Fig. 5. (Color online) Surface chart of illuminance distribution for circular area. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
The lighting system includes light source, reflector and the illuminated plane. Monte Carlo method is used in the simulation for ray-traced 100,000 light rays. In the simulation, absorption and scattering loss of the material are ignored because the reflection ability of the surface is even more concerned. Total flux from LED chip is 100 lumen (lm). The depth of the reflector surface is 15 mm which is the vertical distance from the underside to the vertex. It is expected to achieve uniform lighting in a circular area with radius of 1.25 m from 1 m distance. After design and simulation, the surface chart of illuminance distribution in the circular area is shown in Fig. 5. Simulation results indicate flux in this area is 97.7 lm. That is to say the light efficiency is 97.7%, which is closed to the design goal and is high enough for general lighting. If illuminated area’s radius is enlarged to 1.26 m, efficiency can reach 99.8%. The min E is 19.5 lux, max E is 20.8 lux, so the illuminance uniformity is 97.5%. The maximum luminous intensity (max I) and average luminous intensity (ave I) are 69.7 cd and 7.8 cd, respectively. Fig. 6 is the schematic diagram of luminous intensity distributions for different output angles.
Fig. 6. (Color online) Schematic diagram of luminous intensity distributions for different output angles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Fig. 7. (Color online) Performances of reflectors for different output angle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
The distance from light source to the area is set a constant 1 m. It displays bat-wings type of luminous intensity distribution for desired illuminated area with radius of Fig. 6(a) 0.5 m, (b) 1 m, (c) 2 m and (d) 3 m. That is exactly the type of luminous intensity for uniform illuminance distribution. Reflectors can control the flux in the expected output angles. With the radius increasing, spread angle of luminous intensity distribution also increases. Fig. 7 indicates that the performances of reflectors with different output angles. The distance from LED to illuminated plane is also set to a constant 1 m. In Eq. (4), one radius corresponds to one output angle as indicated. Term “r” and “R” are radii of reflector’s underside and the illuminated area, respectively. From Fig. 7(a), when the radius of illuminated area varies from 150 mm to 3000 mm, reflectors have high efficiency and good illuminance uniformity. Most reflectors have efficiencies and uniformities all above 95%. So this type of reflectors can achieve good lighting effect in a wide range of areas with a given distance. Fig. 7(b) is about the illuminance and luminous intensity data whose values are the natural logarithm. Illuminance decreases with the illuminated radius increasing. This is easy to understand, because the product of illuminance and area is a constant 100 lm. So smaller illuminance corresponds to bigger area. The max I value decreases and then it has little change afterwards with radius increasing. Another two types of lighting patterns are investigated as shown in Figs. 8 and 9. Reflectors are designed to produce annular lighting pattern and floriated lighting pattern. Inside radius and outside radius of annular area are 500 mm and 1000 mm, respectively. In the floriated area, one petal has a stretch angle of 30 degree and maximum radius is 1000 mm. From Fig. 8, it can be seen that the reflectors can control light in the desired areas well. Fig. 9 shows the luminous intensity distributions of the two cases. The luminous intensity is controlled well in the specified angles. For a given reflector, it is needed to study the performances of the reflectors whose distance from illuminated area changes. The reflector producing uniform lighting area whose radius is 1 m and distance is 1 m is investigated. That is to say ˛ is 45 degree. The result is shown in Fig. 10. In Fig. 10(a), all the values are natural algorithm and term “radius” is the illuminated area’s radius including all the flux from LED. In Fig. 10(b), although illuminance uniformity is the best at 1 m, in other position it is also above 72%. So the reflector can
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Fig. 11. (Color online) Performances of converging reflectors. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
When the distance is more than 1 m, almost all of the light rays are controlled in the desired area. Fig. 8. (Color online) Illuminance distributions for (a) annular lighting and (b) floriated lighting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Fig. 9. (Color online) Surface chart of luminous intensity distributions for (a) annular lighting and (b) floriated lighting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
be used within a wide range of distances. The “flux percentage” line is the ratio of the flux in the desired 45 degree to all the flux in the illuminated area. The values of the ratio get more bigger with the distance increasing until they reach nearly 100% at 1 m.
Fig. 10. (Color online) Performances of reflector with different distances from LED to illuminated plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
3.2. Converging reflectors Converging reflectors at the same lighting distance with different lighting radius are designed and investigated. Performances are shown in Fig. 11. From Fig. 11, we can see that the radii of the reflectors’ undersides are much smaller than diverging reflectors which is indicated in Fig. 7(a). That is to say, converging reflectors have much smaller sizes. In addition, the radius of reflector decreases with increasing of illuminate area. Ignoring absorbing and scattering loss, light efficiencies can reach as high as 99.9% indicated in Fig. 11(a) which is higher than diverging reflectors. Illuminance uniformity changes from 80% to 90%. Luminous intensity values and illuminance values are logarithms of e. Other regulation is the same to the diverging reflectors as indicated in Fig. 7(b). Although illuminance uniformities are smaller than diverging reflectors, they are also more than 80%. This performance is able to meet the requirements of many lighting situations. In order to increase the illuminance in the illuminated area, several LEDs are often made to array indicated in Fig. 12(a). It indicates a simple circular array with 5 LEDs and 5 reflectors. Designed reflectors can produce a circular lighting with 1 m radius at 1 m distance from LED source. Lighting effect is studied and shown in Fig. 12(b). It shows that this lighting system has high illuminance uniformity. Maximum luminous intensity and average luminous intensity are
Fig. 12. (Color online) Simulation for circular array. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
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321 cd and 39 cd, respectively. Total illuminance value is 494 lux. That is to say the light efficiency is about 99%. Such lighting effect indicates this system can be used in many applications. 4. Conclusion In this paper, Geometry optics and non-imaging optics are used to design reflectors used in LED lighting. In the meanwhile, LED chip of 1 mm × 1 mm is used to investigate the performances of the designed reflectors under different conditions. Reflectors designed with this method have good illuminance effect. The results show that these reflectors have high flux efficiency and good illuminance uniformity. This work offers important information for manufacturing, installing and choosing lamps. Compared with other design methods, this method does not need long-time optimization processes or complex calculation. It does not need other optical elements in an optical system. These reflectors have good performances and far-ranging applications. Acknowledgment This work was supported by Doctoral Fund of Tangshan College Project tsxybc201310 and Doctoral Fund of Tangshan normal University Project 2014A07.
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