The design of LED rectangular uniform illumination lens system

Accepted Manuscript Title: The design of LED rectangular uniform illumination lens system Authors: Yong Shi, Baicheng Li, Mantong Zhao, Yao Zhou, Dawei Zhang PII: DOI: Reference:

S0030-4026(17)30452-7 http://dx.doi.org/doi:10.1016/j.ijleo.2017.04.049 IJLEO 59091

To appear in: Received date: Revised date: Accepted date:

15-6-2016 30-3-2017 14-4-2017

Please cite this article as: Yong Shi, Baicheng Li, Mantong Zhao, Yao Zhou, Dawei Zhang, The design of LED rectangular uniform illumination lens system, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.04.049 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The design of LED rectangular uniform illumination lens system Yong Shi, Baicheng Li, Mantong Zhao, Yao Zhou, Dawei Zhang University of Shanghai for Science and Technology, Ministry of Education Optical Instrument and Systems Engineering Center, and Shanghai Key Laboratory of Modern Optical System, No. 516 Jungong Road, Shanghai 200093, China Abstract Freeform lenses are playing a more and more important role in LED secondary optics design. In this paper, based on the lighting-energy conservation law, edge-ray principle and Snell's law, we present a freeform lens optical system design method for LED lighting. This system can achieve rectangular lighting area, and it is easier to precisely control the angle of light emitting and processing, with the advantages of uniform illumination. The software Matlab and Rhino were used to get the model of lens, and the PMMA was used as the material to design lens model. Finally, the numerical simulation results showed that the spot shape was close to the expected results. Keyword freeform lens; light emitting diode (LED); rectangular uniform illumination 1. Introduction Theoretically, LED has many advantages, such as long lifetime, environmental protection, high reliability and low-power consumption. With the luminous flux of a single light-emitting diode increasing, LED lighting applications become more widely. However, most LED chips are approximately Lambertian light source, which

makes it hard to meet the requirements of illumination[1, 2]. Therefore, it is essential to design a secondary optics method for high quality LED illumination. Since the light pattern of an LED is approximately a circle spot, circle illumination is easier to achieve and more uniform. However, in some particular situations or systems, circular illumination is not suitable and other shape of light patterns such as rectangular illumination may meet the requirements. Fly eyes is a way of achieving rectangular illumination[3, 4]. But the presence of multiple internal refraction and reflection causes the loss of light, which also reduces the illumination uniformity of the target plane. LED arrays are used in rectangular illumination by means of reversing design[5], which requires a lot of time and can’t be applied in narrow space. Energy feedback freeform lenses design[6] is used in uniform illumination of extended light source LEDs, but it will be more complex when we use this method in rectangular uniform illumination lens system. Because this method needs programming complex programs and doing complicated mathematical calculation and it’s not suitable for low-power lighting design. In this paper, we propose a new system by using lighting-energy conservation law, edge-ray principle and Snell's law, which is easier to implement and can be installed in a very small place. It can save both time and space. Based on the lighting-energy conservation law, edge-ray principle and Snell's law, this paper provides a method to design freeform surface lens, and to distribute the energy of LED light source according to the radiation characteristics of LED and the requirements of the illumination distribution on the target plane. Correspond to the

rectangular illumination area on the target plane, the relationship between the angle of the exit light of LED light source and the target plane coordinates is set[7]. This paper applies correspondence relationship to the refracting and reflecting theory to establish differential equations, and then set the initial conditions to solve the equations in order to obtain the coordinates of these points on the free surface. In this paper, we use Lambertian LED light source to design freeform surface lens, and use optical software to simulate, which can find whether the simulation results are similar to the theoretical ones. 2. Partial Differential Equations We use the ideal Lambertian LED light source and free-form surfaces optical system to obtain a uniform rectangular beam on the illumination surface[8, 9]. Before establish the differential equations, we need to determine the coordinates of the source, free-form surfaces and the lighting surface. In the Cartesian coordinate system, the center of the light emitting surface is set at the origin of the coordinate system, and the lighting surface is rectangular which was set up at a distance of h from the light source plane[10-12]. 2.1. Location formula According to the method to establish the coordinate system above, we set the coordinate system of the optical system, which is shown in Figure 1. The lens has an incident surface and an exit surface. For simply, the incident surface is designed as a spherical surface, and the LED light source is placed in the

center of the sphere, therefore the incident ray does not change the direction after it through the surface. The exit surface is a freeform surface, which can control the distribution of the light energy[13]. The light source coordinate is established as the origin of the coordinate system, the LED screen is set in the XY plane, and the normal direction of the screen is the Z axis. In the two-dimensional case, such as in XZ plane, the vector form of the catadioptric theorem can be written as: [1 + 𝑛2 − 2𝑛(𝒐𝒖𝒕 • 𝒊𝒏)]1/2 𝑵 = 𝒐𝒖𝒕 − 𝑛𝒊𝒏

(1)

In the formula (1), n is the refractive index of the freeform surfaces; N is the normal direction at the intersection A, which is intersection of the freeform surface and the incident light; in and out is the incident and outgoing light respectively, where he target plane and the outgoing light rays intersect at the point B. We assume that the center of the LED light exposure to the center spot of the target surface[14]. This part of the energy in the illumination target surface is 𝐸0 = 𝐼0 /ℎ2 , and h is the distance from the light source to the target surface. The intersection of the incident ray and the freeform surface is point A, and its coordinates is (x, z), the intersection of the refract light and the target surface is point B, and its coordinates is (r, h), thus we can get that out=(r-x, h-z), in=(x, z), N=(-dz, dx). We put the three vectors into the law of the refraction and get the formula (2) below. 𝑑𝑧⁄𝑑𝑥 = (𝑛𝐷 − 𝐵)⁄(𝐴 − 𝑛𝐶)

(2) Where

A=

(ℎ − 𝑧)⁄[(𝑟 − 𝑥)2 + (1 + 𝑧)2 ]1⁄2 ; B = (𝑟 − 𝑥)⁄[(𝑟 − 𝑥)2 + (ℎ − 𝑧)2 ]1⁄2 ;

C = 𝑧⁄[𝑥 2 + 𝑧 2 ]1⁄2 ; D = 𝑥⁄[𝑥 2 + 𝑧 2 ]1⁄2 . 2.2. Establishment of light energy mapping relationship The differential equation (2) contains three variables, r、x and z, and it has no solutions. We use energy conservation to find the relationship between r、x and z. Assuming that the energy of the lens system without absorption loss, and the target surface energy equal to the theoretical output of the energy source, we can achieve energy conservation. 𝑟

𝜃

2𝜋 ∫0 𝐸(𝑟)𝑑𝑟= 2𝜋 ∫0 𝐼0 𝑐𝑜𝑠 𝜃 𝑠𝑖𝑛 𝜃𝑑𝜃

(3)

E(r) is a function of the target surface illumination distribution, because the illumination on the target is uniform, E(r) is constant. If the LED light is incident at the center of the light spot on the target plane, the illumination is 𝐸0 , then 𝐸0 = 𝐼0 /ℎ2 , and the integral formula (3) is r = (ℎ2 ⁄2) sin2 𝜃, due to sin 𝜃⁄𝑥 = (𝑥 2 + 𝑧 2 )−1⁄2 , the x, z is shown in formula (4). 1

𝑥2

𝑟 = 𝑓(𝑥, 𝑧) = 2 ℎ2 𝑥 2 +𝑧 2

(4)

We bring 𝑟 = 𝑓(𝑥, 𝑧) into the formula (2), and get 𝑑𝑧⁄𝑑𝑥 = (𝑛𝐷 − 𝐵)⁄(𝐴 − 𝑛𝐶), which only has variables x and z. We set the initial coordinates of the point (x0，z0), and set length H. The initial coordinates of the point is associated with the size of the lens. Using Runge-Kutta method to calculate the differential equations, we get its numerical solution, that is the

coordinates (X0，Z0)，(X1，Z1)，(X2，Z2)，……(Xm，Zm) of the stub, which is the stub of the freeform surface and the XZ plane. 3. Simulation results According to this design method, one freeform lens will be designed as an example for one LED to form a uniform rectangular illumination area. And the parameters of variables are shown in Table 1. We import the coordinates and parameters into the software Matlab, and it forms the curves of lens. On the basis of a freeform surface we can make a lens, and finally get a lens model. The curves of LED lens are shown in Figure 2. The lens model is created by the software Rhino, which is shown in Figure 3. We put the solid model into light optical simulation software to simulate, and set the practical optical model of Cree XR-E LED with this freeform lens. The simulation result is shown in Figure 4. The LED chip area is 1mm×1mm, and is 100lm/w. Considering the converted light, yellow light, irradiation from the phosphor layer, the area of the light source in the optical module is set to 1.08mm×1.08mm. Since the distance from the chip to the outside surface of the lens is less than 5 times the chip size, this practical LED could not be regarded as a point light source according to the far-field conditions of LEDs. From simulation results shown in Figure 4, we can find that, due to the increasing size of the light source, the edge of the light pattern becomes dim and the effective illumination area is 199.6mm×102.8mm. From the

Illumination Mesh Shade in Figure 5, we can find that the uniformity of the light is 82%. 4. Discussions and Analyses In order to evaluate this system more thoughtfully, we also change the size of the light source and the influence of LED’s size on this system is shown in Figure 6. We can find that the uniformity will decrease a little rapidly when the size is larger than 2mm×2mm, but all the uniformities are still approximately 80% which means this system is suitable for several specific size extended light source. And with this system, we can control the angle of light emitting and processing precisely. We simplify the lighting system we used and take it as an example, which is shown in Figure 7. In this system, light emitting from source along the direction of Z axis (perpendicular to the target surface) won’t change the direction after passing through the free-form surface and will reach the center of the lighting target area. The θ is the angle between Z axis and the emitting light of the source. If the θ is bigger, the light will be closer to the edge of the lighting target area after passing through the free-form surface, and the light with the maximum divergence half-angle (boundary rays) will reach the edge of the lighting target area. Similarly, the smaller the θ is, the closer to the center of the lighting target area the light will reach. The ratio of light intensity between specific region on lighting target area and entire lighting target area equals to the illuminance of the lighting target area times the

area ratio between specific region on lighting target area and entire lighting target area. According to that, we get following formula, 𝜋𝐼0 (1−cos 𝜃) 𝜋𝐼0 (1−cos 𝜃𝑚𝑎𝑥

𝐸∙𝜋𝑟 2

= 𝐸∙𝜋𝑅2 )

(5)

Where 𝑟 = 𝑓(𝑥, 𝑧), r and R are the radius of specific region on lighting target area and entire lighting target area respectively. And because of the uniform illumination, the illuminance E is a constant, so we can get 1−cos 𝜃

r = R√1−cos 𝜃

𝑚𝑎𝑥

𝑧

Where cos 𝜃 = √𝑥 2

+𝑧 2

(6)

.

So we can determine the location range of all light by only considering the boundary rays. Besides, as is shown in Figure 1, according to the mapping relation between the shape parameters and coordinates on lighting target area as well as energy conservation law, we can determine the normal of each point on free-form surface by numerical calculation, and then determine the direction of each light accurately. Thirdly, the refractive index of the free-form lens n can be changed when it’s necessary. These factors make it helpful to control the angle of light emitting and processing. 5. Conclusions In this study, a modified freeform lens design method was presented for rectangular prescribed illumination, with the advantage of a flexible energy mapping relationship. And the numerical simulation results demonstrated that the light pattern of the lens was almost agreement with the expected illumination performance. And

the light area is approximately rectangular and the light is uniform. However, the TIR loss should be considered in the design method in practical manufacture. Acknowledgments This work was supported in part by the National Basic Research Program of China (973 Program) under Grant 2015CB352001, by the National Science Instrument Important Project under Grant 2011YQ14014704, by the Shanghai Municipal Science Instrument Important Project under Grant 14142200902, and by the National Natural Science Foundation of China under Grant 61378060 and Grant 61205156. References [1] G.-h. Yang, L.-h. Mao, C.-h. Huang, W. Wang, W.-l. Guo, Design and fabrication of Si LED with the Nwell-P+ junction based on standard CMOS technology, Optoelectronics Letters, 6 (2010) 15-17. [2] Y. Guiying, J. Ji, N. Xiaowu, Z. Yingjun, Design for LED Uniform Illumination Reflector Based on tendue, Acta Optica Sinica, 29 (2009) 2297-2301. [3] Z. Ping, Fly Eye Lens Array Used in Liquid Crystal Projection Display with High Light Efficiency, Acta Optica Sinica, (2004). [4] M. Shen, H. Li, W. Lu, X. Liu, Method of reflective fly eye lens design for LED illuminating projection system, Acta Photonica Sinica, 35 (2006) 93-95. [5] K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, S. Liu, New reversing design method for LED uniform illumination, Opt Express, 19 (2011) A830-A840. [6] Z. Li, S. Yu, L. Lin, Y. Tang, X. Ding, W. Yuan, B. Yu, Energy feedback freeform lenses for uniform illumination of extended light source LEDs, Applied Optics, 55 (2016) 10375-10381. [7] T.O. Pang, J.M. Gordon, A. Rabl, C. Wen, Tailored edge-ray designs for uniform illumination of distant targets, Opt Eng, 34 (1995) 1726-1737. [8] P.T. Ong, J.M. Gordon, A. Rabl, Tailoring lighting reflectors to prescribed illuminance distributions: compact partial-involute designs, Applied Optics, 34 (1995) 7877. [9] R. Winston, J.C. Miñano, P. Benítez, Nonimaging Optics, 2005. [10] I. Moreno, C.-C. Sun, Modeling the radiation pattern of LEDs, Opt Express, 16 (2008) 1808-1819. [11] K. Wang, X. Luo, Z. Liu, B. Zhou, Z. Gan, S. Liu, Optical analysis of an 80-W light-emitting-diode street lamp, Opt Eng, 47 (2008) 013002. [12] L. Wang, K. Qian, Y. Luo, Discontinuous free-form lens design for prescribed irradiance, Applied Optics, 46 (2007) 3716. [13] K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, X. Luo, Freeform LED lens for rectangularly prescribed illumination, Journal of Optics A Pure & Applied Optics, 11 (2009) 105501. [14] S. Hu, K. Du, T. Mei, L. Wan, N. Zhu, Ultra-compact LED lens with double freeform surfaces for uniform illumination, Optics Express, 23 (2015) 20350-20355.

Figure Caption

Figr-1

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Figr-4

Table 1 Parameters of variables Variable

Parameters

Area S

4cm×2cm

Height H

10cm

Index of refraction n

1.4935