Design of a compact modified total internal reflection ... - OSA Publishing

Design of a compact modified total internal reflection lens for high angular color uniformity Shuiming Li,1 Fei Chen,1 Kai Wang,2 Shuang Zhao,1 Zhili Zhao,1 and Sheng Liu1,3,* 1

Division of Micro-Opto-Electro-Mechanical Systems (MOEMS), Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2

Guangdong Real Faith Opto-Electronic Co., Ltd, Foshan 528000, China

3

Institute of Microsystems, State Key Laboratory of Digital Manufacturing Equipment & Technology, School of Mechanical Science and Engineering, Huazhong University of Science & Technology, Wuhan 430074, China *Corresponding author: [email protected] Received 27 August 2012; revised 16 November 2012; accepted 17 November 2012; posted 19 November 2012 (Doc. ID 175010); published 13 December 2012

Total internal reflection (TIR) lenses are optical components that are used to collimate the light or to generate a desired uniform illumination. However, most TIR designs do not pay attention to color uniformity, an increasingly important issue for the quality of lighting, and have a considerable dimension, which also limits their applications. In this study, we proposed an effective design principle of color mixing, and a phosphor-converted white LED module integrated with a compact modified free form TIR component was presented and optimized to achieve compact size and high angular color uniformity (ACU). Optimization results indicated that modified LED packages could achieve a smaller size in vertical height (∼0.52) within the same horizontal radius, compared with LEDs integrated with classic TIR lenses. Meanwhile, the enhancement of ACU with an optimum appropriate divergence half angle (65°) reached as high as 84% in terms of normalized standard deviation of yellow–blue ratio from 0.888 to 0.429. © 2012 Optical Society of America OCIS codes: 220.3630, 230.3670, 330.1720.

1. Introduction

As a rapidly developing light source, light-emitting diodes (LEDs) have been playing a more and more important role in our daily lives. Brighter, smaller, smarter, and cheaper are the development trends of both LED packaging modules and luminaries [1]. LEDs are not sold separately; instead, they are built into a luminaire that consists of one or more LEDs, an optical system, a heat sink and a nice housing. Unfortunately, it is difficult to create an LED that emits light with a uniform white color over an angle. Accordingly, the design of compact optics and high-quality light output is essential for most LED luminaries.

1559-128X/12/368557-06$15.00/0 © 2012 Optical Society of America

Total internal reflection (TIR) components, which constitute a major part of optical devices distinct from reflectors and Fresnel lenses, have been applied successfully to numerous products with directional emergent light beams, such as collimators for small sources (LEDs and HID lamps), injectors for fiberoptics illumination systems, and solar concentrators [2–4]. Desired uniform illumination within a limited beam angle is easy to achieve by integrating LEDs with freeform TIR lenses [4–9]. However, most TIR designs do not pay attention to the color uniformity and have a considerable dimension, which limits their applications. Since phosphor-converted white LEDs have a color variation over an angle [1], it is vital to design a compact illumination optical system with a consideration of angular color uniformity (ACU). Figure 1 shows a classic TIR lens and its simulation analysis of the ACU. The classic TIR lens 20 December 2012 / Vol. 51, No. 36 / APPLIED OPTICS

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has a considerable dimension of 10.26 mmradius × 10.66 mmheight and its divergence half angle is limited to 42° due to collimated rays irradiating on the top surface. Figure 1(b) gives a model of a phosphor-converted white LED, which has been verified in many literatures [1,10,11]. Simulation results of the white LED module integrated with the classic TIR lens is shown in Fig. 1(c). Here, the term “YBR” shown in the vertical axis means the intensity ratio of yellow light to blue light in the far field of a white LED, which indicates the color temperature of the LED. Flat YBR distribution within the viewing angle implies good ACU. It can be found that the LED module integrated with the classic TIR lens has a large color variation (circle dot curve), compared with the bare white LED (square dot curve), and

leads to yellow rings in a high probability within the viewing angles −60° ∼ 60°. Some research efforts have been done to reduce the angular color variation [1,10–13]. Liu et al. demonstrated that the phosphor coating method was the primary factor affecting the ACU and proposed new phosphor coating methods to win optical consistency of white LEDs [10]. In addition, a LED chip with a truncated-conical geometry [12] and a mix of microparticles within the phosphor layer [13] are also two effective ways of enhancing the ACU. However, these methods are complicated and/or costly. From another perspective, Wang et al. demonstrated a color mixing method based on freeform lenses to realize high ACU, which is low-cost and easy to implement [11]. In this study, according to the above viewpoint of color mixing, a phosphor converted white LED module integrated with a modified free form TIR lens made of polymethyl methacrylate is presented and optimized to achieve compact size and high-quality white light output. The color mixing way of the modified TIR lens is different from that presented in [11], which will be explained in detail in Section 2. This white LED packaging can be used to generate wellperforming LED luminaries applying to general lighting with a large viewing angle. 2. Design Principle for High ACU

Fig. 1. (Color online) (a) Classic TIR lens. (b) Traditional white LED packaging. (c) YBR distributions of traditional LED and the LED integrated with a classic TIR lens. 8558

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White LED technology is at the point of surpassing traditional light technologies such as incandescent and fluorescent lamps in light output and lifetime. Phosphor converted white LED technology is widely adopted and such LEDs are created by coating a blue LED die with a layer of yellow phosphor and possibly an additional layer of red phosphor. This phosphor coating converts part of the blue light into yellow or red light, resulting in white light. The converted blue light depends on the distance that a light ray travels through the phosphor layer. Therefore, it is reasonable that the color of the output white light is angle-dependent. Such a property may cause the LEDs to be disqualified in general lighting. The worse condition is that the serious nonuniform color distribution could be perceived by people and is harmful to human eyes. Figure 2 shows the design principle of our optical design. A verified and accurate phosphor converted white LED model is applied in our study, as shown in Fig. 1(b). The white LED model is mainly composed of a chip, a phosphor layer, and a hemisphere lens. Simulation analysis indicates that traditional white LED without any secondary optics has a nonuniform color pattern, low YBR in the center, and high YBR at the edge, as shown in Fig. 2(a). The light emitted normal to the surface is more bluish white, while the light emitted nearly parallel to the surface is more yellowish. Accordingly, we proposed a designated color mixing principle, as shown in Fig. 2(b). The TIR surface “mirrors” one part of rays (yellowish white light) to “mix” with the other part of rays (bluish white light), which enhances the ACU of

Fig. 3. (Color online) Sketch map of designed ray paths through the modified TIR lens.

Fig. 2. (Color online) Design principle of the modified TIR lens. (a) Original YBR distribution and (b) desired YBR distribution.

the LED integrated with the modified TIR lens. Based on the designated light mixing principle, a flatter YBR distribution can be obtained. Theoretically, this color mixing way can perform better compared with the previous work [11] and lead to a uniform YBR distribution more easily. The flat circle dot curve in Fig. 2(b) is an ideal YBR distribution after the traditional LED integrated with the assumed designed TIR component. 3. Design Method of the Modified TIR Lens

In our study, since the circular target and luminous intensity distribution of the white LED both are rotational symmetric, only the contour line of the modified TIR lens’s cross section needs to be calculated. Then rotating this contour line can generate the lens entity. Figure 3 shows the schematic of the designed ray paths through the modified TIR lens. The emitted luminous flux of the initial light source is split into two parts by Surface 1 and Surface 2 with an angle θ, the sparse meshed and dense meshed parts. Both parts of optical power irradiate on the same far target

plane or into the same divergence half angle (β) through the modified TIR lens. Surface 1 is a concave spherical surface and Surface 2 is a cylindrical wall. The concave spherical surface will not change the transmission directions of light rays, so that we can focus on the design of Surface 4. The cylindrical wall is a considerate choice in our design, which makes the incident angles on the total-reflection surface (Surface 3) large enough to generate total reflections. Surface 3 is a circular truncated conical surface with an inclination angle γ, which could save the height of our designed component, compared with the freeform TIR surface shown in Fig. 1(b). As a consequence, the incident light on the top surface is not collimated, which results in a larger divergence half angle (the divergence half angle of classic lenses with collimated light irradiating on the top surface has a maximum value of 42°). Finally, Surface 4 and Surface 5 mix the two parts of optical power within a divergence half angle (β). Therefore, we propose a design method for modified TIR components with discontinuous refractive top surfaces to achieve compact size and high ACU. Based on the aforementioned design principle and method, the lens design procedure includes three main steps [14,15]. First, divide the light source and illumination target plane into equal numerary grids with equal luminous flux and area, respectively. Energy conservation is an assumption in the design. Second, establish the light energy mapping relationship by Snell’s law and edge ray principle and figure out discrete points of the lens’s contour line [14,16]. Finally, construct the lens by lofting method. Since Surfaces 1, 2, and 3 are either conical or spherical surfaces, the calculation of Surface 4 and Surface 5 is relatively more significant. When the incident rays arrive at the top surface, Surface 4 and Surface 5 redistribute the rays onto the prescribed target plane to achieve uniform illuminance [14]. Figure 4(a) shows the generation method of the discrete points (Pi ). We can calculate these discrete points by the incident and exit rays using the inverse procedure of Snell’s law, which can be expressed as follows: ⃗ − nI∕1 ⃗ • I ⃗ O ⃗ ⃗ 1∕2 ; N n2 − 2nO

(1)

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rays are set in the commercial software TracePro to guarantee the accuracy) indicate that the height and radius distributions of modified LED packages along with β have a minimum radius at 50° and a minimum height at 55°, while the NSD distribution curve along with β is monotone decreasing to a certain degree, as shown in Fig. 5(a). When we take ACU in the first place, the enhancement of ACU with an optimum appropriate divergence half angle (65°) reaches as high as 84% in terms of the NSD of the lens’s YBR distribution, from 0.888 to 0.429; simultaneously, compared with the classic TIR lens [10.26 mmradius × 10.66 mmheight], we can achieve a dimension of 10.23 mmradius × 5.49 mmheight, a smaller size in vertical height (∼0.52) within the same horizontal radius at β 65°. Figure 5(b) shows the detailed simulative YBR distributions of the traditional LED and modified TIR lens with β 65°. The YBR distribution of the modified TIR has increased values in the center and reduced values at the edge, which verifies our design idea. Since little optical power is transmitted to

Fig. 4. (Color online) Sketch map of (a) the generation method of the discrete points of the top surface and (b) a designed TIR lens with (θ 60°, γ 45°, β 65°). Modified TIR lens has a larger divergence half angle than the classic TIR lens.

⃗ are the unit vectors of incident and where I⃗ and O ⃗ is the unit normal vector of the tanemergent rays, N gent plane on a refracted point, and n is the refractive index of the lens. As shown in Fig. 4(a), the emergent rays with the same colors own the same emergent directions and are set to mix with each other in the far field so that the low YBR and high YBR will be mixed to generate a medium YBR. Figure 4(b) shows a designed modified TIR lens with (θ 60°, γ 45°, β 65°), whose radius is 10.23 mm and height is 5.49 mm. 4. Optimization Results and Discussions

In order to find an optimum modified TIR lens, optimization by changing the parameters is essential. For the sake of simplicity, only the divergence half angle (β) is optimized to minimize the dimension and maximize the ACU. θ and γ are set as 60° and 45°, respectively. In our work, normalized standard deviation (NSD) [17] is used to evaluate the variation of YBR and defined as NSD

1 σYBR; EYBR

(2)

where EYBR is the average value of YBRs and σYBR means the standard deviation of the YBR distribution. A lower NSD represents a smaller YBR variation within the viewing angles and a higher ACU. Analysis results of modified TIR components by changing the divergence half angle from 40° to 65° based on Monte Carlo ray tracing method (1 million 8560


Fig. 5. (Color online) (a) Optimization processes of minimizing modified TIR lens dimensions as well as maximizing the ACU and (b) YBR distributions of the traditional LED and modified TIR lens with β 65°.

and Surface 5 are set to overlap and compensate each other on the target plane, respectively, the relative uniform illuminance distribution can still be achieved easily even without any illumination optimization. 5. Conclusions

An effective color mixing method is proposed to enhance the ACU of phosphor converted white LEDs and a modified TIR lens is designed to integrate with the white LED to verify the design idea. From above simulation results, we conclude that the proposed TIR optics can not only be used for traditional directional lighting (small divergence angle) but also be applied to general lighting (large divergence angle) to achieve high ACU. Analysis results of the modified TIR component based on Monte Carlo ray tracing method indicate that by comparing with the traditional LED integrated with the classic TIR lens, the modified LED package has the advantages of low profile, small volume, and high illuminance uniformity. More importantly, an enhanced ACU is achieved based on the modified TIR lens and the optimum divergence half angle is 65°. In summary, the phosphor converted white LED integrated with the compact modified TIR lens can provide high quality lighting within a flexible divergence angle, which can apply to many illumination fields such as local lighting and general lighting. This work was supported by the National Natural Science Foundation of China (No. 50835005) and National High Technology Research and Development Program of China (No. 2011AA03A106). References

Fig. 6. (Color online) (a) Detailed structure of the packaging. (b) Relative illuminance distributions on a 700 mm × 700 mm target based on the extended light source in one meter away. Uniformity of illuminance is enhanced by 19.9% from 53.1% to 63.7%. Larger divergence angle of the modified TIR lens results in lower central illuminance compared with the classic TIR lens while the marginal illuminance of the modified TIR lens on a large enough receiver is higher (not shown here).

the edge angle, the YBR values within more than 75° are meaningless and not presented in the figure. In addition, illuminance analysis of the LED package with the modified TIR component with β 65° is also carried out. As shown in Fig. 6, compared with classic lenses, an enhanced performance of illuminance uniformity (enhancement: ∼20%) on the desired target plane is achieved with the modified LED package. Since the modified TIR lens owns a larger divergence angle, it’s reasonable that its central illuminance is lower than that of the classic lens. Although we adopt the extended white LED model, as the two parts of luminous flux through Surface 4

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