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A novel freeform lens structure made up of two surfaces is proposed and optimized to enhance the color spatial uniformity (CSU) of white light-emitting diodes (LEDs). Compared with our previous method, an improved design method by optimizing the light energy mapping relationship is proposed to eliminate the dark area, which appears in the illumination pattern due to a deep batwing luminous intensity distribution. Moreover, experiments with a significant evaluation function are performed and demonstrate that the CSU in terms of color difference () can be enhanced as high as 92%. In addition, this novel lens can further improve the CSU of white LEDs with conformal coating. High-quality illumination pattern without yellow rings and dark areas can be realized based on this novel freeform lens with little light loss.
©2012 Optical Society of America
1. Introduction
Having advantages of energy saving and environmental friendliness, light-emitting diode (LED) has emerged as a promising light source in many applications, such as road lighting, automotive lighting, general lighting, backlighting for LCD display, etc [1–3]. Over recent years, LED’s luminous efficiency has increased rapidly. Besides efficiency, the major challenge for general lighting is the quality of white light, with one index defined as color spatial uniformity (CSU) [4], especially for phosphor-converted LEDs. Compared with traditional light sources such as incandescent and fluorescent lamps, phosphor-converted white LEDs encounter a critical issue of CSU in general lighting [4,5]. Significant research efforts have been devoted to analyzing the CSU of LED luminaires and phosphor coating method is proved to be the primary factor affecting the CSU [6]. The widely adopted phosphor coating process known as a freely dispersed coating is easy to be realized and at a low cost [6,7], but may result in yellow rings in the illumination pattern [7,8], which will reduce the CSU. This problem can be overcame by adopting other two phosphor coating methods: conformal phosphor coating and remote phosphor coating [6,9]. In addition, novel LED chip with a truncated-conical geometry and mixing micro particles with the phosphor layer are also two effective ways to enhance the CSU [10,11]. Although these methods are effective to achieve high CSU, most of them are complicated and/or costly.
In order to enhance the CSU of phosphor-converted white LEDs, we previously proposed an efficient way based on freeform lenses [12]. Light exiting from the side and top surfaces of the freeform lens overlapped each other and irradiated on the target plane uniformly. Compared with the traditional LED, which adopts a hemispherical dome lens, the modified LED module was demonstrated to be an attractive and low-cost packaging. The Monte Carlo ray tracing simulation results indicated a huge enhancement of 186.5% in CSU. However, this method put more attention on the enhancement of CSU but less on the illumination pattern. Our further analysis shows that the deep batwing luminous intensity distribution may lead to a dark area and a bright ring in the illumination pattern as shown in Fig. 1 , which is mainlycaused by the fact that little light irradiates on the center of the target plane. Here, we introduce the luminous intensity contrast ratio (LICR) to describe the central luminous flux proportion:
wherein I0 and max(I(γ)) are the central and maximum luminous intensities of a light source in −90°-90° and γ is the angle between the light ray and the vertical axis of the luminaire. A higher LICR represents a brighter center. In this study, an improved design method by optimizing the light energy mapping relationship is proposed to eliminate the dark area. Experiments are also conducted to study the effects of the freeform lenses on eliminating yellow rings caused by the freely dispersed coating, and a significant evaluation function (<0.004) is proposed to evaluate the actual color variation. Both simulations and experiments demonstrate that high-quality illumination pattern without yellow rings and dark areas can be achieved based on the new designed freeform lenses.
Fig. 1 (a) Actual illumination pattern taken by a CCD camera and (b) the measured LICR of a white LED integrated a designed freeform lens.
2. Evaluation function of CSU
From a number of studies about the CSU of white LEDs, the angular correlated color temperature (CCT) is commonly used to indicate the CSU [3,12,13]. It seems to be reasonable to take the CCT as a one-dimensional description of the color of near-white light sources. However, Borbély et al. presented seven subjects with the task of matching 12 colors whose chromaticity coordinates were slightly off the Planckian locus with the closest color on the locus and found that the scatter in the individual observations was “tremendously large” [14]. The authors concluded that CCT was nothing more than a shorthand description of whether the light was bluish-white, neutral, or reddish white. On the other hand, the U.S. Department of Energy (DOE) recommended the use of CSU in terms of chromaticity to describe the color uniformity [4], which proves that the variation of chromaticity is more scientific and precise than the angular CCT deviation. When a composite variation of chromaticity within a color pattern exceeds a certain threshold, humans can perceive the color inhomogeneity. Although rough deviations (Δx = xmax-xmin, Δy = ymax-ymin) of chromaticity coordinates are relatively better when compared with the CCT [10], there is still an absence of a scientific evaluation function of CSU which takes human visual perceptions into consideration.
Accordingly, in this paper we introduce an evaluation function color difference () to evaluate the CSU, which is expressed as follows [4,15]:
wherein un and vn are weighted averages of the chromaticity coordinates, is the illuminance of the i-th measured point, and and are the chromaticity coordinates on the CIE 1976 Uniform Color Space (UCS) diagram. If the of every measured point (n points are measured in angular directions) is below 0.004 [4], which implies that the angular chromaticity coordinates fall within one MacAdam ellipse [15], the color of the white LED is regarded as strict homogeneous in space.3. White LED modeling
In this analysis, a proved white LED model is employed for the numerical simulation [16,17], as shown in Fig. 2 . The blue chip dimensions are 1mm1mm0.1mm and the thicknesses and compositions of the LED materials in the blue chip are given in Fig. 2(a). Absorption coefficients and refractive indices for n-GaN, MQW, and p-GaN are 5 mm−1, 8 mm−1, and 5 mm−1 and 2.42, 2.54, and 2.45, respectively. The specular reflectance of the reflecting layer (Ag) is set to 0.95. In this way, we obtain the precise blue chip model, which is encapsulated with a phosphor layer and a hemisphere silicone lens to form a traditional white LED as shown in Fig. 2(b). The phosphor concentration is 0.35g/cm3. Based on the Mie scattering model, the absorption and scattering coefficients of phosphor are 3.18 mm−1 and 5.35 mm−1 for blue light and 0.06 mm−1 and 7.44 mm−1 for yellow light. Blue and yellow light are separately calculated by a Monte Carlo ray-tracing method. To simplify the simulation, specific wavelengths of 465 and 555nm are used in the simulation to represent blue and yellow light. The intensity ratio of the converted yellow light to the escaped blue LED light determines the overall color uniformity of the white LED. Therefore, we introduce the yellow-blue ratio (YBR) to illustrate the CSU in the simulations [12]. CSU is defined as the ratio of the minimum YBR to the maximum YBR in the range of −90°-90°.
Fig. 2 (a) Blue chip adopted for (b) a traditional white LED model. (c) YBR distribution of the traditional white LED.
According to our simulation results, as shown in Fig. 2(c), the YBR distribution is inverted bell-shaped. Traditional LED module has a low CSU (YBRmin/YBRmax) of 0.33, and moreover, high YBRs at side angles may result in yellow rings in the illumination pattern. Mismatch of the yellow and blue luminous intensity distributions in the far field leads to a low CSU. Thus, we propose a freeform lens integrating the traditional LED to redistribute the YBR to improve the white light quality.
4. Optimized design and numerical simulation of freeform lenses
Since both the circular target and luminous intensity distribution of the light point source are central symmetrical, the lens is designed as axis-symmetrical. Therefore, we only calculate the contour line of the lens’ cross section. In general, the lens design method includes three major parts [18]. Firstly, we divide the emitted luminous flux from the point source into two parts. Secondly, we establish the light energy mapping relationship between the luminous fluxes within the two parts and the target plane by edge ray principle and Snell’s law, respectively. In order to achieve high CSUs and LICRs, the light energy mapping relationship is optimized to realize a high-quality illumination pattern, which will be illustrated in detail in the following sections (Section 4.1 and 4.2). Therefore, discrete points of the lens’ contour can be obtained. Finally, we construct the lens using lofting method. For the design and manufacturing convenience, the inner surface of the lens is designed as a concave spherical surface, which will not change the transmission direction of the incident light from a point source. Therefore, we will focus on the construction of the outside surfaces in the lens design process. In addition, it is necessary to note that a start point [18] with an appropriate height ranging from 5.0mm~7.0mm should be fixed first when starting to design the lens, which also determines the central height of the lens. Two of the designed lenses are shown in Fig. 3 and the ray tracings of these two freeform lenses are also presented.
Fig. 3 Lenses designed with different light energy mapping relationships. (a) Uniform and (b) non-uniform illumination design methods.
4.1 Uniform illumination design method
As shown in Fig. 4(a) , light rays within radiation angles of 0°-90° don’t overlap. While the LED is integrated with a freeform lens as shown in Fig. 4(b), the luminous flux is divided into two parts: Part I, within radiation angles of 0°-θ, exits through the top surface and covers the emergence angle of β; Part II, within radiation angles of θ-90°, exits through the side surface and covers the emergence angle of ω at the same time. Here, β and ω are called the divergence half angles (DHAs) of the top and side surfaces. The side and top surfaces of the freeform lens are designed according to a practical optical design method [18]. Light within Part I and Part II will uniformly irradiates on the target plane. Figure 3(a) shows a designed lens with (β:ω) = (60:60) at θ = 45°.
Based on this design concept, different freeform lenses are obtained by varying the DHAs (β:ω) of the top and side surfaces, as shown on the horizontal axis of Fig. 5(b) . According to simulation results, light rays are redistributed due to the freeform lenses. A YBR distribution comparison between the traditional LED and modified LED with (β:ω) = (60:60) at θ = 45° is shown in Fig. 5(a). Compared with the traditional LED (black line), modified LED (red line) has a smaller angular YBR deviation. Freeform lens, by increasing the YBRs within the central region and reducing the YBRs within the marginal region, flats the YBR curve, which means the enhancement of CSU. Essentially, all the designed lenses have the same effect: higher YBRs at central angles and lower YBRs at side angles compared with traditional LED, which agrees with the design idea.
Fig. 5 (a). YBR distributions of the traditional LED and modified LED. (b). Simulated CSUs and LICRs of white modified LEDs based on the uniform illumination design method.
It can be found from Fig. 5(b) that CSU increases and LICR decreases with the increasing DHA (β:ω). At θ = 30°, LED integrated with the freeform lens with 60:60 performs the best with CSU = 0.71. However, its LICR equals 61.5%, which may result in a dark area in the center of its illumination pattern. Further analysis of Fig. 5(b) shows that simulation results of θ = 30° and θ = 45° have a similar situation: CSU increases and LICR decreases as the DHA becomes larger. Therefore, a compromise has to be made between CSU and LICR.
To find out a better compromise between CSU and LICR, we choose θ to be 40°. β:ω is set to be 45:45 and 65:65, respectively. Results are shown in Table 1 . The CSU of the LED integrated with the lens with β:ω = 65:65 is 2.75 times that of the traditional LED, increasing from 0.33 to 0.88, which indicates a significant improvement. But its LICR is 48.2%. It can be found that taking both CSU and LICR into consideration, the freeform lens with (θ = 40°, β:ω = 45:45) is slightly better than most of the lenses at θ = 30° and θ = 45° because of its improved CSU (an enhancement of 70% from 0.33 to 0.56) and a high LICR (>80%).
Table 1. Results of Freeform Lenses at θ = 40°
4.2 Non-uniform illumination design method
In this section, optical power of Part I is set to irradiate on the target plane non-uniformly and optical power of Part II still uniformly irradiates on the target plane. Therefore, the top surface is set to be a spherical surface and θ is fixed at 45°, as shown in Fig. 6(a) . A spherical surface will cause more optical power of Part I to irradiate on the center of the target plane, which helps eliminate the dark area due to the improvement of LICR. Based on this design method, Fig. 3(b) shows one designed lens with (R,ω) = (20mm,60°) at θ = 45°.
Fig. 6 (a). Sketch map of the light output of a modified LED. (b). Simulated CSUs and LICRs of white modified LEDs based on the non-uniform illumination design method.
There are two groups of lenses, ω = 45deg and ω = 60deg. Each group contains five lenses, whose radii of the top surfaces vary as shown in Fig. 6(b). It is obvious from the figure that CSU increases and LICR decreases as the radius increases, which implies the same inverse relation as the uniform illumination design method. However, the LICRs are less sensitive to the radius and always higher than 75%, compared with those of the lenses shown in Fig. 5(b). More than half of these lenses have a CSU higher than 0.50 and a LICR higher than 80%.
Based on the above analyses of 22 lenses, we conclude that freeform lenses, no matter they are designed with the uniform or non-uniform illumination design methods, can improve LED’s CSU. However, LED’s luminous intensity is redistributed from Lambertian type to batwing type, which may lead to a dark area and a bright ring in the illumination pattern. It has been found that as the DHA increases, CSU becomes higher and LICR gets lower. This is because a larger DHA results in more light being transmitted towards side angles. Further analysis shows that the lenses based on the non-uniform illumination design method lead to an acceptable compromise more easily than the ones based on the uniform illumination design method. Good optical performance can be achieved by optimizing the parameters (the DHA and radius) of freeform lenses.
5. Experiments and analyses
Three lenses, whose CSUs are greater than 0.5 and LICRs are more than 80%, are selected among the 22 lenses for experiments, as shown in Table 2 . Also, another lens (Lens I) is selected because it has the highest CSU and lowest LICR.
Table 2. Lenses Chosen for Manufacturing
Figure 7(a) shows the manufactured lenses, made of PMMA (n = 1.49) using the machining process with a diamond cutter. The machining process adopts CAD/CAM system to control the numerical control machine. The four lenses are labeled and integrated with a white Lambertian LED as shown in Fig. 7(b). We fabricate the bare white LED with the freely dispersed phosphor coating process, which accords with the simulated white LED model.
In order to test the performance of the modified LEDs, we have designed a test system, as shown in Fig. 8 . A heat sink shown in Fig. 8(c) carries the LED and strengthens the heat dissipation, which reduces the chromaticity shifts caused by heat at the p-n junction. An angle regulator shown in Fig. 8(d) is used to control the angle of LED rotation. In other words, the heat sink is rotated around the vertical axis relative to the ground along with the angle regulator. In the experiment, we employ a digital colorimeter provided by Xinye Optoelectronic Engineering Co., Ltd. The colorimeter is connected to a computer, which displays and stores the measured data, as shown in Fig. 8(e). Besides, the fixed LED is one meter away from the colorimeter, which ensures the test is in the far field. The test system is applicable to virtually any LED module and can measure various important parameters including the illuminance, CCT, and chromaticity coordinates in the range of −90° to 90° in steps of 5°. Therefore, 37 sets of data are achieved in one test. To improve the test accuracy, the entire testing process should be completed in a darkroom, which ensures there is no stray light.
Fig. 8 (a). Schematic diagram of (b) the test system. (c). Heat sink. (d). Angle regulator. (e). User interface of the software.
5.1 Analysis of CSU
By substituting the measured data into the evaluation function of CSU, we can obtain the angular color difference () distributions of the LEDs ranging from −90° to 90°. Figure 9(a) shows the distributions of the bare LED and Lens IV. The distribution of the bare LED is “W” type, which implies that the central and marginal colors deviate much from the average white color. This can be explained by the property of white LEDs with the freely dispersed phosphor coating: bluish white at around 0° and yellowish white at around 90°. Color inhomogeneity influences the actual illumination effects and results in discomfort in human eyes, as shown Fig. 10(a) . Compared with the bare LED, the distribution of Lens IV is flatter and more points (<0.004) meet the requirements for solid state lighting luminaires. Statistic analysis of qualified points of each LED is shown in Fig. 9(b). The quantities of <0.004 ranging from −90° to 90° for the bare LED, Lens I, Lens II, Lens III, and Lens IV are 12, 17, 15, 14, and 23, which demonstrate that Lens I, Lens II, Lens III,and Lens IV have enhanced the CSU by 41.7%, 25.0%, 16.7%, and 91.7%, respectively. A remarkable improvement of around 92% is achieved by Lens IV.The blue and yellow light rays are redistributed and a more uniform white color pattern has been realized via freeform lenses.
Fig. 9 (a). Color difference () distributions of the bare LED and Lens IV in −90°-90°. (b). Quantities of qualified points of different LEDs.
Fig. 10 Comparison of (b) measured luminous intensity distributions and illumination patterns of (a) the bare LED, (c) Lens I, (d) Lens II, (e) Lens III, and (f) Lens IV. The actual LICRs of Lens I, Lens II, Lens III, and Lens IV are 32.6%, 61.4%, 64.4%, and 71.8%, respectively.
The comparison of the illumination patterns of the LEDs is shown in Fig. 10. Obviously, yellow rings are eliminated for the modified LEDs. Freeform lenses distribute the central rays into side angles especially for blue light and the side rays into central angles especially for yellow light. Therefore, central bluish white light and side yellowish white light compensate each other and an enhanced CSU is obtained. However, the dark area appears as predicted in the simulation. It can be found from Fig. 10(b) that Lens I has a low LICR of 32.6%, so there is a dark area and a bright ring in its illumination pattern as shown in Fig. 10(c). Nevertheless, other measured LICRs of Lens II, Lens III, and Lens IV are 61.4%, 64.4%, and 71.8% respectively and these three lenses perform well in the aspect of dark areas. Compared with the illumination pattern of Lens I, dark area is virtually eliminated in other patterns because of the improvement of LICR.
From the simulation as well as the corresponding experiment, we find deviations, especially for LICRs. These deviations could come from the simulation error in the white LED model, the error in manufacturing freeform lenses and the installation error in horizontal and vertical directions [19]. However, the simulations are still instructive and the experiments prove the effectiveness of our proposed method.
The effects of other LEDs integrated with the selected lenses on the CSU are also studied. K2, a powerful product of Philips Lumileds Lighting Company, adopts the conformal phosphor coating process, which is widely known for the advantages of product consistency and color uniformity. In this study, the chosen lenses integrated with K2 also undergo the experiment. Their CCT distributions are shown in Fig. 11(a) . We can find that both the CCT distribution and color difference (small angular CCT deviation and 21 qualified points from 37 points) demonstrate that bare K2 has a considerable performance because of its adopted conformal coating. Further analysis indicates that those four lenses can further improve the CSU in terms of the qualified as shown in Fig. 11(b), while the CCT distributions don’t show the improvement. Accordingly, is a better indicator of CSU than CCT and can better distinguish the color inhomogeneity.
5.2 Analysis of efficiency
As mentioned before, improving the CSU at the expense of efficiency is not desirable. We measured the light output efficiency (LOE) of each selected lens by using an integrating sphere. Results are shown in Table 3 . We set the LOE of the bare LED to 100% as a reference.
Table 3. Light Output Efficiencies of Freeform Lenses
The efficiencies of the modified LEDs are all maintained at a high level, which indicates that the freeform lenses cause little light loss. Further analysis shows that the lenses based on the non-uniform illumination design method (Lens II and Lens IV) have higher efficiencies than the ones based on the uniform illumination design method (Lens I and Lens III). This phenomenon is probably caused by the fact that incident angles of most incident rays at the top surface of Lens I and Lens III are larger than those of Lens II and Lens IV, which results in more Fresnel loss in freeform lenses.
6. Conclusion
In this study, high-quality illumination pattern without yellow rings and dark areas is realized based on the novel freeform lens with little light loss. The light energy mapping relationship is optimized and a compromise has been made between CSU and LICR. It has been found that the lenses based on the non-uniform illumination design method lead to an acceptable compromise more easily than the ones based on the uniform illumination design method. An evaluation function of CSU is also proposed and a test system is developed to measure various important parameters such as the illuminance, CCT, and chromaticity coordinates. Experimental results demonstrate that CSU is enhanced with little light loss and Lens IV with (R,ω) = (100mm,45°) at θ = 45° performs the best in the aspects of the illumination pattern and color difference. Compared with the bare LED, this modified LED module can obtain an enhancement of 92% in CSU, from 12 qualified points to 23 qualified points without any dark areas. Further analysis demonstrates that is a better metric than CCT and can distinguish color more accurately. Additionally, this novel freeform lens is able to work on both of the freely dispersed coating and the conformal coating. Future work will focus on improving the white LED model to accord with the experiments better. Optimizing the parameters of the freeform lenses by computer automatically should also be considered to shorten the design time.
Acknowledgments
This work was supported by the Nature Science Foundation of China (NSFC) Key Project under grant number 50835005, NSFC Project under grant 50876038, and Guang Dong Real Faith Optoelectronics, Co. Ltd.
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