An optimization system for LED lens design

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An optimization system for LED lens design

Wen-Chin Chen

a

, Tung-Tsan Lai

a

, Min-Wen Wang

b,c,⇑

, Hsiao-Wen Hung

b,c a

Graduate Institute of Management of Technology, Chung-Hua University, No. 707, Sec. 2, WuFu Road, Hsinchu, Taiwan

b

Graduate Institute of Mechanical & Precision Engineering, National Kaohsiung University of Applied Sciences, 415 Chien Kun Road, Kaohsiung City 807, Taiwan

c

Industrial Technology Research Institute, Taiwan/Center for Micro/Nano Science and Technology, National Cheng Kung University, Taiwan

a r t i c l e

i n f o

Keywords: LED

Taguchi method

Back-Propagation Neural Network Genetic Algorithms

a b s t r a c t

This study proposed a two-stage LED lens design optimization system, and used the viewing angle and the luminance uniformity as the optical quality objective. Optical design software (TracePro) and the orthogonal table of Taguchi method were used for simulation experiment. In the first stage, the viewing angle was used as the optical quality objective to find out the preliminary optimization of lens shape. The optimal LED lens size parameter combination of the first stage was used in the second stage to create L25(56) orthogonal table, and then the Back-Propagation Neural Network (BPNN) was used to establish the LED lens quality predictor to predict the FWHM angle and luminance uniformity in different overall sizes. The Genetic Algorithm (GA) with the quality predictor was used to find out the optimum design parameter combination of overall size according to the required quality objective. A LED with wide view-ing angle and high luminance uniformity was taken as an example in this study to design a LED optical lens with 135° FWHM angle and 93.35% uniformity.

1. Introduction

LED (Light Emitting Diode) has been widely applied due to its advantages of energy saving, environmental friendliness, long life, quick response, small volume, and anti-vibration. Therefore, it has been applied extensively. LED is a type of luminous module made of semiconductor material. It releases the energy derived from the combination of electrons and holes in the form of light, so as to achieve cold light luminescence. Generally, the maximum lumi-nance intensity of a LED without lens is located at the lumilumi-nance surface perpendicular to LED epitaxy, i.e. 0°. The range of half maximum viewing angle (the angular region at the center of the maximum luminous intensity of the LED) is usually ±60°. For dif-ferent applications, LED lenses were designed to refract and reflect the light ray according to optical principle, so as to change the traveling path of the light and attain specific radiation patterns. Typical radiation patterns can be divided into four kinds, which are the collimating radiation pattern, the Lambertian radiation pattern, the side-emitting radiation pattern, and the batwing radi-ation pattern. The collimating radiradi-ation pattern LED has concen-trated light beams, thus, it is mostly applied to flash light, architectural lighting and decorative lighting which need strong light sources. The Lambertian radiation pattern is widely used

for its moderate viewing angle and uniformity, such as projec-tion-type head lamps and flashlights. The side-emitting radiation pattern leads the vertical emerging ray to a horizontal emergence through a cone-shaped device. It is mostly applied to the backlight module of LCD and reflection-type head lamps. The batwing radi-ation pattern was originally designed for traffic signal lamps.

In recent years, with the advancement of high-speed computing and optical analysis software packages, the computer-aided optical analyses of LED (Chang, Ou, Tsai, & Juang, 2009), LCD light guide plate (Chang & Fang, 2007), optical ﬁlm (Wang & Tseng, 2009) and optical lens (Maeda, Catrysse, & Wandell, 2005) can be accel-erated, so as to save time, manpower and costs. However, for all analytical software used, a lens shape model must be set up before LED design analysis. The trial-and-error method was usually used for the optimal design in the past, designers needed to adjust the size parameters according to intuition and experience, and build the model of the optimization parameters for analysis and observe the result. In addition, the analysis of each sample would require several to tens of minutes. Although it is not a long time, when the quantity of samples increased, the analysis time would be con-siderable, and only the local optimal solution could be obtained. In order to design the optimal lens, the optimization needs to be cor-rected for many times, and it is time-consuming to complete an overall optimization ﬂow. The Taguchi method is also a common method for lens design (Fang, Tzeng, & Li, 2008). The lens design parameters are divided into different levels according to the response of each parameter to the quality, such as luminance and uniformity. It can obtain a design with preferable quality

⇑Corresponding author at: Graduate Institute of Management of Technology, Chung-Hua University, No. 707, Sec. 2, WuFu Road, Hsinchu, Taiwan. Tel.: +886 7 3814526x5318; fax: +886 7 3831373.

E-mail address:mwwang@cc.kuas.edu.tw(M.-W. Wang).

Expert Systems with Applications 38 (2011) 11976–11983

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within the preset range of parameters, but the Taguchi method cannot obtain continuous and global optimum design (Chen & Hsu, 2007). To solve these problems, many researchers used the Neural Network with the Genetic Algorithm to reach continuous and global optimum design in problem analysis. The relevance between set-up parameters and quality can be constructed effectively based on the training and testing of Neural Networks, so as to predict the quality characteristics (Chen, Chen, Tsai, & Ho, 2006; Chiu, Shin, & Wei, 1991; Choi, Lee, Chang, & Kim, 1994; Covas, Cunha, & Oliveira, 1999). For example,Li, Fang, and Cheng (2009)applied neural optical model and Genetic Algorithm to optical design for light guide plate, and reached 92% luminance uniformity.

Though automatic optimization optical design functions have been built-in in modern commercial software like TracePro, ZE-MAX, Light tools and ASAP, users can apply the design function with limited design variables and with the merit functions avail-able from the software. The purpose of this study is to set up an optimal design system for LED lens development. An optimization system is proposed to develop the geometric shape of the lens. The experiment design adopts TracePro software, Taguchi method and Back-Propagation Neural Network to create the optical quality pre-dictor for LED lens, and conduct quick and accurate analysis according to the preset overall size parameters of LED lens. The proposed system can predict the viewing angle and luminance uni-formity, and combine optical quality predictor with GA to ﬁnd out the optimal solution of design parameters.

2. The proposed optimization system

Traditionally, engineers use the trial-and-error method or Tagu-chi method to obtain the optimal parameters, but the TaguTagu-chi method is a discontinuous optimization approach, which can only obtain the local discontinuous optimal solution of pre-selected parameter level value, and cannot find out the global optimal solu-tion. Therefore, this study proposes a two-stage optimization sys-tem to design the geometric shape of lens. In this study, a new type of LED lens will be developed based on basic optical principles of refraction and reflection. The LED shape of lenses integrates with the characteristics of the Lambertian radiation pattern and the side-emitting radiation pattern. The geometric shape of lens can al-low LED to have wide viewing angle and emit light uniformly, thus applicable to the direct-light-type backlight module of LCD panel display. The first stage is the preliminary optimization of viewing angle, and the Taguchi method is used for preliminary analysis of the overall size and viewing angle of lens. The setting range values of control factors are divided into five levels equally, all the factor levels are put in L25(56) orthogonal table, and the TracePro

soft-ware is used for optical analysis. The viewing angle is converted into S/N ratio (signal-to-noise ratio) according to the larger-the-better characteristic. The S/N ratio response chart of various factor levels is made to find out the optimal LED lens size parameter com-bination of the first stage. In the second stage, the experimental de-sign adopts Taguchi method, BPNN, and TracePro software to create the quality predictor for LED lens, in order to conduct quick and accurate analysis effectively according to the preset overall size parameters. The quality predictor is to forecast the viewing an-gle and luminance uniformity. The quality predictor and Genetic Algorithm are used to obtain the continuous global optimal solu-tion of design parameters. The proposed optimal design system is simplified, and the overall flow is accelerated, so as to find out the optimal parameter by using the least time, cost and resource. Moreover, non-professional optical designers can also design the optimal LED lens design according to product requirements by

using this system. The procedures of the proposed system are shown inFig. 1, described as follows:

(1) Identify the experimental lens size parameters and quality characteristics of LED lens and plan the experiment.

I. Identify the feasible optical quality response as the target requirement of the experiment. The optical response must be confirmed to have significant influences on the final optical product quality.

II. Determine the feasible lens size parameters and levels that inﬂuence the performance of the optical quality char-acteristic. The number of control parameters which should be included in the experiment and the number of levels for each parameter can be decided using experi-ence, preliminary studies, or brainstorming.

III. Select an appropriate orthogonal array for arranging the experiment and acquiring the experimental treatments. (2) Preliminary optimization of LED lens shape.

In the ﬁrst stage, Taguchi method is applied to determine the preliminary optimal design parameter of lens and the view-ing angle is employed as the optical quality objective. (3) Create quality predictor by using BPNN.

The optimal LED lens size parameter combination of the ﬁrst stage is used in the second stage to create L25(56) orthogonal

table and perform the Taguchi experiment, and then the BPNN is used to establish the LED lens quality predictor to forecast the Full-Width Half-Max (FWHM) viewing angle

Fig. 1. Flow chart of the proposed optimization system.

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3.2.3. Optimization model

This study aims to achieve wide viewing angle and high unifor-mity in LED lens design. The optical quality predictor is combined with Genetic Algorithm, while the larger-the-better optimization of viewing angle and luminance uniformity is carried out. The 8th and the 11th parameter combinations in Taguchi experiment are used as the base, and the up-and-down 1/2 level is used as the bound of the search area of Genetic Algorithm. The bound of search area of Genetic Algorithm is shown inTable 5. The ﬁtness function of Genetic Algorithm is as follows:

Min FðXÞ ¼ ð1 uÞ2 s:t: TNPTO 0:6625 6 A 6 0:7125 4:9 6 B 6 5:025 3:875 6 C 6 3:975 2:5875 6 D 6 2:6 2:375 6 F 6 2:4375 ð2Þ

where u and TNare the luminance uniformity and viewing angle

predicted by the BPNN, TOis the acceptable threshold to the viewing

angle. The optimum parameter combination of Genetic Algorithm search is A = 0.688, B = 5.024, C = 3.924, D = 2.588, F = 2.386, the predicted value of optical quality predictor is u = 92.95% and TN= 134.67°. The optimum size parameter combination is inputted

into LED lens model and TracePro software for analysis. The light distribution curve diagram obtained is shown inFig. 8. The lumi-nance uniformity is 93.35%, and the viewing angle is 135°. The re-sult conﬁrms that this optimization system can predict the viewing angle and uniformity of LED lens effectively. The optical quality of lens size parameters is better than that of lens size parameters obtained by Taguchi method.

4. Conclusions

This study designs a new type of LED lens combining the Lam-bertian radiation pattern and the side-emitting radiation pattern.

The geometric shape of lens can allow LED to have wide viewing angle and high luminance uniformity. The experimental design adopts Taguchi method and TracePro software, and BPNN is em-ployed to construct the quality predictor for LED lens. The quality predictor was combined with Genetic Algorithm to ﬁnd out the optimum size parameters of lens, so as to set up an optimization system for lens design and obtain an optical lens with 135° viewing angle and 93.35% uniformity. The proposed system can analyze the viewing angle and luminance uniformity rapidly and accurately, according to the overall size parameters of lens. It can be applied to the optimal design of various LED lenses, so as to help the LED industry improving the lens design technology and increasing the development efﬁciency.

Acknowledgement

This work was supported by the National Science Council of Tai-wan (Under the grant of 982C19) and Industry Technology Re-search Institute of Taiwan (Under the project 99C029). The ﬁnancial supports from NSC and ITRI are acknowledged.

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