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Precise optical modeling for LED lighting verified by cross correlation in the midfield region Ching-Cherng Sun, Tsung-Xian Lee, Shih-Hsin Ma, Ya-Luan Lee, and Shih-Ming Huang Institute of Optical Sciences, National Central University, Chung-Li 320, Taiwan Received March 10, 2006; revised April 26, 2006; accepted April 26, 2006; posted May 2, 2006 (Doc. ID 68859) A novel LED modeling algorithm for precise three-dimensional light pattern simulation is proposed and demonstrated. We propose to use normalized cross correlation to verify the validity of the simulation in onedimensional intensity patterns as well as two-dimensional irradiance patterns in various midfield distances and to provide feedback to achieve a successful model. The model is demonstrated to obtain an average of 99% in normalized cross correlation between the simulation light pattern and experimental measurement for a truncated inverse pyramid LED. © 2006 Optical Society of America OCIS codes: 230.3670, 350.4600.
LEDs have been regarded as the best potential light source for next-generation lighting.1,2 The current study issues include enhancement in efficiency, brightness, and lighting design so that LEDs might replace most light sources in current lighting devices, including automotive forward lighting and other projection devices. In such applications, the management of optical etendue as well as illumination contrast is important, and a precise optical model of LED lighting is necessary to lighting design.3,4 However, each LED may have its own specific light pattern owing to the difference in chip structure, package, and other factors. Thus developing a useful modeling algorithm, which is generally suitable for most LEDs, is demanded. In this Letter we propose a novel modeling algorithm to model the optical behavior of LEDs, which is not only useful in LED lighting design but also useful in package design. The model contains a simple measurement of LED geometry, Monte Carlo ray tracing, and a comparison between the simulation patterns and experimental measurements at various distances in the midfield region. The algorithm in modeling the light pattern of LEDs starts at finding or estimating some key important parameters for Monte Carlo simulation.5–7 The parameters include chip dimensions, the location of the active layer, and the refractive indices and absorption coefficients of all optical media. Since the emitting area of the LED is located at the active layer with spontaneous emission, the active layer is assumed to be a Lambertian surface. We use a commercial software program to perform Monte Carlo ray tracing. Under most conditions a large number of rays are necessary to have a stable simulated light pattern, since most rays cannot escape from the LED die.8 This condition becomes worse when one needs to develop an optical system based on the LED. Thus the simulation is time consuming and impractical. In the proposed modeling algorithm, we first record the distribution of the ray vectors of the six exit faces of the LED die. Therefore the LED becomes a light source that has multiple emitting faces instead of a Lambertian active layer inside the chip. Then the lights are reemitted from the six faces, and the loss of rays inside the chip is 0146-9592/06/142193-3/$15.00
avoided. Consequently, the developed optical model of the LED contains a smaller number of rays for simulation of the light pattern. We may simulate the light distribution across the whole space based on these emitting faces of the LED die. To verify the optical model, we need to measure the light pattern of the LED. In addition, a comparison between the simulation and the measurement under the same parameters should be made. The verification of the optical model contains two parts. One part is measurement, and the other is the comparison between the measurement and the simulation. Since most optical elements of a LED-based lamp are close to the LED, the comparison between the simulation and the real patterns of a LED should be made in this region, which is neither the near field nor the far field. For convenience, we define the distance between the near-field (vector region) and the far-field (Fraunhofer region) regions9 as the midfield region, as shown in Fig. 1. In the midfield region, the light pattern varies from one distance to another, so the comparison should be made at various distances (e.g., from 1 cm to 1 m). In the measurement process, not only are one-dimensional only (1D) light patterns measured but two-dimensional (2D) light patterns are measured as well. In 1D light pattern measurement, we use a powermeter to measure the intensity of the tested LEDs. Such a measurement scheme is simple and easy but is not enough if the light pattern is not symmetric so that 2D measurement is necessary. The 2D irradiance measurement system contains a quasi-Lambertian scattering plate to scatter the incident lights emitted by the tested LED into the
Fig. 1. (Color online) Midfield. © 2006 Optical Society of America
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LED in measurement is along either the x or y axis. The NCC of the same model varies from one piece of LED to another, since there is no exact replica of any emitter. Thus we cannot have a model with very high NCC if the emitters have low NCC among them-
Fig. 2. (Color online) Geometrical structure of the TIP emitter in amber.
Fig. 3. (Color online) Simulated light pattern (red lines) versus experimental measurement (blue lines) for three samples.
Fig. 4. (Color online) NCC of various samples versus different midfield distances. Black dots, 1D light patterns; yellow dots, 2D patterns with a positive lens.
CCD, which is located at the image plane of the scattering plate. The distance between the scattering plate and the CCD is as large as 1 m and longer to ensure that only the lights with small scattering angles are caught by the CCD. A precise calibration is made to ensure that the gray level by the CCD precisely corresponds to the irradiance on the scattering plate. The following is an example where we demonstrate the optical modeling of a special LED by the Lumileds in Luxeon series,10 which is a truncated inversed pyramid (TIP) LED in amber,11 as shown in Fig. 2. The reason that we choose the TIP LED is that the light pattern is more complicated than others. We first made some simple measurements to determine the geometrical parameters and estimated the location of the active layer. We obtained the emitting light distribution across each surface by using Monte Carlo ray tracing from the active layer. Then, more than a million rays were emitted from the exit faces of the die, and the light distribution in three dimensions was obtained. To determine the similarity between the simulation pattern and the experimental measurement, normalized cross correlation12 (NCC) is applied. The NCC is written as
NCC =
兺x 兺y 共Axy − A¯兲共Bxy − B¯兲
冑兺 兺 共A x
y
xy
¯ 兲2 −A 兺 兺 共Bxy − B¯兲2 x
,
共1兲
y
where Axy and Bxy are the intensity or irradiance of ¯ 共B ¯兲 the simulation 共A兲 and experimental values 共B兲; A is the mean value of A共B兲 across the x – y plane. Figure 3 shows the simulation result as well as the corresponding measurement of three pieces of LED at a distance of 10 cm, where the optical axis is along the z axis shown in Fig. 2, and the rotation axis of the
Fig. 5. Modeling algorithm for a LED lighting source. T, threshold value.
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selves. A summary of the NCC of the 1D intensity between the simulation and experimental measurement at distances of 1, 5, 10, 20, and 100 cm in the midfield is shown in Fig. 4 (black dots), where the NCC is always as large as 99%. In addition, to verify the optical model in a different way, we measure the 2D irradiance pattern of the emitter attached to a positive lens with an F-number of 4.95. The summary of the NCC between the simulation and the measurement is shown in Fig. 4 (yellow dots), where the NCC at different distances is always as large as 99% and even larger. It means that the optical model in describing the emitter has been built successfully. The modeling algorithm is summarized in Fig. 5, where the threshold value (T) of the NCC may vary from one case to another, depending on the application. If the NCC is below a threshold value, the parameters, such as chip dimensions and geometry, absorption and reflection coefficients, and surface scattering characteristics, could be adjusted. In developing the model for high beam and low beam in automotive applications and other projection applications, a higher NCC threshold value (suggested 99%) could be necessary. However, a higher NCC threshold value means that the requirement of a higher NCC value among the emitters should be demanded. Therefore precise package of a LED is quite important. This is another contribution of the proposed model, since all the geometrical tolerances in the LED package can be obtained in the modeling process. In summary, a precise optical modeling algorithm was proposed and demonstrated. We propose to verify the model by using the NCC feedback between the simulation and the measurement at various distances in the midfield region. We demonstrate a precise modeling process for TIP LEDs. The NCC values are larger than 99% for different samples in most
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cases; even a lens is attached on the LEDs. The modeling scheme is not only useful for studying the optical design of LED lighting but is also useful for determining the geometrical tolerances in package. This study was sponsored by the Ministry of Economic Affairs of the Republic of China with contract 94-EC-17-A-07-S1-043. Corresponding author C.-C. Sun’s e-mail address is
[email protected]. References 1. D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, IEEE J. Sel. Top. Quantum Electron. 8, 310 (2002). 2. F. Nguyen, B. Terao, and J. Laski, in Proc. SPIE 5941, 31 (2005). 3. M. S. Kaminski, K. J. Garcia, M. A. Stevenson, M. Frate, and R. J. Koshel, in Proc. SPIE 4775, 46 (2002). 4. H. Zerfhau-Dreihöfer, U. Haack, T. Weber, and D. Wendt, in Proc. SPIE 4775, 58 (2002). 5. S. J. Lee, Appl. Opt. 40, 1427 (2001). 6. C. C. Sun, C. Y. Lin, T. X. Lee, and T. H. Yang, Opt. Eng. 43, 1700 (2004). 7. T. X. Lee, C. Y. Lin, S. H. Ma, and C. C. Sun, Opt. Express 13, 4175 (2005). 8. A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-State Lighting (Wiley, 2002), Chap. 5. 9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996). 10. M. R. Krames, M. Ochiai-Holcomb, G. E. Hofler, C. Carter-Coman, E. I. Chen, I.-H. Tan, P. Grillot, N. F. Gardner, H. C. Chui, J.-W. Huang, S. A. Stockman, F. A. Kish, M. G. Craford, T. S. Tan, C. P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser, and D. Collins, Appl. Phys. Lett. 75, 2365 (1999). 11. Philips Lumileds Lighting Company, http:// www.lumileds.com/. 12. For example, J. P. Lewis, in Vision Interface 95 (Canadian Image Processing and Pattern Recognition Society, 1995), p. 120.
