LED beam shaping lens based on the near-field illumination

This paper presents a novel method in near-field beam shaping based on the precise optical modeling of a gallium nitride light-emitting diode (GaN LED). A Monte Carlo ray tracing simulation has been utilized to calculate the spatial photon distribution near the LED’s top. By analyzing the ray data in near-field, the miniaturized lens profile is created and machined with aspherical surfaces and total internal reflection (TIR) Fresnel facets. The prototype lens reduce the viewing angle of the LED from 150° to 17.5° at full width half maximum (FWHM) while increasing the peak luminous intensity 10 times. The array of proposed lens with CSP LEDs exhibits feasibility of ultra thin uniform illumination in near-field. ©2009 Optical Society of America OCIS codes: (230.3670) Light emitting diodes; (350.4600) Optical engineering; (220.2945) Illumination design; (220.4298) Nonimaging optics; (220.1920) Diamond machining References and links 1. J. Carr, M. Y. P. Desmulliez, N. Weston, D. Mckendrick, and G. Gunningham G. McFarland, W. Meredith, A. McKee, and C. Langton, “Miniaturized Optical encoder for ultra precision metrology systems,” Precis. Eng. 33(3), 263–267 (2009). 2. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform nearfield irradiance,” Appl. Opt. 45(10), 2265–2272 (2006). 3. X. J. Yu, Y. L. Ho, L. Tan, H. C. Huang, and H. S. Kwok, “LED Based Projection Systems,” J. Disp. Technol. 3(3), 295–303 (2007). 4. Y. H. Kwon, C. S. Lee, and W. B. Kang, “Wafer-level-chip-scale package and method of fabrication,” US patent, 7569423 (2008). 5. L. Nguyen, “Wafer-Level chip-scale packaging,” in Proceedings of Professional Development Course 55th Electronic Components & Technology Conference, (Orlando, Florida, 2005), pp. 4–19. 6. D. K. Woo, K. Hane, S. C. Cho, and S. K. Lee, “Development of an integral optics system for a slim optical mouse in a slim portable electric device,” J. Vac. Sci. Technol. B 27(3), 1422–1427 (2009). 7. http://www.crucialtec.com/ 8. http://www.et-trends.com/files/ELEC_DESIGN-MOEMS.pdf 9. http://www.luminus.com/ 10. P. Schreiber, S. Kudaev, P. Dannberg, and A. Gebhardt, “Microoptics for homogeneous LED-illumination,” Proc. SPIE 6196, 61960–1 61960–9 (2006). 11. X. Zhao, Z. L. Fang, and J. C. Chu, X. A. Mu and G. G. Mu, “ Illumination system using LED sources for pocket-size projectors,” Appl. Opt. 46(4), 522–526 (2007). 12. J. Carves, Introduction to nonimaging optics, (CRE Press, New York, 2008). 13. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009). 14. I. Moreno, and C. C. Sun, “LED array: where does far-field begin?” Proc. SPIE 7058, 70580R–70580R–9 (2008). 15. Y. Ding, X. Liu, Z. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008). 16. T. X. Lee, K. F. Gao, W. T. Chien, and C. C. Sun, “Light extraction analysis of GaN –based light-emitting diodes with Surface texture and/or patterned substrate,” Opt. Express 15(11), 6670–6676 (2007). 17. F. Hu, K. Y. Qian, and Y. Luo, “Far-field pattern simulation of flip-chip bonded power light-emitting diodes by a Monte Carlo photon-tracing method,” Appl. Opt. 44(14), 2768–2771 (2005). 18. A. David, T. Fujii, R. Sharma, K. McGroddy, S. Nakamura, S. P. DenBaars, E. L. Hu, C. Weisbuch, and H. Benisty, “Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution,” Appl. Phys. Lett. 88(6), 061124–061126 (2006). #118075 $15.00 USD Received 21 Oct 2009; revised 9 Nov 2009; accepted 9 Nov 2009; published 7 Dec 2009 (C) 2009 OSA 21 December 2009 / Vol. 17, No. 26 / OPTICS EXPRESS 23449 19. http://www.crosslight.jp/Products/lastip/MRS_06Fall3.pdf 20. H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103–1, 026103–3 (2007). 21. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). 22. I. Moreno, and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008). 23. I. Ashdown, and M. Salsbury, “A Near-field Goniospectroradiometer for LED Measurements,” Proc. SPIE 6342, 634215–1 634215–11 (2006). 24. B. V. Giel, Y. Meuret, and H. Thienpont, “Design of axisymmetrical tailored concentrators for LED light source application,” Proc. SPIE 6196, 619603–1 619603–10 (2006).


Introduction
The interest in using light-emitting diodes (LEDs) in various applications such as sensing, display, and illumination has been growing steadily over the past several years [1][2][3]. In particular, a noticeably growing market of portable multimedia devices such as personal digital assistants (PDA), mobile phones, and navigators has been adopting LEDs as an attractive light source. This is because it offers portability by achieving thin and lightweight design. In addition to LEDs' high brightness, the light output, coupled with optical components, plays an important role from the perspective of high illumination quality control and miniaturization of such devices. More recently, packing researchers have attempted to apply chip-scale packaging (CSP) for LEDs [4,5] because of the potential for more compact and thinner illumination system design.
These specialized LEDs are drawing interest as competitive lighting sources for the ultra thin micro optical mouse, an optical scanner in low-image quality, and the miniaturized projector in mobile phones [6][7][8][9][10]. In these miniaturized projection or scanning optical systems, the imagers such as the digital micromirror device (DMD) or the micro liquid crystal display (LCD) of a projector represent the limiting component regardless of imaging technology. These LED illuminated imagers require small illuminated areas and restricted angular input, both of which result in a small value of a conserving optical quantity known as étendue. The étendue of these imagers is defined in Eq. (1).
where θ is a half-angle of angular beam distribution. Since the maximum invariant in an optical system is limited by the component with the smallest étendue factors, the imager's restricted étendue directly affects that of the beam shaping illumination optics with CSP LEDs. To meet the étendue requirements for the illuminated plane, CSP LEDs with beam shaping optics must possess a sufficient luminous flux within a small area of the imagers. However, the more the imagers' étendue increases, the larger the illumination optics' total size. The compound parabolic concentrator (CPC), often used for étendue-limited illumination optics, dramatically decreases light collection efficiency when reducing its length-diameter ratio [11,12]. To meet a slim mobile phone's volume constraints, high-quality LED-based miniaturized illumination optics requires a specialized thin optical component whose light output provides small étendue with minimum light loss. This miniaturized component near the top surface of the LED called near-field is thus of fundamental importance in the beam shaping of a CSP LED. In the following, near-field light distribution based on the precise modeling of the CSP LED will be analyzed. The design of near-field beam shaping lens (NBSL) will then be described, and its optical performance will be verified. Further, arrayed CSP LEDs with the NBSL will demonstrate the feasibility of ultra thin uniform illumination in near-field.

Precise LED Modeling
The LED's radiation pattern basically maintains three distribution conditions along with the distance from the LEDs per se: far-field, mid-field, and near-field [13]. Generally, the far-field zone begins at a distance of five times the largest dimension of the light source, and LED in far-field can be easily simulated or measured as a point source with a constant angular intensity distribution despite the distance variation [14]. Many LED beam shaping lens have been designed by assuming LED as a quasi-point source with Lambertian power distribution; this allows for easier and more convenient design process [14,15]. In the midfield region, the LED's radiation pattern varies from one distance to another. The radiation pattern on the top of LED, near-field region, is dominantly affected by an epitaxial structure of LED, a chip fabrication method and its package type. Thus, an LED is no longer a light source, but an optical system that transmits light from the six faces of a specific epitaxial chip structure. Therefore, the precise modeling of LED, proven in empirical similarity from its epitaxial structure to realistic package, can provide full information on near-field light distribution. This is a fundamental resource for near-field beam shaping lens (NBSL) design.
In this study, a Monte Carlo ray tracing simulation was utilized to calculate spatial photon distribution. This is a powerful means of tracing each photon and thus has been adopted for calculating light extraction efficiencies and radiation distribution patterns [16,17]. To model the actual behavior of numerous photons emitted from the multiple-quantum wells (MQWs), this study is anchored on two previous reports, which have revealed that merely about 12% of light generated in a typical GaN epitaxial structure on sapphire LED [18], as well as light distribution of a CSP LED [19].
In the GaN chip's precise optical model, the realistic epitaxial structures have been adopted to model blue CSP LED, as illustrated in Fig. 1(a). The structure parameters for the simulated GaN-based LEDs are described in Table 1. In reality, these layers generally consist of a GaN buffer layer, a thick highly conductive n-type GaN layer, n-AlGaN, InGaN/GaN MQW active layers, p-AlGaN, and a thin p-type GaN layer. Given that the light emitted from an active layer experiences minor differences in refractive indexes between the InGaN and GaN layers, the InGaN/GaN active layer is assumed to be one dielectric layer.    In simulation, a hundred of millions of rays are generated from the MQWs and 11.97% of light is extracted from the chip to the air. Right above the p-GaN, a transparent indium tin oxide (ITO) film is deposited. The SiO 2 passivation layer preserves the chip's top surface and the sidewall. Dislocation-related optical absorption coefficient is assumed to be 7mm −1 [20]. Fresnel losses have taken any interface into account. The modeled GaN chip's far-field radiation pattern in Fig. 1(b) is fairly similar to the referring paper [19].
Realistic package modeling is the other crucial task that ensures the effective functioning of all the remaining optical elements. In the package modeling, the smallest CSP LED (1.0 х 0.8 х 0.4 mm, λ = 468 ± 20 nm) is adopted. Its physical dimension is measured and the chip's position in the package is established, as illustrated in Fig. 2(a). Then, its angular luminous intensity distribution and total luminous flux in simulation is calculated in schematic of Fig.  2(b). The measurement principle of those data with the real CSP LED is shown in Fig. 2(c).
The package's contour profile is described with a Bezier spline while the modeled CSP LED integrates scattering, refraction, absorption, and reflection. For the modeled LED's verification, angular luminous intensity distribution is experimentally measured in far-field, as demonstrated in Fig. 3(a). To determine the similarity between the simulated light distribution pattern and that of the measured accurately, the normalized cross correlation (NCC) is applied [13,21, where Is and Ie are the simulated and experimental values of relative luminous intensity, respectively. Longitudinal angle (φ i ) and latitudinal angle (θj) are the i-th and j-th angular displacement, respectively, while Īs and Īe are the mean values of simulation and measurement, respectively. The CSP LED has a rotationally asymmetric geometry, thus Eq.
(2) is utilized, where the X + Xcross-section stands for φ 1 = 0°, and the Y + Ycross-section stands for φ 2 = 90°. The precisely modeled LED exhibits 96.2% of the NCC in far-field. In the CSP LED, the chip is translated into approximately 150 µm from the center of the compact asymmetric rectangular package. This makes requiring NCC for asymmetric angular distribution slacker compared with the rotationally symmetric packaged LED; the latter often yields over 99% accuracy [15]. However, even though it is higher than 99% of NCC in far-field, it gradually drops as the distance between the detector and the LED becomes closer and finally reaches less than 70% when near the LED's top surface [15]. This is because a simple approximation of the chip and its packaging status can only be validated in far-field. Hence, further empirical verification of the near-field angular light distribution's accuracy is necessary [23].
In Fig. 2(c), the near-field goniophotometer based on luminance measuring cameras combines a motorized goniometer stage with a charge-coupled device (CCD) of an imaging photometer. The camera captures the real radiation characteristics of the CSP LED L(x, y, φ, θ) while the goniometer moves around it. If any ray at the specific location (x, y) is emitted from the top surface of the LED, it reaches the corresponding pixel of the CCD (x´, y´) at two directional camera position angles (φ i , θ j ) through the zoom lens. Thus, the goniophotometer performs a near-field angular measurement of the luminance. All luminance images taken together results in a four-dimensional data field Lʹ ʹ ʹ ʹ(xʹ, yʹ, φʹ, θʹ), which is a full description of the light emission. These data field can be converted into ray data with spatial directions and can be calculated further into a luminous intensity distribution, I(φ i , θ j ) In this manner, the CSP LED's relative luminous intensity distribution is measured. The NCC between the simulation and experimental measurement right on the top of the LED top is roughly 95.8%, as illustrated in Fig. 3(b). Based on this result, the modeled LED's precision is believed to improve the NCC's accuracy in near-field. Further, the relative luminous flux of each of the CSP LED's five surfaces between measured and modeled LEDs is compared in Fig. 3(c), where this CSP LED can be interpreted as a volume light source. The size of the detector for each five surfaces in simulation is the same as the area of contour of the CSP LED.
Based on these results, the source model in this study offers a fairly good agreement for optical design both in near-field and far-field. Thus, the modeled LEDs are sufficient for describing the GaN-based blue LED's optical characteristics within a complete possible variation range.

Design of near-field beam shaping lens
Based on the near-field luminous distribution pattern in Fig. 3(d), this angular distribution can be modeled simply with regard to size and position of the chip and geometry of an encapsulant. Generally, the chip is bonded on a substrate with high reflectivity. Thus, it is apparent that the dominant light's extracted feature is placed either on the top of the ITO or on the side of active region [18].  The optical output from the chip can be approximated as a point source of light passing through an encapsulant, which considers the extended source size of the LED for the design of NBSL. The geometry of the CSP LED is simplified in square although actual geometry of the CSP LED is not perfectly squared, as shown in Fig. 2(a). This simplification makes the design procedures of the NBSL comprehensible and is still reasonable because the luminous flux passing through the unsquared corners of the CSP LED is very small compared with the total luminous flux, as shown in Fig. 3(c). More precisely, the light refracting from the flat top or side of encapsulant to the air appears to originate from a certain location within the package. The light reflecting on the bottom and refracting at the side wall of the encapsulant appears to come from outside of the packaged LED, as illustrated in Fig. 4(a). The optimal position of ideal point source for the extracted light of three representative directions can be expressed by Eqs.    Fig. 4(a).
( ) Judging from these equations, the extent of the extracted light appears to originate from a range of location called "focal smear." These focal smears overlap and thus create an elongated region, as demonstrated in Fig. 4(b). Consequently, near-field beam shaping lens (NBSL) must be designed on this extent ideal point source model, which includes the detailed optical models of LEDs.
The beam shaping principle of the NBSL and its design method are explained in Fig. 5(a). The NBSL consists of a series of eccentric prismatic facets and a central aspheric lens. The profile of the central aspheric lens is designed to capture the dominant light from the top emission and redirect it. TIR Fresnel facets redirect the emission from each of the four sides of the LED, which is roughly half of the total luminance flux, in a controlled manner. The design parameter of the NBSL, such as the radius of curvature of the central aspheric lens (R) in Eq. (8) and three distinctive angle (α´, E, and N) in Eq. (9), can be determined by analyzing the special and angular information from the near-field light distribution that conforms to the focal smear.
For the design of the central aspheric lens, the focal smear of the top emission of the LED can be expressed by Eq. (3). As NBSL has a miniaturized special geometry, the primary design limits of a central aspheric lens are the sag and the lens diameter, which limits the effective focal length (F e.f. ) of a lens. Generally, P T should be smaller than F e.f. because P T is determined in the compact packaged profile of LEDs and the small curvature of the central part of the aspheric profile. For the spherical planoconvex refractive lens in parallel approximation, the ratio of the effective focal length of the central aspheric lens to the lens distance from the focal smear (m) limits the output diverging angle. The radius of the curvature of the lens can be defined in Eq. (8). R can be determined at the corresponding angle ( φ ) with specific package structure (h and h c ). Thus, an aspheric profile is created.
The prismatic TIR Fresnel facets have an interior face, a totally internally reflecting face, and an exterior face. The profile of a TIR Fresnel facet can be specified by three angles, two that give its shape (E and N) and one its orientation (α´). A ray radiating from the ideal point sources (P´S T or P´S L ) with a view angle (α´) is refracted at the interior face with incident angle (E), reflected at the TIR face, and propagates to the air with a bend angle β. Here, the radius of the curvature of each interior facet (ρ) can be determined by the combination of apparent angle (α´) emitted from the LED and shape angle E and N in Eq. (10).
The geometry of each TIR Fresnel facet is numerically calculated at a radial distance (r) from the vertex of the NBSL. The proper combinations of the values of N, E, and α´ are chosen, where N (≥30°) and E (0°≤ E ≤60°) due to the manufacturing constraints. Figure 5(b) presents a cross-sectional view of the designed NBSL.

Verification of the design
Optical designs must always be prototyped and tested for reliability in the illumination system design process. To verify the proposed design methods, a prototype of the NBSL is manufactured by single-point diamond turning (AHN05, JTEKT Co.). The machined shape tolerance in Fig. 6 has less than 1 µm deviation, and surface quality is deemed sufficient for total internal reflection on the outer facets.
To accurately verify the NBSL's empirical performance, a near-field goniophotometer was again employed . Figures 7(a) and 7(b) show the central aspherical lens and TIR facets successfully redistributing the beam in near-field, thus reducing the viewing angle from 150° to 17.5° at full width half maximum (FWHM). Light collection efficiency, the ratio of total flux with the lens to that of the LED is calculated at approximately 63.5%. The étendue of the testing CSP LED is approximately 5.65 mm 2 ·sr and the CPC-based concentrator exhibits very low light collection efficiency of approximately less than 20% in this much lower étendue at 20° viewing angle, wherein its length is approximately 20 mm [24]. This simple comparison exhibits NBSL's extremely high compatibility with the compact miniaturized illumination system. As shown in Fig. 7(a), asymmetry is evident in the performance of the NBSL due to several structural asymmetries in both package and chip. The elliptical shape of the NBSL manufactured by a fast tool servo (FTS) may be able to further enhance its performance. However, manufacturing such a miniaturized shape with high asymmetry will decrease the surface quality of the TIR Fresnel facet resulting in low light collection efficiency. Therefore, a single-point diamond turning machine is the better solution for the NBSL.
The LED's translation's influence from the NBSL posture can distort the near-field illumination pattern. Thus, the alignment tolerance of beam shaping components for the LED is testified, as illustrated in Fig. 8. When the LED light source is translated along ± X and ± Y, the peak luminous intensity gradually begins to drop for more than 50 µm error. Meanwhile, total luminous flux is largely maintained because the output viewing angles gradually decrease, as shown in Fig. 8(a). Figure 8(b) shows that the NBSL is generally sensitive to the translation of the + Z axis, and it exhibits a linear characteristic of approximately12.6% loss per 100 µm. Uniformity control in near-field is another critical issue in miniaturized projection or scanning illumination optical design. Figure 9 presents the conjunct design using an array of LEDs in conjunction with an array of NBSL. Their illuminance view on an imager above 5 mm from the LED top is likewise presented. The number of LEDs is selected to meet the flux requirement. The novel optical design can achieve a fairly good uniformity with an increase of illuminance, which is 10 times higher compared with the sole use of LEDs. The overall length of uniform illumination is approximately 6 mm while maintaining a small viewing angle at 17.5°. Compared with the CPC-based illumination system, the designed illumination system is almost a fifth in length.

Conclusion
This paper suggests the method of LED beam shaping in near-field. A near-field beam shaping lens for CSP LEDs is proposed based on the precise modeling of a GaN chip and its packaging. By analyzing the ray data in near-field and relaxing several design constraints, the lens profile is created and machined with a solution of aspherical surfaces and TIR facets. The prototype lens reduces the viewing angle of CSP LED from 150° to 17.5° at FWHM while increasing the peak illuminance intensity 10 times. The array of proposed lens conjunct with CSP LEDs provides a good starting point for the near-field design of ultra thin optical system, which will produce extreme compactness as well as efficiency compared to the CPC-based system.