Energy feedback freeform for uniform illumination of extended source LEDs

1 1 2 1 1,* ZONGTAO LI, SHUDONG YU, LIWEI LIN , YONG TANG, XINRUI DING, WEI 1 1 YUAN, BINHAI YU 1 Key Laboratory of Surface Functional Structure Manufacturing of Guangdong High Education Institutes, South China University of Technology, Guangzhou 510640, China 2 Department of Mechanical Engineering, University of California, Berkeley, California 94720, United States *Corresponding author: [email protected] Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX Using freeform lenses to construct uniform illumination systems is important in light-emitting diode (LED) devices. In this paper, the energy feedback design is used for freeform (EFFL) constructions by solving a set of partial differential equations that describe the mapping relationships between the source and the illumination pattern. The simulation results show that the method can overcome the illumination deviation caused by the extended light source (ELS) problem. Furthermore, a uniformity of 95.6% is obtained for chip-on-board (COB) compact LED devices. As such, prototype LEDs manufactured with the proposed freeform lenses demonstrate significant improvements in luminous efficiency and emission uniformity. © 2016 Optical Society of America OCIS codes: (220.4298) Nonimaging ; (220.2945) Illumination design; (230.3670) Light-emitting diodes.

sources (PLSs). For LED applications, the brightness of these LEDs is 1. Introduction not sufficient. Although a module with multiple sources makes it possible to obtain sufficient luminous flux, Kuo found that such a Solid-state devices, especially light-emitting diodes (LEDs), solution would lead to the “multi-shadow” phenomenon, which causes have gained attention recently as a result of their outstanding features the eyes to feel tired [9]. [1], which include low energy consumption, ultra-fast response, For high-quality illumination, chip-on-board (COB) LEDs achieve a environmental friendliness, and tunable emitting spectra. These high-power output from one source. In such components, the large size features have made LEDs penetrate deeply into our daily life, in forms of the luminous area has greatly worsened the performance of the such as large-scale backlights, high-performance projectors, freeform lens system [4, 10], which causes the so-called “extended light automobile , and especially general lighting systems. At source (ELS) problem”. The simultaneous multiple surfaces (SMS) present, the angular intensity patterns of most LEDs are circularly method [11], in which two freeform surfaces are simultaneously symmetric, with the highest energy output lying in the normal designed to refract or reflect a set of input/output bundles, direction (i.e., Lambertian distributions), which cause glare upon provides a viable solution. Nevertheless, for compact packages in human eyes. On the other hand, LED lighting systems are always which only single freeform lenses are available, the SMS method is not installed at a certain height, and only the downward-emitting light suitable. On the other hand, optimizations based on tailoring method fulfills the illuminating function, whereas the light emitted at large also demonstrated potentials for solving the COB ELS problems [5], but viewing angles leads to energy losses. Therefore, specially designed calculation errors would be introduced due to the pre-discrete optical lenses are required in order to collect and guide the light into feedback, lowering the design accuracy and efficiency. uniform illumination patterns. In this study, we further develop the PDE freeform lens design method, The freeform lens is one of the most popular optical devices for present the concept of “effective rectification function” for COB performing this job owing to its distinct advantages, such as compact compact sources based on a set of energy feedback functions. size and precise light controlling [2–5]. Compared with the traditional Additionally, an engineering example is discussed, and the trial and error method [6] or the tailoring method [7], solving a set of performance of the lens is experimentally investigated. The results partial differential equations (PDE) [2,8] that describe the mapping show that the improved design method is capable of handling the ELS relationships between the source and the illumination pattern is of problems, and that it exhibits excellent system efficiency. The findings higher accuracy and extensibility for different illumination patterns of this study will offer a valuable reference to LED optics researchers. (such as rectangle or octagon). More importantly, this method is high efficient, and fast [2]. However, existing studies are limited to LEDs with small emitting areas (single chip component) – e.g., point light 2. Modeling Figure 1 shows the lighting model of a freeform lens designed for flux of the specific area on the target plane to the total luminous flux on uniform illumination. The light source O is located at the origin of the the target plane equals that of the luminous flux of the specific solid coordinate system. The target plane T is located at a distance z0 from angle to the total luminous flux: the origin, and is perpendicular to the z-axis. The unit normal vector of θ 2 22 2cossinπθθθId the target plane T is =(0, 0, −1), and the points on plane T can be Eyyπ()− θ 0 021= 1 expressed as (, , ). The points on the freeform lens P can be θ , (5) π 2 max expressed in spherical coordinates as (,,(,)), where γ is the ER0 2cossinπθθθId 0 0 angle between the x-axis and the projection of on the x-y plane, and θ is the angle between the z-axis and . The unit normal vector at where is the angle corresponding to the maximum light emission, and R is the radius of the illumination pattern. Equation (5) is the so- point P is , and ρ(γ, θ) is the module of . Let be the unit vector called “energy mapping function.” This mapping function is very of , and be the direction vector of . According to Snell’s law: important in the PDE freeform lens design method, which contains        information regarding the illumination distribution on the target plane. 22+− ⋅ = − nnoI2 nnOINnOnI00 I() p I. (1) Altering the energy mapping function can alter the designed illumination distribution. Therefore, Eq. (3) can be transformed into: z − ρ cosθ z θθ0 −− sin (nn0 I cos ) T（x，y，z0） θρθ−+−22 ρ θ (()fz sin) (0 cos) f ()θρθ− sin cosθθ (nn− sin ) , (6) 0 θρθ−+−22 ρ θ I uuur ∂ρ (()fz sin) (0 cos) N = ρ p − ρθ ∂θ z0 cos (γ，θ，ρ(γ，θ)) cosθθ (nn−+ cos ) P 0 θρθ−+−22 ρ θ I (()fz sin) (0 cos) f ()θρθ− sin O sinθ (nn− sinθ ) 0 θρθ−+−22 ρ θ I y (()fz sin) (0 cos)

x By solving Eq. (6), the profile of the freeform lens can be obtained, as shown in Fig. 2. Fig. 1. The lighting model of the freeform lens for uniform illumination.

The relationship between the incident light and the refracted light can be derived: ∂∂ρρ  2 −+sinγθθγρθγ sin cos cos − sin cos  ∂∂γθ nO− nI = 0 xIx  ∂ρ 2 nO− nI  −−sinθρ sin θ cos θ 0 z Iz  ∂θ , (2)

 ∂∂ρρ  cosγθθγρθγ+− sin cos sin sin2 sin ∂∂γθ nO− nI Fig. 2. Molding of freeform light-emitting diodes (LEDs).  = 0 yIy  ∂ρ 2 nO− nI  −−sinθρ sin θ cos θ 0 zIz  ∂θ where and are the refractive indices of the lens material (which is set as 1.54) and air, respectively. In order to simply the discussion, we focus on a uniform circular illumination pattern, and the specific value of = 90° s selected. We therefore obtain:

∂ρ sinθθ (nO−− nI ) cos ( nO − nI ) = ρ 00z Iz x Ix , (3) ∂−+−θθ θ cos (nO00z nIIz ) sin ( nO x nI Ix ) which can be solved as ordinary differential equations in this specific situation. In order to solve Eq. (3), an additional condition = () should be introduced. The illuminance E0 on the target plane is constant since Fig. 3. The simulation results of the illumination distribution for the uniform illumination is expected. Therefore, the total luminous flux on case of a point light source (PLS). the target plane can be written as: - φφγθ===ES I(, ) d Ω, (4) For the convenience of discussion, the ratio of the lens central height total0 l v  to the source diameter is defined as the L-S factor. Figure 3 shows the , where is the illumination area, (, ) is the luminous intensity at simulated (Monte Carlo ray tracing (MCRT) typical wavelength of 450 the viewing angle (, ) from the light source, and is the unit solid nm is utilized) results for a PLS, from which it can be seen that the angle relative to the light source. Generally, angular intensity patterns illumination on the target plane is quite uniform; this is rather suitable of LEDs are Lambertian distributions.Considering the energy loss for LEDs, especially concerning indoor applications. However, as the L- during light traveling, it can be derived that the ratio of the luminous S factor decreases (i.e., as the PLS gradually transforms into an ELS), the light spots become bright in the center and dark along the edge; Let = () be the input illumination distribution function (IIDF) of this is referred to as PLS-ELS deviation, and is illustrated in Fig. 4. the circular light spot on a given target plane. The energy mapping Obviously, the freeform lens designed by the PLS method is not function is therefore: suitable for the case of an ELS. Further modifications are required in θ y22 order to obtain uniform illumination. 2()ππθθθf yydy 2()sin I d y θ 11= (8) R θ 2()ππθθθf yydymax 2()sin I d 00 To solve Eq. (6), the energy mapping function is reconstructed as follows:.

y θ 222(ππθθθkE+ k f ()) y ydy 2 I ()sin d y 10 22 θ 11= , (9) R θ 2(ππθθθkE+ k f ()) y ydymax 2 I ()sin d 0010 22

where k1 and k2 are the weighting coefficients, such that k1+ k2 = 1 (k1=k2=0.5 is selected in this study), but in practice k1

Simulated illumination when the PLS-ELS deviation is large, and a k1>k2 combination is recommended when the optimization object is close. For Eq. (9) the

IIDF is = () = +(). There must be a special form of Fig. 4. The effect of the L-S factor on illumination distribution along the () = () that will make the calculated freeform lens meet the light spot diameter on the target plane. design requirements. The equation () is therefore called the “effective rectification function” for the process of transforming a PLS into an ELS. In this work, the rectification function is calculated from 3. Design of energy feedback freeform lens (EFFL) the PLS-ELS deviation, so it is also called the “energy feedback function.” Based on these considerations, we develop an energy feedback Consequently, the task of designing the freeform lens for an ELS is to freeform lens (EFFL) method to further optimize the freeform lens, as find the appropriate energy feedback function. shown in Fig. 5. The PLS-ELS deviation is first quantitatively calculated, Considering a more general condition, the uniform light spot is realized and then applied as an additional input (i.e., an energy feedback after n generations of rectification, and we obtain: function) for the process of optimization. Simply put, the primary n y2 θ purpose of the EFFL method is to darken the bright area and brighten π 2 2()kfii yydy 2()sinπθI θθd the dark area. y1 θ i=1 = 1 θ (10) Since the energy appears to be focused at the center of the light spot, R n max we can expect that, if the input of the energy mapping function 2()π kf yydy 2()sinπθI θθd 0  ii 0 contains an illumination distribution with a dark center and bright i=1 edges (i.e., a non-uniform distribution), then the PLS-ELS deviation should be corrected to a certain degree. The key components of the Equation (10) is called the “effective energy mapping function” for the EFFL method are described in what follows of this section. process of transforming a PLS into an ELS.

A. Calculating the freeform lens B. Modeling of the ELS illumination system The method of calculating the freeform lens for an ELS is similar to the The model of the ELS illumination system consists of the lens, the light case of a PLS. The general form of the energy mapping function is: sources, and the target plane. The freeform lens is established by solving Eq. (6). Next, it is imported into MCRT. The ELS is then θ 2 simplified to a circular or square light-emitting plane with certain 22 2()sinπθId θθ Eyyπ ()− θ 021= 1 dimensions with the Lambertian distribution. For the purpose of θ (7) π 2 max calculating the PLS-ELS deviation in the next step, a far-field target ER0 2()sinπθId θθ 0 plane is required. The axis of the lens, the light source, and the target plane lie along the same line.

Fig. 5. The flow chart for the energy feedback freeform lens (EFFL) method. IIDF: input illumination distribution function (see below). ELS: extended light source. C. Calculation of IIDF

Simulated illumination

Fig. 7. Comparison of the lens profiles before and after rectification.

4. Application: EFFL design for COB-LED illumination devices In order to practically assess the feasibility of the EFFL method, a freeform lens for a compact COB-LED is designed and manufactured based on the following requirements. 1) The distance from source to the target plane is 2000 mm; 2) the radius of the light spot is 3500 mm; 3) the diameter of the source is 5 mm; 4) the central-height of the freeform lens is 8 mm; 5) the of the lens material is 1.54 (OE6650 silicone from Dow Corning); 6) the uniformity of

Input illumination illumination (which is defined as the ratio of minimum illumination to the maximum illumination in the specific region) is >95% within the light spot radius of 2000 mm. Figure 8 shows the schematic of the COB illumination device. A reflective cup with a diameter of 5 mm is located in the center of the

lead frame. Twenty-one LED chips (0.25 mm × 0.76 mm) were die- Fig. 6. (a) The energy is concentrated in the central area when the L-S bonded in the reflective cup evenly with a connection of 3-series and 7- factor is 3. (b) The calculated rectification function according to the parallel. A high-efficiency convex [12] phosphor coating was applied to point light source-extended light source (PLS-ELS) deviation. the LEDs by precise dispensing. Finally, a freeform lens was molded on the lead frame by using a specially designed mold. Because the central- Here we assume that the L-S factor is 3. Figure 6 (a) shows the height of the lens was 8 mm, the L-S factor was less than 2, which simulated result of the original lens. It is apparent that a large amount constituted a typical ELS problem, and this was much more difficult to of the energy is concentrated in the center of the light spot. This implement than that in [5] whose L-S factor was only 2.5. In order to constitutes the PLS-ELS deviation, and hence the rectification function shorten the calculation time, we used the Euler method to solve the () can be acquired by subtracting the deviation from the equations with a discrete step of 0.9º. optimization object, as shown in Fig. 6 (b). Earlier in the paper, the original freeform lens was calculated based on the PLS. In that situation, the IIDF was constant: () =. Therefore, it is reasonable to construct the new IIDF = () +(). Moreover, we can expect that when the recalculated lens is applied to the PLS, the light spot no longer takes on a uniform distribution. Instead, it becomes dark in the middle and bright along the boundary. After n generations Fig. 8. Schematic of high-power, chip-on board (COB) light-emitting of rectification, the IIDF on the target plane will be = ∑ (). diode (LED) device with compact molded freeform lenses.

D. Calculating the new freeform lens Figure 9 shows the IIDFs of different generations of lenses. It can be Substituting the new IIDF of the light spot into Eq. (10), we can seen that a uniform distribution was adopted to calculate the first- recalculate the new profile of the freeform lens, as displayed in Fig. 7. generation lens (i.e., the original freeform lens). A rather uniform Compared with the original profile, the rectified profile of the freeform illumination could be obtained in the case of the PLS. However, for an lens experiences a slight adjustment, with an increased concavity in the extended source with a diameter of 5 mm, the illumination uniformity middle of the lens. became fairly poor. The central illumination was maximum and The rectified lens is then imported into MCRT so as to calculate the decreased rapidly outward. Moreover, the uniformity of the new PLS-ELS deviation. By using this method, from generation to illumination was only 73.5%, as shown in Fig. 10(a). generation, the bright region gradually diminishes, and the dark area gradually becomes bright. In this way, the light spot ultimately satisfies the design requirements.

the PLS (PLS-LED); and 3) a freeform lens LED designed by the EFFL method for ELS (ELS-LED), as shown in Fig. 11.

Input illumination

Fig. 9. The input illumination distribution functions (IIDFs) of different generations of lenses.

By calculating the new energy mapping function based on the PLS-ELS deviation, the second-generation freeform lens could be obtained. It is clear that the new IIDF presents a notable downward modification to the concavity in the central area. The MCRT shows that the energy in this area begins to decrease, as shown in Fig. 10 (g). Meanwhile, the radius of the light spot remains unchanged, and the uniformity increases to 75.7%. Nevertheless, the light spot is still bright in the center and dark at the edge. In this manner, new deviations are obtained, new generations of lenses are produced, and the optimization process continues. It can be seen that in the early stage of optimization (i.e., from the second to sixth generations), IIDF modifications in the central area become increasingly larger, with the downward inflection point moving toward the boundary. This indicates that the EFFL method extends the uniformity of the light spot from the center to the edge. By observing the ray-tracing result of the sixth-generation lens (Fig. 10(c)), it can be seen that the central illumination decreases to 0.77. At this stage, the location with the highest illumination of 0.80 is located 750 Simulated illumination mm away from the central point. This represents the so-called “over- suppressed phenomenon”. The uniformity has increased to 89% within the radius of 2000 mm, which approaches the convergence criteria. Figure 10(d) shows the simulated light spot of the eleventh-generation Fig. 10 The simulated light spot of different generations of lenses , (a) lens, which reveals that the illumination at the edge has been light spot of the lens before optimizing (i.e., the first-generation lens), (b) significantly improved, and that the bright boundary becomes clear as of the second-generation lens, (c) of the sixth-generation lens, (d) of the the illumination gradient increases; the uniformity at this point is eleventh-generation lens; (e) of the sixteenth-generation lens, and (f) of 91.6%. Unfortunately, because of the over-suppressed phenomenon, the nineteenth-generation lens. (g) The simulated illumination of the central illumination is apparently insufficient. According to the different generations of lenses, inset (1) the profile of the optimized rectification rule, an increased luminous flux should be distributed to freeform lens, inset (2) the 3d model of the optimized freeform lens. this area. The illumination uniformity reaches 94% when the lens reaches the sixteenth generation. The EFFL method finally converges during the nineteenth-generation lens with a final illumination uniformity of 95.6%, which is 22.1% higher than the original and satisfies the design requirements, the profile and 3d model of the optimized freeform lens is shown in Fig. (10) insets.

5. Manufacturing and Experiments The COB freeform lens compact devices (obtained in section 4) were manufactured and tested in order to investigate their optical performance. First, a mold with an accurate freeform surface was Fig. 11. High-power, chip-on-board (COB), compact light-emitting fabricated by a multi-spindle numerical control machine. Next, lead diode (LED) devices with (a) a non-freeform lens, (b) a freeform lens frames with 21 LED chips coated with YAG:Ce phosphors we prepared. with a design based on the point light source (PLS), and (c) a freeform Finally, the components we encapsulated with DOW CONING 6650 lens designed by the energy feedback freeform lens (EFFL) method for silicone by compression molding. For the purpose of comparison, three an extended light source (ELS). LED structures were manufactured: 1) a conventional compact LED (non-freeform lens LED (NL-LED]); 2) a freeform lens LED based on Figure 12 shows the variation of the luminous flux for each LED as a Considering the PLS-ELS deviation, we can expect that the light spot of function of the drive current. Overall, the two LEDs with freeform the ELS-LED is more uniform, and that the bright boundaries are much lenses emit more light than does the NL-LED. The ELS-LED has the clearer. highest luminous flux, which is 13% higher than that of the NL-LED. Finally, the illumination of the LEDs was field-tested, as shown in the This discrepancy can be explained as follows. In conventional LEDs, the insets of Fig. 14. The LEDs were fixed on a height-adjustable carrier scale of the lens is fit for the luminous area. The emitted light that is that emitted light downward. An illuminometer was used to measure back-reflected by the lens-air interface is quite likely to be absorbed by the illumination at a step of 50 cm from the center to the edge. Figure the chips or phosphors, which will lower the luminous efficiency 14 shows the illumination distributions with various heights. It can be [13,14]. However, concerning the freeform-lens-encapsulated LEDs, seen that, for the PLS-LED, the highest illumination appears at the the reflected light that is incident to the non-luminous area maintains center, and decreases along the radial direction. When the height is 2 m, the possibility of escaping. the illumination uniformity is only 76.4% in the light spot radius of 2 m. The inset in Fig. 12 shows the typical spectra of the LEDs, consisting of As the LED’s height is lowered, the illumination considerably increases, a blue wavelength peak (442 nm) and a yellow-green wavelength peak and the uniformity worsens. In particular, the uniformities are 71.1% (550 nm), with correlated color temperatures (CCT) of about 5000 K. and 52.0% at heights of 1.75 m and 1.5 m, respectively. Obviously, the ELS-LED emits a higher radiant flux, especially around the blue wavelength peak. This implies that ELS-LEDs will have a higher energy efficiency in real lighting applications.

10 9 8 7 6 5 4 Measured illumination 3 2 1 0 400 500 600 700 800

Fig. 12. Variation of the luminous flux of different white-light devices as a function of the drive current.

Figure 13 shows the angular intensity distribution of the LEDs. It can be observed that the NL-LED presents a Lambertian-like distribution; the highest intensity occurs along the central normal direction, and decreases gradually toward the boundary. The half-peak side boundaries are ±65º. Nevertheless, a designed wing-like angular intensity distribution has been achieved in the PLS-LEDs, and the directions of highest intensity appear at viewing angles of ±50º. We can expect that such an angular intensity distribution is closer to the design Measured illumination requirements. According to non-imaging optics, the area illuminated by luminous flux per unit solid angle becomes larger as the viewing angle (i.e., the normal direction) increases. Fig. 14. Illumination distributions with various heights of (a) the point light source light-emitting diode (PLS-LED) and (b) the extended light source light-emitting diode (ELS-LED).

For the ELS-LED, the illumination is moderate and uniform in the central area, though it increases at the edge, resulting in uniformities of 85.3%, 83.3%, and 74.0% at heights of 2 m, 1.75 m, and 1.5 m, respectively. It can be seen that the observed uniformity is inferior to that of the simulated results; this can be explained by the following Fig. 13. Angular intensity distributions of different illumination devices. considerations. First, the light source is simplified to an ideal The ELS-LED also exhibits a wing-like angular intensity distribution, Lambertian distribution in the simulations, though manufacturing but with the highest light intensity occurring at viewing angles of ±55º, errors are unavoidable in practice. Second, an unexpected color and a half-peak side boundary of ±60º. Compared with the PLS-LED, variance (i.e., a yellow ring) appeared during the LED field tests, which there are two main differences to note. First, the intensities at viewing was probably caused by the dispensing phosphor configurations [15]. angles of ±60º become steep and strong; second, the central intensity This indicates that the EFFL method is still at a young stage in its drops significantly. These findings indicate that more luminous flux is development, and that further improvements are required. In general, removed from the central area, and guided to the edge for the ELS-LED. however, the effect of using the ELS-LED to improve the illumination 13. Z.-T. Li, Q.-H. Wang, Y. Tang, C. Li, X.-R. Ding, and Z.-H. He, “Light quality is quite significant. extraction improvement for LED COB devices by introducing a patterned leadframe substrate configuration,” IEEE T. Electron. Dev. 6. conclusions 60(4), 1397-1403 (2013). 14. Z.-T. Li, Y. Tang, Z.-Y. Liu, Y.-E. Tan, and B.-M. Zhu, “Detailed study on A novel EFFL method is proposed in this paper in order to design pulse-sprayed conformal phosphor configurations for LEDs,” J. Display uniform illumination freeform lenses for use in high-power, compact, Technol. 9(6), 433-440 (2013). COB-LEDs. This represents a further development of the PDE design 15. Z. Liu, S. Liu, K. Wang, and X. Luo. Optical analysis of color distribution in method. which offers high efficiency, but also illumination deviation in white LEDs with various packaging methods. IEEE Photon. Technol. Lett. ELS cases. The new method introduces a pre-rectifying regime to the 20(24), 2027-29 (2008). lens calculation by using an anti-deviation IIDF for the source energy mapping. A detailed derivation of the EFFL method is presented, and a practical engineering case is field-tested. The results show that the method is able to diminish the bright region and brighten the dark area after generations of optimization, all while remaining a very high calculation efficiency. The simulated illumination uniformity of the lens designed by the EFFL method has been improved by 22.1%. Even though the manufacturing errors and the unexpected color variance would worsen the illumination performance, the effect of using the EFFL method to improve the illumination quality is still quite significant. Furthermore, the ELS-LED has the highest luminous flux, which is 13% higher than that of the NL-LED (i.e., the conventional compact COB-LED).

Funding. National Natural Science Foundation of China (U1401249, and No.51405161); Postdoctoral Science Foundation of China (2014M560659); Science & Technology Program of Guangdong Province (2014B010121002, 2014B090901065);

Acknowledgment. The authors thank technical help from Foshan Nationstar Optoelectronics Co.Ltd.

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