## Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating |

Optics Express, Vol. 20, Issue 13, pp. 13727-13737 (2012)

http://dx.doi.org/10.1364/OE.20.013727

Acrobat PDF (3006 KB)

### Abstract

A conformal phosphor coating can realize a phosphor layer with uniform thickness, which could enhance the angular color uniformity (ACU) of light-emitting diode (LED) packaging. In this study, a novel freeform lens was designed for simultaneous realization of LED uniform illumination and conformal phosphor coating. The detailed algorithm of the design method, which involves an extended light source and double refractions, was presented. The packaging configuration of the LED modules and the modeling of the light-conversion process were also presented. Monte Carlo ray-tracing simulations were conducted to validate the design method by comparisons with a conventional freeform lens. It is demonstrated that for the LED module with the present freeform lens, the illumination uniformity and ACU was 0.89 and 0.9283, respectively. The present freeform lens can realize equivalent illumination uniformity, but the angular color uniformity can be enhanced by 282.3% when compared with the conventional freeform lens.

© 2012 OSA

## 1. Introduction

## 2. Problem statement

## 3. Design method for freeform lens for conformal coating

- 1. Establishing the light–energy mapping relationship between the light source and the target plane.
- 2. Constructing the freeform lens. A circular target plane is adopted as the example in the following design, but the design method can also be extended to other target planes, such as a rectangular plane.

### 3.1 Establishing the light–energy mapping relationship

*M × N*grids with equal luminous flux, where the latitude is divided into

*N*parts and the longitude is divided into

*M*parts. Due to the central symmetry of the energy distribution of the light source, the light energy of each grid at the same latitude is the same. Then we can integrate the

*N*grids along the latitude together and just consider the

*M*parts along the longitude. According to the principle of photometry, the luminous flux of the unit area of the

*M*parts

*Ф(θ)*and the total light source

*Ф*can be calculated as Eq. (1) and Eq. (2), respectively. where

_{total}*I(θ)*is the light intensity, and

*θ*and

*φ*are the notions shown in Fig. 2. The edge angle

*θ*(

_{i}*i = 1,2,...,M*) of each part, which defines the direction of edge light of each source grid, can be calculated by Eq. (3). Thus the light source is divided into

*M*parts with equal luminous flux.

*M*concentric rings with unequal areas by inserting optimization coefficient

*C*. For an arbitrary circle area with a radius of

_{i}*r*, it is the summation of

_{i}*i*concentric rings and we can obtain

*r*of each concentric ring on the target plane can be calculated as

_{i}*C*to make the trend of illumination distribution on the target plane to be the inverse of the trend of light-performance deterioration caused by the rays emanating from the edge area of the LED chip. However, it should be noted that the assignment of

_{i}*C*is not arbitrary. Since the radius of the arbitrary circle area

_{i}*r*is incremental, according to Eq. (5), the series {

_{i}*iC*} must be an ascending series. The last term of the series

_{i}*MC*must be the largest, and at this situation,

_{M}*r*must equal to

_{M}*L*; thus,

*C*must be 1. Therefore, each term of {

_{M}*iC*} must be less than

_{i}*M*. According to the edge ray principle, rays from the edge of the light source should strike the edge of the target [14]. With the above gridding method, we can establish the light–energy mapping relationship between the extended light source and the target plane. As a result, we can obtain the edge angle

*θ*and the corresponding radius

_{i}*r*of each ray.

_{i}### 3.2 Constructing the freeform lens

*R*on the target plane. According to Snell's law, the ray

*n*,

_{1}*n*, and

_{2}*n*are the refractive indices of each area, respectively;

_{3}*n*is the refractive index of the phosphor silicone matrix;

_{1}*n*is the refractive index of the lens material; and

_{2}*n*equals 1.00 because the area is air.

_{3}*a*and a height of

*b*. Therefore, as shown in Fig. 4 , there exists a turning point

*A*on the inner surface. The edge angle of the incident ray corresponding to

_{T}*A*is denoted as

_{T}*θ*, which can be determined by

_{T}*θ*. According to relationship between the edge angle of the incident angle

_{T}= arctan(a/b)*θ*, the inner surface can be divided into two cases:

_{i}and θ_{T}- ● Case I: when the edge angle
*θ*is less than_{i}*θ*, the light path is illustrated as the light path of “_{T}*O-A*”._{i}-B_{i}-R_{i} - ● Case II: when the edge angle
*θ*is larger than_{j}*θ*, the light path is illustrated as the light path of “_{T}*O-A*”._{j}-B_{j}-R_{j}

*Case I*, when the inner surface is given, the coordinates of

*A*can be denoted as (

_{i}*b*× tan

*θ*). From the geometrical relationship in Fig. 4,

_{i}, b*α*equals

_{i}*θ*; therefore, the vector

_{i}*β*in Eq. (8). To obtain the coordinates of points

_{i}*B*on the outer surface, as shown in Fig. 5 , we first fix an initial point

_{i}*B*as the vertex of the outer surface of the lens, and the normal vector at this point is vertical up. The second point

_{0}*B*can be calculated by the intersection of the incident ray

_{1}*B*. Since the corresponding point

_{0}*R*was determined previously, according to Eq. (7), we can then calculate the unit normal vector on point

_{1}*B*on the outer surface and consequently obtain the tangent plane. The tangent plane on point

_{1}*B*can help obtain the coordinates of the next point

_{1}*B*. By repeating this process until the edge angle

_{2}*θ*approaches

_{i}*θ*, we can get all of the points

_{T}*B*and their unit normal vectors on the outer surface.

_{i}*Case II*, the coordinates of

*A*can be denoted as (

_{j}*a*,

*a*× cot

*θ*). From Fig. 4,

_{j}*α*equals to (

_{j}*π/2*-

*θ*), therefore the vector

_{j}*β*in Eq. (8). With the similar method in

_{j}*Case I*, we could obtain the coordinates of

*B*on the outer surface.

_{j}## 4. Simulation methodology

### 4.1 Model setup

^{−1}and 2.45, 2.54, and 2.42, respectively [28,29]. The reflection coefficient of the reflecting layer (Ag) was set as 0.95. By setting the absorption coefficients and refractive indices of the materials, the precise model of a conventional GaN blue LED chip could be achieved successfully.

### 4.2 Simulation process

*C*until the lighting performance satisfied the requirements of some specific applications.

_{i}^{3}. The necessary parameters in the simulations can be found in our previous works [28,29,32–34]. For modeling the light conversion process, the rays of blue and yellow light were simulated separately by the Monte Carlo ray-tracing method. In the simulation, two wavelengths were ray traced separately, namely 465 nm and 555 nm, which represent the blue LED light and the phosphor-converted yellow light, respectively [28,29]. The blue light emanated from the top surface of the chip and the yellow light was emitted from the volume of phosphor silicone matrix according to the distribution of phosphor particles inside the silicone matrix.

## 5. Results and discussions

## 6. Conclusions

## Acknowledgments

## References and links

1. | S. Pimputkar, J. S. Speck, S. P. Denbaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics |

2. | E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science |

3. | S. Tonzani, “Lighting technology: Time to change the bulb,” Nature |

4. | Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Status and prospects for phosphor-based white LED packaging,” Front. Optoelectron. China |

5. | N. Narendran, “Is solid-state lighting ready for the incandescent lamp phase-out?” Proc. SPIE |

6. | S. Liu and X. B. Luo, |

7. | K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express |

8. | P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. |

9. | J. C. Miñano, P. Benítez, J. Y. Liu, J. Infante, J. Chaves, and W. Lin, “Applications of the SMS method to design of compact optics,” Proc. SPIE |

10. | H. Ries and J. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE |

11. | Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express |

12. | K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. |

13. | L. Wang, K. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. |

14. | K. Wang, D. Wu, Z. Qin, F. Chen, X. B. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express |

15. | F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. |

16. | F. Chen, K. Wang, Z. Qin, D. Wu, X. B. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express |

17. | Z. Qin, K. Wang, F. Chen, X. B. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express |

18. | S. Wang, K. Wang, F. Chen, and S. Liu, “Design of primary optics for LED chip array in road lighting application,” Opt. Express |

19. | C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. |

20. | K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett. |

21. | W. D. Collins, M. R. Krames, G. J. Verhoeckx, and N. J. M. Leth, “Using electrophoresis to produce a conformal coated phosphor-converted light emitting semiconductor,” US Patent 6576488 (2001). |

22. | B. Hou, H. B. Rao, and J. F. Li, “Phosphor coating technique with slurry method in application of white LED,” Proc. SPIE |

23. | J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y |

24. | B. P. Loh, N. W. Medendorp, Jr., P. Andrews, Y. Fu, M. Laughner, and R. Letoquin, “Method of uniform phosphor chip coating and LED package fabricated using method,” US Patent 20080079017 A1 (2008). |

25. | B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE |

26. | H. Zheng, X. B. Luo, R. Hu, B. Cao, X. Fu, Y. M. Wang, and S. Liu, “Conformal phosphor coating using capillary microchannel for controlling color deviation of phosphor-converted white light-emitting diodes,” Opt. Express |

27. | L. Piegl and W. Tiller, |

28. | Z. Y. Liu, K. Wang, X. B. Luo, and S. Liu, “Precise optical modeling of blue light-emitting diodes by Monte Carlo ray-tracing,” Opt. Express |

29. | R. Hu, X. B. Luo, and S. Liu, “Study on the optical properties of conformal coating light-emitting diode by Monte Carlo simulation,” IEEE Photon. Technol. Lett. |

30. | C. Sommer, F. Reil, J. R. Krenn, P. Hartmann, P. Pachler, H. Hoschopf, and F. P. Wenzl, “The impact of light scattering on the radiant flux of phosphor-converted high power white light-emitting diodes,” J. Lightwave Technol. |

31. | C. Sommer, F. P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett. |

32. | Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging,” Appl. Opt. |

33. | R. Hu, X. B. Luo, H. Feng, and S. Liu, “Effect of phosphor settling on the optical performance of phosphor-converted white light-emitting diodes,” J. Lumin. |

34. | Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(220.3630) Optical design and fabrication : Lenses

(230.3670) Optical devices : Light-emitting diodes

(350.4600) Other areas of optics : Optical engineering

(220.2945) Optical design and fabrication : Illumination design

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: April 16, 2012

Revised Manuscript: May 16, 2012

Manuscript Accepted: May 21, 2012

Published: June 4, 2012

**Citation**

Run Hu, Xiaobing Luo, Huai Zheng, Zong Qin, Zhiqiang Gan, Bulong Wu, and Sheng Liu, "Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating," Opt. Express **20**, 13727-13737 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13727

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### References

- S. Pimputkar, J. S. Speck, S. P. Denbaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics3(4), 180–182 (2009).
- E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005).
- S. Tonzani, “Lighting technology: Time to change the bulb,” Nature459(7245), 312–314 (2009).
- Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Status and prospects for phosphor-based white LED packaging,” Front. Optoelectron. China2, 119–140 (2009).
- N. Narendran, “Is solid-state lighting ready for the incandescent lamp phase-out?” Proc. SPIE8123, 812302 (2011).
- S. Liu and X. B. Luo, LED Packaging for Lighting Applications: Design, Manufacturing and Testing (John Wiley & Sons, 2011).
- K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
- P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).
- J. C. Miñano, P. Benítez, J. Y. Liu, J. Infante, J. Chaves, and W. Lin, “Applications of the SMS method to design of compact optics,” Proc. SPIE7717, 771701 (2010).
- H. Ries and J. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE4442, 43–50 (2001).
- Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008).
- K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
- L. Wang, K. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt.46(18), 3716–3723 (2007).
- K. Wang, D. Wu, Z. Qin, F. Chen, X. B. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express19(Suppl 4), A830–A840 (2011).
- F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
- F. Chen, K. Wang, Z. Qin, D. Wu, X. B. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express18(20), 20926–20938 (2010).
- Z. Qin, K. Wang, F. Chen, X. B. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express18(16), 17460–17476 (2010).
- S. Wang, K. Wang, F. Chen, and S. Liu, “Design of primary optics for LED chip array in road lighting application,” Opt. Express19(Suppl 4), A716–A724 (2011).
- C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater.31(6), 837–848 (2009).
- K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
- W. D. Collins, M. R. Krames, G. J. Verhoeckx, and N. J. M. Leth, “Using electrophoresis to produce a conformal coated phosphor-converted light emitting semiconductor,” US Patent 6576488 (2001).
- B. Hou, H. B. Rao, and J. F. Li, “Phosphor coating technique with slurry method in application of white LED,” Proc. SPIE6841, 684106 (2007).
- J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al4O12:Ce0.05 phosphor coating methods for white light-emitting diode on gallium nitride,” Proc. SPIE4445, 60–69 (2001).
- B. P. Loh, N. W. Medendorp, Jr., P. Andrews, Y. Fu, M. Laughner, and R. Letoquin, “Method of uniform phosphor chip coating and LED package fabricated using method,” US Patent 20080079017 A1 (2008).
- B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE6486, 64860X (2007).
- H. Zheng, X. B. Luo, R. Hu, B. Cao, X. Fu, Y. M. Wang, and S. Liu, “Conformal phosphor coating using capillary microchannel for controlling color deviation of phosphor-converted white light-emitting diodes,” Opt. Express20(5), 5092–5098 (2012).
- L. Piegl and W. Tiller, The NURBS Book, 2nd ed. (Springer, 1996).
- Z. Y. Liu, K. Wang, X. B. Luo, and S. Liu, “Precise optical modeling of blue light-emitting diodes by Monte Carlo ray-tracing,” Opt. Express18(9), 9398–9412 (2010).
- R. Hu, X. B. Luo, and S. Liu, “Study on the optical properties of conformal coating light-emitting diode by Monte Carlo simulation,” IEEE Photon. Technol. Lett.23(22), 1673–1675 (2011).
- C. Sommer, F. Reil, J. R. Krenn, P. Hartmann, P. Pachler, H. Hoschopf, and F. P. Wenzl, “The impact of light scattering on the radiant flux of phosphor-converted high power white light-emitting diodes,” J. Lightwave Technol.29(15), 2285–2291 (2011).
- C. Sommer, F. P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
- Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging,” Appl. Opt.49(2), 247–257 (2010).
- R. Hu, X. B. Luo, H. Feng, and S. Liu, “Effect of phosphor settling on the optical performance of phosphor-converted white light-emitting diodes,” J. Lumin.132(5), 1252–1256 (2012).
- Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).

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