Abstract

A Fresnel lens is an optical component that can be used to create systems more compact, cost-effective, and lightweight than those using conventional continuous surface optics. However, Fresnel lenses can usually cause a loss of flux efficiency and non-uniform distribution of illuminance due to secondary refraction by surface discontinuities, especially along the groove facet. We therefore proposed to modify a groove angle in the Fresnel lens and analyzed interrelation between the groove angle and multiple optical performances, such as flux efficiency and the uniformity of illuminance and color. The groove angle was optimized to maximize the uniformity and efficiency in the target viewing angle considering various weights of merit functions. Specifically, in our study, when the uniformity of illuminance had a little more weight than the flux efficiency (ratio of 0.6:0.4), final optimum groove angles of 24.7°, 29.4°, and 31.3° were obtained at target viewing angles of 20°, 30°, and 40°, respectively. We also fabricated a modified Fresnel lens with a groove angle of 29.4° using UV-imprinting. The real optical performance of the fabricated Fresnel lens was then compared to that of a spherical lens.

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References

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    [CrossRef]
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    [CrossRef]
  6. L. Frank, S. J. Pedrotti, L. M. Pedrotti, L. S. Pedrotti, Introduction to Optics, 3nd Edition (Pearson, ST., San Francisco, 2007)
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. G. Wyszecki and W. S. Stiles, Color Science 2nd Edition (Wiley, New York, 1982).
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    [CrossRef]
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    [CrossRef] [PubMed]

2008

2007

Y. Zhen, Z. Jiaa, and W. Zhang, “The Optimal Design of TIR Lens for Improving LED Illumination Uniformity and Efficiency,” Proc. SPIE 6834, 68342K (2007).
[CrossRef]

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

2006

2005

Á. Borbély and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44(11), 111308 (2005).
[CrossRef]

Y. Uchida and T. Taguchi, “Lighting theory and luminous characteristics of white light-emitting diodes,” Opt. Eng. 44(12), 124003–1 (2005).
[CrossRef]

1951

Avendaño-Alejo, M.

Bierhuizen, S.

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

Borbély, Á.

Á. Borbély and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44(11), 111308 (2005).
[CrossRef]

Fournier, F.

Harbers, G.

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

Hovila, J.

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

Huang, S.-M.

Ikonen, E.

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

Jiaa, Z.

Y. Zhen, Z. Jiaa, and W. Zhang, “The Optimal Design of TIR Lens for Improving LED Illumination Uniformity and Efficiency,” Proc. SPIE 6834, 68342K (2007).
[CrossRef]

Johnson, S. G.

Á. Borbély and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44(11), 111308 (2005).
[CrossRef]

K¨arh¨a, P.

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

Kang, S.

Kim, H.

Kim, S. M.

Krames, M.

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

Lee, T.-X.

Lee, Y.-L.

Ma, S.-H.

Manninen, P.

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

Mcleod, J. H.

Miller, O. E.

Moreno, I.

Rolland, J.

Sherwood, W. T.

Sun, C.-C.

Taguchi, T.

Y. Uchida and T. Taguchi, “Lighting theory and luminous characteristics of white light-emitting diodes,” Opt. Eng. 44(12), 124003–1 (2005).
[CrossRef]

Tzonchev, R. I.

Uchida, Y.

Y. Uchida and T. Taguchi, “Lighting theory and luminous characteristics of white light-emitting diodes,” Opt. Eng. 44(12), 124003–1 (2005).
[CrossRef]

Weijers, G.

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

Zhang, W.

Y. Zhen, Z. Jiaa, and W. Zhang, “The Optimal Design of TIR Lens for Improving LED Illumination Uniformity and Efficiency,” Proc. SPIE 6834, 68342K (2007).
[CrossRef]

Zhen, Y.

Y. Zhen, Z. Jiaa, and W. Zhang, “The Optimal Design of TIR Lens for Improving LED Illumination Uniformity and Efficiency,” Proc. SPIE 6834, 68342K (2007).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Meas. Sci. Technol.

P. Manninen, J. Hovila, P. Karha, and E. Ikonen, “Method for analysing luminous intensity of light-emitting diodes,” Meas. Sci. Technol. 18(1), 223–229 (2007).
[CrossRef]

Opt. Eng.

Á. Borbély and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44(11), 111308 (2005).
[CrossRef]

Y. Uchida and T. Taguchi, “Lighting theory and luminous characteristics of white light-emitting diodes,” Opt. Eng. 44(12), 124003–1 (2005).
[CrossRef]

Opt. Lett.

Proc. SPIE

Y. Zhen, Z. Jiaa, and W. Zhang, “The Optimal Design of TIR Lens for Improving LED Illumination Uniformity and Efficiency,” Proc. SPIE 6834, 68342K (2007).
[CrossRef]

S. Bierhuizen, M. Krames, G. Harbers, and G. Weijers, “Performance and trends of high power light emitting diodes,” Proc. SPIE 6669, 66690B (2007).
[CrossRef]

Other

L. Frank, S. J. Pedrotti, L. M. Pedrotti, L. S. Pedrotti, Introduction to Optics, 3nd Edition (Pearson, ST., San Francisco, 2007)

G. Wyszecki and W. S. Stiles, Color Science 2nd Edition (Wiley, New York, 1982).

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Figures (14)

Fig. 1
Fig. 1

Schematic distribution of the intensity Iθ and the illuminance Eθ of an original source with no lens and an optical lens in far field distance

Fig. 2
Fig. 2

Analysis of white LED module by (a) microscope image at surface of slice AA’, (b) main path of rays emitted from each surface of the chip.

Fig. 3
Fig. 3

Concept to design the discontinuous surface of a Fresnel lens and the optical path difference of each case with (a) normal groove angle of 0°, (b) modified groove angle of θ degree

Fig. 4
Fig. 4

Geometrical configuration to design (a) a normal spherical lens and (b) a modified Fresnel lens for a target viewing angle

Fig. 5
Fig. 5

Simulation result of intensity distributions to verify corrected specifications of Fresnel lens with groove angle of 0° for each target viewing angle.

Fig. 6
Fig. 6

Simulation result of illuminance distributions of each Fresnel lens in normalized area, where r/z is 0.364, 0.577 and 0.839 at each viewing angles of 20°, 30° and 40°.

Fig. 7
Fig. 7

Optimum design process of Fresnel lens with modified groove angle for various viewing angle

Fig. 8
Fig. 8

Graph of (a) the flux efficiency, (b) the normalized deviation of illuminance, (c) the normalized deviation of color calculated at various groove angle for each target viewing angle

Fig. 10
Fig. 10

Comparison of color and normalized illuminance distribution of rays emitted from each surface of the LED source (a) without any lens, (b) with a spherical lens (c) with a Fresnel lens with a groove angle of 0° and (d) with a Fresnel lens with the optimum groove angle of 29.4° at weight ratio of w1: w2 = 0.4: 0.6

Fig. 11
Fig. 11

Comparison of the normalized deviation of illuminance and color, (a) 0.334, 0.01761 for a spherical lens, (b) 0.314 and 0.00714 for a Fresnel lens with groove angle of 0° and (c) 0.218 and 0.007 for a Fresnel lens with optimum groove angle of 29.4° at weight ratio of w1: w2 = 0.4: 0.6

Fig. 9
Fig. 9

Calculated optimum groove angles, which are 24.7°, 29.4°, 31.3° as values to be dMF/dθ = 0 at weight ratio of w1: w2 = 0.4: 0.6 for each target viewing angles

Fig. 12
Fig. 12

(a) Process flow of UV-imprinting for the fabrication of modified Fresnel lens and (b) microscope image and surface profile of the fabricated modified Fresnel lens with optimum groove angle for target viewing angle of 30°.

Fig. 13
Fig. 13

fabricated modified Fresnel lens with optimum design and accompanying LED module

Fig. 14
Fig. 14

Measured results of (a) the intensity distributions of each lens for target viewing angle of 30° and (b) the distribution of illuminance and color with the normalized deviation of illuminance and color, 0.331, 0.0214 for spherical lens and 0.214 and 0.0079 for fabricated Fresnel lens.

Tables (1)

Tables Icon

Table 1 Corrected final specifications of Fresnel lens with groove angle of 0° for the each target viewing angle.

Equations (10)

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R=snL(nL1)tanθin+tn1(nLn1)tanθinnL(tanθoutn1tanθin),
yn=R2(RnTN)2+(n1)TNtan(θgroove)   ,(n=1,2,...N),
yn'=yn+TNtan(θgroove)
Zn(y)=nTN(RR2(y(n1)TNtan(θgroove))2)   ,(yn1'<y<yn),
F1(θgroove)   =ΦθΦinput,
F2(θgroove)   =1Lavgk=1n(LkLavg)2n,
F3(θgroove)   =1(uavg,vavg)k=1n((ukuavg)2+(vkvavg)2)n,((uavg,vavg)=uavg2+vavg2),
Fi   =n=03ai,nxn(i=1,2),
f¯i(θgroove)   =Fi.maxFiFi.maxFi.minorFiFi.minFi.maxFi.min   (i=1,2),
MF   =i=12wif¯i,i=12wi=1,

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