Abstract

Versatility in the design of optical systems is one of the key features of light-emitting diodes (LEDs) that has attracted considerable attention. In the analysis of systems using LEDs, it is useful to know if the distance is far enough from the LED to allow the radiation pattern to be simulated by the point source approach. We propose three far-zone conditions for LED light modeling: the far-field distance, and for practical purposes the quasi far-field and minimum far-field distances. Different types of LEDs have different far-field ranges. We analyze these differences by modulating key parameters like geometrical structure of encapsulating lens, chip size, chip shape, chip position, and package errors. We find that far-field region considerably depends more on the shape of both lens and chip than all other parameters.

© 2009 OSA

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References

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  1. C. C. Sun, C. Y. Chen, H. Y. He, C. C. Chen, W. T. Chien, T. X. Lee, and T. H. Yang, “Precise optical modeling for silicate-based white LEDs,” Opt. Express 16(24), 20060–20066 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
    [CrossRef] [PubMed]
  7. A. Pawlak and K. Zaremba, “Reflector luminaire with high power light-emitting diodes for general lighting,” Appl. Opt. 47(3), 467–473 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
    [CrossRef]
  14. H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
    [CrossRef]
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    [CrossRef]

2009 (2)

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

I. Moreno, C. C. Sun, and R. Ivanov, “Far-field condition for light-emitting diode arrays,” Appl. Opt. 48(6), 1190–1197 (2009).
[CrossRef]

2008 (9)

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

A. Pawlak and K. Zaremba, “Reflector luminaire with high power light-emitting diodes for general lighting,” Appl. Opt. 47(3), 467–473 (2008).
[CrossRef] [PubMed]

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008).
[CrossRef] [PubMed]

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[CrossRef] [PubMed]

C. H. Tsuei, J. W. Pen, and W. S. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express 16(23), 18692–18701 (2008).
[CrossRef]

C. C. Sun, C. Y. Chen, H. Y. He, C. C. Chen, W. T. Chien, T. X. Lee, and T. H. Yang, “Precise optical modeling for silicate-based white LEDs,” Opt. Express 16(24), 20060–20066 (2008).
[CrossRef] [PubMed]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

2007 (2)

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express 15(12), 7572–7577 (2007).
[CrossRef] [PubMed]

2006 (2)

2004 (1)

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Avendaño-Alejo, M.

Beni´tez, P.

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Bergmans, J. W. M.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

Chao, P. C. P.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Chen, C. C.

Chen, C. Y.

Chi, S.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Chien, W. T.

Chiu, C. W.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Ding, Y.

Dross, O.

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Feng, D.

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Gan, Z. Y.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Gu, P. F.

He, H. Y.

Huang, J. S.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Huang, S. M.

Ivanov, R.

Kao, Y. Y.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Kim, H. C.

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Kim, W.

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Lee, T. X.

Lee, Y. L.

Lin, H. W.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Linnartz, J. P. M. G.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

Liu, S.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Liu, X.

Liu, Z. Y.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Luo, X. B.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Ma, S. H.

Miñano, J. C.

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Moreno, I.

Muñoz, F.

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Nagatani, K.

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Parkyn, B.

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Pawlak, A.

Peifu, G.

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

Pen, J. W.

Rietman, R.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

Schenk, T. C. W.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

Shen, C. Y.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Sun, C. C.

Sun, W. S.

Tsai, S. Y.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Tsuei, C. H.

Tu, T. Y.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Tzonchev, R. I.

Wang, C. L.

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Wang, K.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Xiang, H.

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

Xu, L.

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

Yang, H.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16(26), 21641–21646 (2008).
[CrossRef] [PubMed]

Yang, T. H.

Yoo, J.

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Zaremba, K.

Zheng, Z. R.

Zhenrong, Z.

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

Zhou, B.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Signal Process. (1)

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57(3), 1044–1057 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10(7), 075005 (2008).
[CrossRef]

J. Soc. Inf. Disp. (1)

P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16(2), 317–327 (2008).
[CrossRef]

Jpn. J. Appl. Phys. (1)

D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(2), 563–565 (2007).
[CrossRef]

Opt. Eng. (2)

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

F. Muñoz, P. Benı́tez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

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Figures (13)

Fig. 1.
Fig. 1.

There are three basic working conditions for the optical modeling and experimental characterization of the radiation pattern of an LED: near-field, mid-field and far-field.

Fig. 2.
Fig. 2.

(a) Schematic diagram used in the simulation of the angular intensity distribution of an LED. Distance D is measured from the LED tip. (b) Geometric model of batwing LED from Lumileds Lighting.

Fig. 3.
Fig. 3.

The simulated and the measured radiation patterns of the LED depicted in Fig. 2(b). The radiation patterns are measured at (a) D = 15mm, (b) D = 30mm, (c) D = 60mm and (d) D = 300mm.

Fig. 4.
Fig. 4.

NCC in function of distance D from the LED. This NCC is for the LED shown in Fig. 2(b) Also are shown the minimum far-field (MFF), quasi far-field (QFF), and far-field (FF) distances of this LED.

Fig. 5.
Fig. 5.

Lens size dependence. (a) NCC in function of distance D from the LED. Inset shows geometry of the encapsulated LED. (b) Far field region for several lens sizes.

Fig. 6.
Fig. 6.

Lens thickness dependence. (a) NCC in function of distance from the LED tip. (b) Far field region for several lens thicknesses.

Fig. 7.
Fig. 7.

Lens width dependence. (a) NCC in function of distance from the tip of LED. (b) Far field range for several lens widths.

Fig. 8.
Fig. 8.

Chip size dependence. (a) NCC in function of distance D from the LED. (b) Far field region for several chip sizes A.

Fig. 9.
Fig. 9.

Diameter dependence for an hemispherical source. (a) NCC in function of distance D from the LED. (b) Far field range for several source sizes Rs.

Fig. 10.
Fig. 10.

Diameter dependence for an elliptic source. (a) NCC in function of distance D from the LED. (b) Far field range for several ellipse semi-axis sizes Ls.

Fig. 11.
Fig. 11.

Backward displacement of chip. (a) NCC in function of distance D from the LED. (b) Far field region for several chip displacements h.

Fig. 12.
Fig. 12.

Forward displacement of chip. (a) NCC in function of distance D from the LED. (b) Far field range for several chip displacements H.

Fig. 13.
Fig. 13.

Chip transverse displacement dependence. (a) NCC in function of distance D from the LED. (b) Far field range for several chip displacements t.

Equations (1)

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NCC=n[I(θn)DI¯D][I(θn)RI¯R]n[I(θn)DI¯D]2n[I(θn)RI¯R]2 ,

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