Abstract

Algorithms for selecting LEDs to imitate a group of daylight spectra, instead of fixed-spectrum lighting, are based on minimizing two indices. The first index related to the LEDs only is minimized for determining LED candidates. Minimizing the second index obtained by applying the daylight spectra to the candidates achieves a minimax solution. The sum of the second indices of the daylight spectra can be well approximated by that of the average spectrum of the daylight spectra and is treated as a target spectrum for the LED selection. A pruning process is followed to delete redundant LEDs.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2007 (1)

M. Liu, B. Rong, and H. W. M. Salemink, “Evaluation of LED application in general lighting,” Opt. Eng. 46, 074002(2007).
[CrossRef]

2005 (3)

H. Y. Chou, T. H. Hsu, and T. H. Yang, “Effective method for improving illuminating properties of white-light LEDs,” Proc. SPIE 5739, 33-41 (2005).
[CrossRef]

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44, 1-9 (2005).
[CrossRef]

2004 (1)

J. Y. Tsao, “Solid-state lighting: lamps, chips, and materials for tomorrow,” IEEE Circuits Devices Mag. 20(3), 28-37(2004).
[CrossRef]

2003 (2)

D. G. Pelka and K. Patel, “An overview of LED applications for general illumination,” Proc. SPIE 5186, 15-26(2003).
[CrossRef]

H. Ries, I. Leike, and J. Muschaweck, “Mixing colored LED sources,” Proc. SPIE 5186, 27-32 (2003).
[CrossRef]

2002 (2)

D. A. Steigerwald, J. C. Bhat, and D. Collins, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310-320 (2002).
[CrossRef]

F. J. P. Schuurmans and M. D. Pashley, “Red, green, and blue LEDs for white light illumination,” IEEE J. Sel. Top. Quantum Electron. 8333-338 (2002).
[CrossRef]

1997 (1)

1972 (1)

Bhat, J. C.

D. A. Steigerwald, J. C. Bhat, and D. Collins, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310-320 (2002).
[CrossRef]

Blake, R.

R. Sekuler and R. Blake, Perception, 3rd ed., (McGraw Hill, 1994), p. 195.

Chou, H. Y.

H. Y. Chou, T. H. Hsu, and T. H. Yang, “Effective method for improving illuminating properties of white-light LEDs,” Proc. SPIE 5739, 33-41 (2005).
[CrossRef]

Collins, D.

D. A. Steigerwald, J. C. Bhat, and D. Collins, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310-320 (2002).
[CrossRef]

García-Beltrán, A.

Hernández-Andrés, J.

Hsu, T. H.

H. Y. Chou, T. H. Hsu, and T. H. Yang, “Effective method for improving illuminating properties of white-light LEDs,” Proc. SPIE 5739, 33-41 (2005).
[CrossRef]

Leike, I.

H. Ries, I. Leike, and J. Muschaweck, “Mixing colored LED sources,” Proc. SPIE 5186, 27-32 (2003).
[CrossRef]

Liu, M.

M. Liu, B. Rong, and H. W. M. Salemink, “Evaluation of LED application in general lighting,” Opt. Eng. 46, 074002(2007).
[CrossRef]

Meyer, C. D.

C. D. Meyer, Matrix Analysis and Applied Linear Algebra (Society for Industrial and Applied Mathematics, 2000).
[CrossRef]

Muschaweck, J.

H. Ries, I. Leike, and J. Muschaweck, “Mixing colored LED sources,” Proc. SPIE 5186, 27-32 (2003).
[CrossRef]

Nascimento, S. M. C.

Nieves, J. L.

Ohno, Y.

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44, 1-9 (2005).
[CrossRef]

Ohta, N.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes 2nd ed. (McGraw-Hill, 1984), p. 167.

Pashley, M. D.

F. J. P. Schuurmans and M. D. Pashley, “Red, green, and blue LEDs for white light illumination,” IEEE J. Sel. Top. Quantum Electron. 8333-338 (2002).
[CrossRef]

Patel, K.

D. G. Pelka and K. Patel, “An overview of LED applications for general illumination,” Proc. SPIE 5186, 15-26(2003).
[CrossRef]

Pelka, D. G.

D. G. Pelka and K. Patel, “An overview of LED applications for general illumination,” Proc. SPIE 5186, 15-26(2003).
[CrossRef]

Ries, H.

H. Ries, I. Leike, and J. Muschaweck, “Mixing colored LED sources,” Proc. SPIE 5186, 27-32 (2003).
[CrossRef]

Romero, J.

Rong, B.

M. Liu, B. Rong, and H. W. M. Salemink, “Evaluation of LED application in general lighting,” Opt. Eng. 46, 074002(2007).
[CrossRef]

Salemink, H. W. M.

M. Liu, B. Rong, and H. W. M. Salemink, “Evaluation of LED application in general lighting,” Opt. Eng. 46, 074002(2007).
[CrossRef]

Schuurmans, F. J. P.

F. J. P. Schuurmans and M. D. Pashley, “Red, green, and blue LEDs for white light illumination,” IEEE J. Sel. Top. Quantum Electron. 8333-338 (2002).
[CrossRef]

Sekuler, R.

R. Sekuler and R. Blake, Perception, 3rd ed., (McGraw Hill, 1994), p. 195.

Steigerwald, D. A.

D. A. Steigerwald, J. C. Bhat, and D. Collins, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310-320 (2002).
[CrossRef]

Tsao, J. Y.

J. Y. Tsao, “Solid-state lighting: lamps, chips, and materials for tomorrow,” IEEE Circuits Devices Mag. 20(3), 28-37(2004).
[CrossRef]

Urabe, H.

Valero, E. M.

Watkins, D. S.

D. S. Watkins, Fundamentals of Matrix Computations (Wiley, 1991).

Yang, T. H.

H. Y. Chou, T. H. Hsu, and T. H. Yang, “Effective method for improving illuminating properties of white-light LEDs,” Proc. SPIE 5739, 33-41 (2005).
[CrossRef]

Appl. Opt. (2)

IEEE Circuits Devices Mag. (1)

J. Y. Tsao, “Solid-state lighting: lamps, chips, and materials for tomorrow,” IEEE Circuits Devices Mag. 20(3), 28-37(2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

F. J. P. Schuurmans and M. D. Pashley, “Red, green, and blue LEDs for white light illumination,” IEEE J. Sel. Top. Quantum Electron. 8333-338 (2002).
[CrossRef]

D. A. Steigerwald, J. C. Bhat, and D. Collins, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8, 310-320 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44, 1-9 (2005).
[CrossRef]

M. Liu, B. Rong, and H. W. M. Salemink, “Evaluation of LED application in general lighting,” Opt. Eng. 46, 074002(2007).
[CrossRef]

Proc. SPIE (3)

H. Ries, I. Leike, and J. Muschaweck, “Mixing colored LED sources,” Proc. SPIE 5186, 27-32 (2003).
[CrossRef]

D. G. Pelka and K. Patel, “An overview of LED applications for general illumination,” Proc. SPIE 5186, 15-26(2003).
[CrossRef]

H. Y. Chou, T. H. Hsu, and T. H. Yang, “Effective method for improving illuminating properties of white-light LEDs,” Proc. SPIE 5739, 33-41 (2005).
[CrossRef]

Other (8)

A. Papoulis, Probability, Random Variables, and Stochastic Processes 2nd ed. (McGraw-Hill, 1984), p. 167.

Nichia, “LED products,” http://www.nichia.com/cn/product/led.html.

Jiann Wa, “LED products,” http://www.jiannwa.com/con-1.htm.

Unity Opto, “LED products,” http://www.unityopto.com.tw/products/index.htm.

Laster Tech, “LED products,” http://www.lastertech.com/Tchinese/s3_2.htm.

R. Sekuler and R. Blake, Perception, 3rd ed., (McGraw Hill, 1994), p. 195.

C. D. Meyer, Matrix Analysis and Applied Linear Algebra (Society for Industrial and Applied Mathematics, 2000).
[CrossRef]

D. S. Watkins, Fundamentals of Matrix Computations (Wiley, 1991).

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Figures (5)

Fig. 1
Fig. 1

Peak relationship between three individual LED curves and the synthesized curve with 50 nm FWHM. (a) Peaks of individual curves are the same as the peaks of the synthesized curve. (b) The middle peak has disappeared, while the remaining two peaks of the individual curves are the same as the peaks of the synthesized curve.

Fig. 2
Fig. 2

Ten peaks and their corresponding wavelengths of E avg ( λ ) . These wavelengths are chosen as the peak wavelengths of ten LEDs for synthesizing daylight spectra.

Fig. 3
Fig. 3

Linearly combined spectrum of the ten LEDs in Fig. 2 with unity coefficients. Two LEDs whose peak wavelengths are 510 and 585 nm are added to form a 12-LED set with a lower SRSE value.

Fig. 4
Fig. 4

E avg ( λ ) and its synthesized waveforms by the 12-LED set with a GFC of 0.999710 and synthesis error of 0.023828 in an ideal case, and with a GFC of 0.998312 and synthesis error of 0.050371 for the 12-LED set in a practical case.

Fig. 5
Fig. 5

33 LED spectra collected from websites of different companies.

Tables (5)

Tables Icon

Table 1 10 LEDs Selected According to the Peaks of E avg ( λ ) in Fig. 2 and Two More LEDs Added to Form a 12-LED Set with Less SRSE Value a

Tables Icon

Table 2 Synthesis Metrics for Synthesizing E avg ( λ ) in Each Pruning Process from 12 LEDs to 6 LEDs a

Tables Icon

Table 3 Synthesis Metrics for the 416 Daylight Spectra Synthesized by the 6-LED Set Selected According to Table 2

Tables Icon

Table 4 Top 10 6-LED Set Combinations Selected from 12 LEDs with Small SRSE Values and Their Associated AC / DC Energy Ratios

Tables Icon

Table 5 416 Daylight Spectra Synthesized by the 12 LEDs Selected from 33 Commercial LEDs with Broad FWHM and Pruned to 7 or 6 LEDs

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

E ^ j ( λ ) = i = 1 M C i , j d i ( λ ) ,
C j = ( A A T ) 1 A E j = A + E j .
A = [ d 1 ( 1 ) , d 1 ( 2 ) d 1 ( 61 ) d M ( 1 ) , d M ( 2 ) d M ( 61 ) ]
E ^ j = A T C j = A T A + E j .
E j E j ^ = ( I A T A + ) E j ,
E j = η j [ 1 1 ] + E a c , j = E d c , j + E a c , j ,
E j E ^ j = ( I A t A + ) ( E d c , j + E a c , j ) = η j ( I A t A + ) [ 1 1 ] + ( I A t A + ) E a c , j = η j [ s 1 s 61 ] + ( I A t A + ) E a c , j ,
E j E ^ j = η j [ s 1 s 61 ] + [ σ 1 , j σ 61 , j ] ,
E j E ^ j = [ i = 1 61 ( η j s i + σ i , j ) 2 ] 1 / 2 = η j [ i = 1 61 ( s i + σ i , j η j ) 2 ] 1 / 2 = η j [ i = 1 61 ( s i 2 + 2 s i σ i , j η j + ( σ i , j η j ) 2 ) ] 1 / 2 .
E j E ^ j η j [ i = 1 61 s i 2 + 2 ( i = 1 61 s i 2 ) 1 / 2 ( i = 1 61 σ i , j 2 η j 2 ) 1 / 2 + i = 1 61 ( σ i , j η j ) 2 ] 1 / 2 .
i = 1 61 s i 2 , i = 1 61 ( σ i , j η j ) 2 .
i = 1 61 ( σ i , avg η avg ) 2 = 1 η avg 2 i = 1 61 ( σ i , avg ) 2 ,
j = 1 N i = 1 61 ( σ i , j η j ) 2 ,
j = 1 N i = 1 61 ( σ i , j η j ) 2 1 η avg 2 j = 1 N i = 1 61 ( σ i , j ) 2
i = 1 61 ( σ i , avg ) 2 i = 1 61 1 N [ σ i , 1 2 + + σ i , j 2 + + σ i , N 2 ] .
C j = A + E d c , j + A + E a c , j = η j [ t 1 t M ] + [ ρ 1 , j ρ M , j ] ,
C avg = η avg [ t 1 t M ] + [ ρ 1 , avg ρ M , avg ] ,
E avg = 1 N ( E d c , 1 + + E d c , N ) + 1 N ( E a c , 1 + + E a c , N ) .
( I A t A + ) E a c , avg = [ σ 1 , avg σ 61 , avg ] = 1 N ( [ σ 1 , 1 σ 61 , 1 ] + + [ σ 1 , N σ 61 , N ] ) = [ 1 N j = 1 N σ 1 , j 1 N j = 1 N σ 61 , j ] .
i = 1 61 ( σ i , avg ) 2 = i = 1 61 ( 1 N j = 1 N σ i , j ) 2 .
i = 1 61 ( σ i , avg ) 2 = [ ( I A t A + ) E a c , avg ] t [ ( I A t A + ) E a c , avg ] = E a c , avg t ( I A t A + ) t ( I A t A + ) E a c , avg = E a c , avg t B E a c , avg ,
= E a c , avg t B E a c , avg = 1 N 2 [ ( E a c , 1 + E a c , N ) ] t B [ ( E a c , 1 + E a c , N ) ] = 1 N { 1 N [ E a c , 1 t B E a c , 1 + + E a c , i t B E a c , 1 + + E a c , N t B E a c , 1 ] + 1 N [ E a c , 1 t B E a c , 2 + + E a c , i t B E a c , 2 + + E a c , N t B E a c , 2 ] + + 1 N [ E a c , 1 t B E a c , N + + E a c , i t B E a c , N + + E a c , N t B E a c , N ] } .
i = 1 61 ( σ i , avg ) 2 = 1 N { i = 1 61 1 N [ σ i , 1 2 + + σ i , j 2 + + σ i , N 2 ] } + 1 N { k = 1 N m = 1 m k N 1 N E a c , k t B E a c , m } .
E a c , k t B E a c , m + E a c , m t B E a c , k = E a c , k t B E a c , k + ( E q c , m t E a c , k t ) B ( E a c , k ) + E a c , m t B E a c , m + ( E a c , m t E a c , k t ) B ( E a c , m ) = E a c , k t B E a c , k + E a c , m t B E a c , m + ( E a c , m t E a c , k t ) B ( E a c , k E a c , m ) .
1 N { k = 1 N m = 1 m k N 1 N E a c , k t B E a c , m } ( N 1 ) N { i = 1 61 1 N [ σ i , 1 2 + + σ i , j 2 + + σ i , N 2 ] } .
i = 1 61 ( σ i , avg ) 2 { i = 1 61 1 N [ σ i , 1 2 + + σ i , j 2 + + σ i , N 2 ] } .

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