Abstract

In this paper, condition for uniform lighting generated by light emitting diode (LED) array was systematically studied. To take human vision effect into consideration, contrast sensitivity function (CSF) was novelly adopted as critical criterion for uniform lighting instead of conventionally used Sparrow’s Criterion (SC). Through CSF method, design parameters including system thickness, LED pitch, LED’s spatial radiation distribution and viewing condition can be analytically combined. In a specific LED array lighting system (LALS) with foursquare LED arrangement, different types of LEDs (Lambertian and Batwing type) and given viewing condition, optimum system thicknesses and LED pitches were calculated and compared with those got through SC method. Results show that CSF method can achieve more appropriate optimum parameters than SC method. Additionally, an abnormal phenomenon that uniformity varies with structural parameters non-monotonically in LALS with non-Lambertian LEDs was found and analyzed. Based on the analysis, a design method of LALS that can bring about better practicability, lower cost and more attractive appearance was summarized.

© 2012 OSA

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References

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2012 (1)

2011 (1)

2010 (3)

2009 (2)

A. J. W. Whang, Y. Y. Chen, and Y. T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

2008 (1)

2006 (1)

2005 (2)

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE5941, 594101 (2005).
[CrossRef]

I. Moreno and L. M. Molinar, “Color uniformity of the light distribution from several cluster configurations of multicolor LEDs,” Proc. SPIE5941, 59411S (2005).
[CrossRef]

2003 (1)

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE5294, 231–238 (2003).
[CrossRef]

1993 (1)

1990 (1)

1987 (1)

1977 (1)

C. F. Hall and E. L. Hall, “A nonlinear model for the spatial characteristics of the human visual system,” IEEE Trans. Syst. Man Cybern.7(3), 161–170 (1977).
[CrossRef]

1968 (1)

F. W. Campbell and J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol.197(3), 551–566 (1968).
[PubMed]

1962 (1)

1956 (1)

1936 (1)

W. A. Hendricks and K. W. Robey, “The sampling distribution of the coefficient of variation,” Ann. Math. Stat.7(3), 129–132 (1936).
[CrossRef]

1916 (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

Avendaño-Alejo, M.

Barten, P. G. J.

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE5294, 231–238 (2003).
[CrossRef]

P. G. J. Barten, “Evaluation of subjective image quality with the square-root integral method,” J. Opt. Soc. Am. A7(10), 2024–2031 (1990).
[CrossRef]

Bergmans, J. W. M.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

Campbell, F. W.

F. W. Campbell and J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol.197(3), 551–566 (1968).
[PubMed]

Chen, F.

Chen, Y. Y.

A. J. W. Whang, Y. Y. Chen, and Y. T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Craford, M. G.

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE5941, 594101 (2005).
[CrossRef]

Depalma, J. J.

Hall, C. F.

C. F. Hall and E. L. Hall, “A nonlinear model for the spatial characteristics of the human visual system,” IEEE Trans. Syst. Man Cybern.7(3), 161–170 (1977).
[CrossRef]

Hall, E. L.

C. F. Hall and E. L. Hall, “A nonlinear model for the spatial characteristics of the human visual system,” IEEE Trans. Syst. Man Cybern.7(3), 161–170 (1977).
[CrossRef]

Hendricks, W. A.

W. A. Hendricks and K. W. Robey, “The sampling distribution of the coefficient of variation,” Ann. Math. Stat.7(3), 129–132 (1936).
[CrossRef]

Johnston, A.

Linnartz, J.-P. M. G.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

Liu, S.

Liu, Z. Y.

Lowry, E. M.

Luo, X. B.

Molinar, L. M.

I. Moreno and L. M. Molinar, “Color uniformity of the light distribution from several cluster configurations of multicolor LEDs,” Proc. SPIE5941, 59411S (2005).
[CrossRef]

Moreno, I.

Owsley, C.

Qin, Z.

Rietman, R.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

Robey, K. W.

W. A. Hendricks and K. W. Robey, “The sampling distribution of the coefficient of variation,” Ann. Math. Stat.7(3), 129–132 (1936).
[CrossRef]

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol.197(3), 551–566 (1968).
[PubMed]

Rohaly, A. M.

Schade, O. H.

Schenk, T. C. W.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

Sparrow, C. M.

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

Sun, C.-C.

Teng, Y. T.

A. J. W. Whang, Y. Y. Chen, and Y. T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Tzonchev, R. I.

Wang, K.

Whang, A. J. W.

A. J. W. Whang, Y. Y. Chen, and Y. T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

Wu, D.

Yang, H.

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

Ann. Math. Stat. (1)

W. A. Hendricks and K. W. Robey, “The sampling distribution of the coefficient of variation,” Ann. Math. Stat.7(3), 129–132 (1936).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

IEEE Trans. Signal Process. (1)

H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J.-P. M. G. Linnartz, and R. Rietman, “Uniform illuminance rendering using an array of LEDs: a signal processing perspective,” IEEE Trans. Signal Process.57(3), 1044–1057 (2009).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

C. F. Hall and E. L. Hall, “A nonlinear model for the spatial characteristics of the human visual system,” IEEE Trans. Syst. Man Cybern.7(3), 161–170 (1977).
[CrossRef]

J. Disp. Technol. (1)

A. J. W. Whang, Y. Y. Chen, and Y. T. Teng, “Designing uniform illumination systems by surface-tailored lens and configurations of LED arrays,” J. Disp. Technol.5(3), 94–103 (2009).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Physiol. (1)

F. W. Campbell and J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol.197(3), 551–566 (1968).
[PubMed]

Opt. Express (3)

Opt. Lett. (3)

Proc. SPIE (3)

I. Moreno and L. M. Molinar, “Color uniformity of the light distribution from several cluster configurations of multicolor LEDs,” Proc. SPIE5941, 59411S (2005).
[CrossRef]

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE5941, 594101 (2005).
[CrossRef]

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE5294, 231–238 (2003).
[CrossRef]

Other (1)

P. G. J. Barten, “The SQRI method: A new method for the evaluation of visible resolution on a display.” Proc. SID 28, 253–262 (1987).

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Figures (18)

Fig. 1
Fig. 1

LED array lighting system observed by human vision system with foursquare arrangement and an enlarged view of the region around the observation point in the center

Fig. 2
Fig. 2

Six characteristic points used for critical uniformity condition calculation with SC method for LALS-Lambertian.

Fig. 3
Fig. 3

Functional image of contrast sensitivity function (CSF) where region above or below the curve indicates uniform or nonuniform lighting respectively

Fig. 4
Fig. 4

Characteristic lines used for critical uniformity condition calculation with CSF method

Fig. 5
Fig. 5

Differences between CS of E ¯ (x, y k ) corresponding to each characteristic line and their thresholds under different system thicknesses z in LALS- Lambertian with d = 10mm. Region above or below the zero line indicates uniform or nonuniform lighting respectively

Fig. 6
Fig. 6

Differences between CS of E ¯ (x, y k ) corresponding to each characteristic line and their thresholds under different LED pitches d in LALS-Lambertian with z = 10mm. Region above or below the zero line indicates uniform or nonuniform lighting respectively.

Fig. 7
Fig. 7

Optimum system thicknesses and LED pitches achieved through SC and CSF method. Blue or red line denotes SC or CSF method respectively: (a) from given LED pitches to optimum system thicknesses; (b) from given system thicknesses to optimum LED pitches

Fig. 8
Fig. 8

Comparison of illuminance distributions corresponding to optimum z achieved through CSF method and SC method: (a) under given d = 10mm; (b) under given d = 20mm

Fig. 9
Fig. 9

Comparison of illuminance distributions corresponding to optimum d achieved through CSF method and SC method: (a) under given z = 10mm; (b) under given z = 20mm

Fig. 10
Fig. 10

Polar SRD curve of LUXEON® Batwing LED

Fig. 11
Fig. 11

Differences between CS of E ¯ (x, y k ) corresponding to each characteristic line and their thresholds under different system thicknesses z in LALS-Batwing with d = 10mm. z1, z3 and z5 are thicknesses those can lead to the minimal average value of all the curves at troughs; z2 is the thickness that can lead to the maximal average value of all the curves at a peak; z4 and z6 are thicknesses those can make all the curves just above the zero line.

Fig. 12
Fig. 12

Visual illuminance distributions of LALS-Batwing with d = 10mm corresponding to z1 to z6 in Fig. 13 respectively. ΔCSavg and CV (RMSE) are also provided for each sub-figure.

Fig. 13
Fig. 13

Second derivative of illuminance distribution function varying with z at point (0,0) (upper sub figure) and differences between CS of E ¯ (x, y 0 ) and its thresholds varying with z (down sub figure)

Fig. 14
Fig. 14

Second derivative of illuminance distribution function varying with z at point (0,d/2) (upper sub figure) and differences between CS of E ¯ (x, y 5 ) and its thresholds varying with z (down sub figure)

Fig. 15
Fig. 15

Differences between CS of E ¯ (x, y k ) corresponding to each characteristic line and their thresholds under different LED pitches d in LALS-Batwing with z = 20mm. d1 and d3 are LED pitches those can make all the curves just above the zero line; d2, d4 and d6 are LED pitches those can lead to the minimal average value of all the curves at a trough; d5 is the LED pitch that can lead to the maximal average value of all the curves at a peak.

Fig. 16
Fig. 16

Visual illuminance distributions of LALS-Batwing with z = 20mm corresponding to d1 to d6 in Fig. 15 respectively. ΔCSavg and CV (RMSE) are also provided for each sub-figure.

Fig. 17
Fig. 17

Square wave S(x) with a cycle of T, amplitude of 2A and mean of X

Fig. 18
Fig. 18

Two situations of application of CSF in perceiving square wave with the aid of Fourier series: (1) when spatial frequency of the square wave is quite large, it is accurate to use CS of the fundamental harmonic instead of that of the original square curve for the perception, as marked with blue triangles; (2) when spatial frequency of the square wave is quite small, it is inaccurate to use CS of the fundamental harmonic instead of that of the original square curve for the perception, as marked with red circles

Tables (5)

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Table 1 Critical values of system thickness corresponding to 6 characteristic points under given LED pitches

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Table 2 Critical values of LED pitch corresponding to 6 characteristic points under given system thicknesses

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Table 3 Optimum system thicknesses for given LED pitches in LALS-Lambertian calculated through CSF method

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Table 4 Optimum LED pitches for given system thicknesses in LALS-Lambertian calculated through CSF method

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Table 5 Results of the visual experiment in which six students judged whether illuminance distributions in Fig. 8 and Fig. 9 were uniform

Equations (10)

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

E(x,y)= E 0 E ¯ (x,y)= i=1 M E i (x,y)
E(x,y)= E 0 E ¯ (x,y)= i=1 N i=1 N E ij (x,y) = E 0 i=1 N i=1 N z 2 cosθ r ij 2
E ¯ (x,y)= i=1 10 i=1 10 z 4 { [x(i5.5)d] 2 + [y(j5.5)d] 2 + z 2 } 2
CS= L max + L min L max L min E max + E min E max E min
C S th (ω)=aωexp(bω) 1+cexp(bω)
ω= 2Htan(0.5π/180) dcosα 0α< π 2
E ¯ (x,0) | z=5 =11.15× 10 1 cos π 5 x+2.43× 10 3 cos 2π 5 x3.40× 10 5 cos 3π 5 x..... E ¯ (x,0) | z=10 =11.05× 10 2 cos π 5 x+3.50× 10 5 cos 2π 5 x2.35× 10 5 cos 3π 5 x.....
I(θ,φ)= P 1 exp[(ln2) ( θ P 3 ) 2 ]cosh(P2 180θ π )+ P 4 exp[(ln2) ( |θ| P 5 P 6 ) 2 ]
CV(RMSE)=RMSE/ x ¯ =σ/ x ¯
S(x)=X+ n=1 4A (2n1)π sin 2π(2n1)x T

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