Color uniformity of the light distribution from several cluster configurations of multicolor LEDs Ivan Moreno*, Luis M. Molinar Unidad Academica de Fisica, Universidad Autonoma de Zacatecas, 98060, Zacatecas, Zac., Mexico. ABSTRACT We analyze the effects on color uniformity of the near-field light distribution due to different cluster configurations (at optimum packaging density for uniform irradiance) of light sources using mixed red, green and blue (RGB) light emitting diodes (LEDs). A photometric analysis and experimental results that show the near-field performance that can be achieved with several cluster configurations of multicolor LEDs is presented. Contour maps for the color variation (in reference to illuminant D65) in function of spatial coordinates of light distribution are given. Key words: LEDs, RGB, color uniformity, cluster configurations.
1. INTRODUCTION In addition, the rapid development of light-emitting diodes (LEDs) over the last few years has surpassed the characteristics of incandescent lamps in luminous efficiency, durability, reliability, safety, and power requirements.1,2 Though modern high power LEDs produce up 120 lumens per device, several LEDs must be mounted on panels to obtain practical powers. The color adjustability in light emitting diode (LED) sources made of red, green, and blue LEDs (RGB-LEDs) allows the user to dynamically select the desired color point of the lamp.3 However the output color distribution from RGB-LED arrays shows distinctive patterns with clear color separation, which is in function of the array configuration and the degree of packaging density. In this paper, we analyze the effects on color homogeneity of light sources consisting of multiple LEDs (bare LED arrays) due to different cluster configurations of LEDs, considering each LED as an imperfect Lambertian emitter. We analyze LED panels in the absence of any diffuser component4,5 in order to create practical design tools for a wider variety of illumination systems. .
2. SPATIAL DISTRIBUTION OF COLOR The output color distribution from bare RGB-LED arrays shows distinctive patterns with clear color separation. The precise color uniformity requirements depend upon the application. The major requirement of many illumination applications is that the light source has the required color point. The perceived color uniformity depends on several factors including distance of the observer to the target field, incidence angle of illuminating beam, background luminance, and target reflectance. Therefore, to create a practical design tool, we only consider the color distribution over a flat area (white screen) parallel to the surface of the LED array in a dark environment. The lighting industry usually quantifies the color error of a light source based on the distance in color space of the lamp from a reference color point. Thus, a homogeneous color illumination has a color variation value of zero over the illuminated area. To quantify the non-homogeneity of color, we will use the color error distribution ∆uv(x,y) over a target plane (screen) given by
∆uv( x, y ) =
[u ′(x, y ) − u 0′ ]2 + [v′(x, y ) − v0′ ]2 ,
(1)
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Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, Editors, Proceedings of SPIE Vol. 5941 (2005) 2005 SPIE ⋅ ISBN 0-8194-5946-1 ⋅ $ 15.00
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where (u´0, v´0) are the color coordinates of reference. [u´(x,y), v´(x,y)] are the color coordinates of the light source, and (x,y) are the Cartesian coordinates of each point on the screen. This color error distribution is simply the distance in (u´,v´) color space of the lamp from the desired color point. The most common chromaticity diagram is the CIE 1931 coordinate system xy.6 However, the just noticeable color difference is not a constant length over xy space, e.g., the color may change faster in one particular direction than in other directions. For the purposes of this paper we use the CIE 1976 system where the just noticeable color difference is approximately uniform. As a result the color error between two locations is directly proportional to the geometrical distance between these points. The uniform chromaticity coordinates are calculated from the tristimulus according to6
u ′( x, y ) =
4 X ( x, y ) , X ( x, y ) + 15Y ( x, y ) + 3Z ( x, y )
(2)
9Y ( x, y ) , X ( x, y ) + 15Y ( x, y ) + 3Z ( x, y )
(3)
and
v ′( x, y ) =
where X(x,y), Y(x,y) and Z(x,y) are the tristimulus values of the light source at each point (x,y) of the illuminated screen.
3. LED IRRADIANCE PATTERNS AND PHOTOMETRIC CONSIDERATIONS Ideally, a LED source is a Lambertian emitter which means the irradiance distribution is also a cosine function of the viewing angle. In practice, this dependence turns out to be a power law that primarily depends on the encapsulant and semiconductor region shapes. A practical approximation for the irradiance distribution is given by7 E(r,θ) =E0 (r) cosm θ ,
(4)
where θ is the viewing angle, and E0 (r) is the irradiance [W/m2] on axis at distance r from the LED. If m =1, the source is a perfect Lambertian (many high-power LEDs have m-values near to 1, e.g., some Lamina® LEDs). Common LEDs often have m >30, and the drop with viewing angle is pronounced. The number m depends on the angle θ½ (a value typically provided by the manufacturer, defined as the view angle when irradiance is half of the value at 0°), and this is given by m=
− ln 2 ln(cos θ 1 )
.
(5)
2
The irradiance distribution, Eq. (4), for a LED displaced to position (x0,y0) over a panel plane, can be written in terms of Cartesian coordinates (x,y,z). The irradiance over every point (x,y) on a flat screen at distance z from the LED array can then be expressed as
E ( x, y , z ) =
[(x − x ) 0
z m LLED ALED 2
+ ( y − y0 ) + z 2
2
]
m+ 2 2
,
(6)
where LLED is the radiance [Wm-2sr-1] of the LED chip and ALED is the LED emitting area [m2]. In practice, the non-homogeneity and shape irregularities of low quality encapsulating materials also affect the irradiance distribution of LEDs. However the main source of irregularities in the irradiance distribution of LEDs is the small mirror placed behind the chip to increase the flux. Modern high-brightness phosphor LEDs have high quality encapsulants and the phosphor layer avoids the imperfections due to the back mirror. As a result, the irradiance pattern is nearly that
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which is produced by Eq. (4). In order to create a practical design tool for a quick estimation, we will not consider these problems. We will use the irradiance distribution given by Eq. (6) for each single LED, and all LEDs of each color will have equal values of m and LLEDALED. Photometric quantities are obtained from the color matching functions and the spatial distribution of radiation given by Eq. (6). The modeled tristimulus values (X, Y, Z) over the illuminated screen, due to an array of N LEDs, are N
X( x, y ) = ∑ Fi ( x, y ) Ci X i ,
(7)
i =1
N
Y ( x, y ) = ∑ Fi ( x, y ) CiYi ,
(8)
i =1
N
Z( x, y ) = ∑ Fi ( x, y ) Ci Z i ,
(9)
i =1
where the normalized irradiance function of the i-th LED is
Fi ( x, y ) =
z mi + 2
[(x − x ) i
2
+ ( y − yi ) + z 2
2
]
mi + 2 2
.
(10)
Here Xi, Yi, and Zi are the tristimulus values (normalized) of the i-th LED, and Ci is the relative radiant flux at the wavelength at which the radiation peak of the i-th LED occurs. To normalize the tristimulus values we used the peak spectral flux [W/µm] because the normalized value changed less than the tristimulus normalized with the radiant flux [W] when we incremented LED flux. To match the color point of reference in the screen center, the relative peak powers must incorporate the dependence with the screen position of LEDs (xi,yi). Cartesian coordinates (xi,yi) indicate the position of the i-th LED on the array. For each single LED we consider the color coordinates independent of the spatial variation of the irradiance distribution.
4. RHOMBOIDAL LED CLUSTER First we consider a simple case, which is that of a trichromatic LED cluster with rhomboidal geometry. In this case, the array is a rhomboid with a LED in the center, as shown in Fig. 1. For each group of equal color LEDs we optimize the irradiance uniformity in the central region of the illuminated screen in order to optimize color uniformity. The optimum LED-to-LED distance to obtain homogeneous illumination over a plane surface is a function of m-parameter and the source-screen distance z. The optimum LED separation between the pair of green or blue LEDs to obtain a highly even irradiance distribution over the flat region near the center of screen is8
d G,B =
4 mG , B + 3
z
.
(11)
Figure 2 shows the spatial distribution of color error over the screen. This graph is for the LED array of Fig. 1 with a color point of reference (u’0=0.198, v’0=0.468), which lies on the locus of points that follows the line of a black-body radiator (T=6500K, illuminant D65). The analysis is based on the measured and calculated optical parameters of the LEDs we used in laboratory. For green LEDs mG=81.01 (dG/z =0.218), xG= 0.469, yG=0.531 and XG= 24.2978. For the red LED (centered in the cluster) mR=150.95, CR/CG=0.523, xR= 0.710, yR=0.290 and XR= 9.915. For blue LEDs mB=129.23, dB/z =0.174, CB/CG=1.239, xB= 0.113, yB=0.134 and XB= 4.7912. As shown in this figure, the spatial distribution of color error is even over the flat region near (x=0, y=0) on the screen.
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Fig. 1. Cluster configuration of RGB-LEDs with rhomboidal geometry.
Fig. 2. Spatial distribution of color error ∆uv(x,y) over a screen illuminated by the LED array shown in Fig. 1.
5. NON-REGULAR HEXAGONAL LED CLUSTER We now take the case of a LED cluster with non-regular hexagonal geometry. The array is a hexagon that has three different side lengths, as shown in Fig. 3. Figure 4 shows the spatial distribution of color error over the screen. This graph is for a color point of reference (u’0=0.198, v’0=0.468.) for a color temperature of 6500K. In this case, the red LEDs have the values: dR/z =0.162 and CR/CG=0.429. The other optical parameters of the RGB LEDs are the values used for the rhomboidal array.
Fig. 3. Cluster configuration of RGB-LEDs with nonregular hexagonal geometry.
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Fig. 4. Spatial distribution of color error ∆uv(x,y) over a screen illuminated by the LED array shown in Fig. 3.
6. SQUARE LED CLUSTER We now take the case of a trichromatic LED cluster with square geometry. The array has nine LEDs, as shown in Fig. 5. For this case the optimum LED separations dB and dR to obtain a highly even irradiance distribution over the flat region near the center of screen are different from Eq. (11). In this case the square geometry of red or blue LEDs gives an optimum LED-to-LED separation8
d R, B =
8 m R, B + 2
z
,
(12)
Figure 6 shows the spatial distribution of color error over the screen. This graph is for a color point of reference (u’0=0.198, v’0=0.468) for a color temperature of 6500K. For red LEDs dR/z =0.228, and CR/CG=0.288. For blue LEDs dB/z =0.246 and CB/CG=0.833. The other optical parameters of the RGB LEDs are the values used for the rhomboidal array. As shown in this figure, spatial distribution of color error is even over the flat region near (x=0, y=0) on the screen.
Fig. 5. Cluster configuration of RGB-LEDs with square geometry.
Fig. 6. Spatial distribution of color error ∆uv(x,y) over a screen illuminated by the LED array shown in Fig. 5.
7. THREE-TRIANGLE LED CLUSTER We now take the case of a LED cluster with the geometry of three superposed triangles. The array has nine LEDs, as shown in Fig. 7. For this case the optimum radius ρR, ρG and ρB (of the circles that encircle the triangles) to obtain a highly even irradiance distribution over the flat region near the center of screen for this array geometry is8
ρ R,G,B =
1.851 z mR,G,B + 2.259
,
(13)
Figure 8 shows the spatial distribution of color error over the screen. This graph is for a color point of reference (u’0=0.198, v’0=0.468) for a color temperature of 6500K. For red LEDs ρR/z =0.11, and CR/CG=0.43. For blue LEDs ρB/z =0.119, and CB/CG=1.241. For green LEDs ρG/z =0.149. The other optical parameters of the RGB-LEDs are the values used for the rhomboidal cluster. As shown in this figure, the central region (on the screen) with uniform color is larger than in the other cluster configurations.
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Fig. 7. Cluster configuration of RGB-LEDs with a threetriangle geometry.
Fig. 8. Spatial distribution of color error ∆uv(x,y) over a screen illuminated by the LED array shown in Fig. 7.
8. EXPERIMENT For the purpose of demonstration, rather than the optimized design, we assembled the RGB-LED clusters that showed the most uniform color pattern in our simulations, i.e., the rhomboidal and the three-triangle array. The mounted LEDs (STEREN9 catalog number 5/ULTRA BLUE, 5/ULTRA RED, and E5/GREEN-C) have red, green and blue emissions; and measured ranging values of mR =150.95, mG=81.01, and mB=129.23. The measured LED values for the tristimulus and color coordinates are the values we used in the simulations of sections 4-7 (5 mm LEDs were used because of the limited available LEDs.) We optimized the global illumination provided by the two panels for a panel-target distance of 10cm. In the case of the rhomboidal cluster, we assembled the green LEDs with a LED-to-LED distance of dG = 2.18 cm (along y-direction), blue LEDs with dB = 1.74 cm (along x-direction), and the red LED on the central point of the array. The relative peak powers were CR/CG=0.523 and CB/CG=1.239. In the case of the three-triangle cluster, we assembled the triangles with radius ρR =1.1 cm, ρG =1.49 cm, and ρB =1.19 cm; the relative peak powers were CR/CG=0.523 and CB/CG=1.239. The center point of each array was aligned with the optical axis. A fiber optic spectrometer (Ocean Optics USB2000) was positioned 10 cm from the LED panel. The spectrum and color coordinates of the LED array were measured every millimeter in a horizontal direction through the center axis of the optical axis, to form a strip 30 mm long. The theoretical and experimental data are plotted in Fig. 9 and Fig 10. The discrepancy between experimental and modeled data is explained by the fact that the irradiance pattern of each LED has the irregularities explained in section 3. This is not critical because the purpose of this analysis is to create a practical design tool for a quickly estimation. In addition, measurement requires other particular considerations, e.g., the careful orientation and alignment of each LED.
Fig. 9. Measured color error ∆uv(x,0) over a screen (z=10cm) illuminated by a rhomboidal LED cluster.
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Fig. 10. Measured color error ∆uv(x,0) over a screen (z=10cm) illuminated by a three-triangle LED cluster.
9. SUMMARY We have presented an investigation of the effects of light sources consisting of multiple RGB-LEDs on color uniformity of illumination due to different cluster configurations with optimized packaging densities. We analyzed the performance of various cluster configurations using a photometric analysis and experimental results. We used the optimum LED-to-LED distance to obtain (separately for each RGB color) homogeneous irradiance over a plane surface for red, green and blue colors; these LED separations guaranty that color mixing is constant over larger screen regions. Spatial patterns of color error were displayed graphically for the rhomboid cluster, the non-regular hexagonal cluster, the square cluster, and the three-triangle cluster of LEDs. Experiments with a rhomboidal cluster and the three-triangle cluster were performed to confirm our analysis. Experimental data agreed quite well with theoretical expectations, even though our simulations were first order approximations for LED clusters without diffuser components.
ACKNOWLEDGMENTS This research was supported by CONACYT (Consejo Nacional de Ciencia y Tecnologia) grant J48199-F, and partially by PROMEP.
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