Analytical Method for Computing Color Patterns in LEDs

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Anne L. Fischer

The use of solid-state lighting is expanding, with arrays of LEDs found in everything from automotive to medical to architectural applications. This is due in large part to the fact that LEDs have surpassed incandescent lamps in longevity, safety, luminous efficacy and power consumption. But another real advantage is that the user can tune color LEDs to select the desired color point. This is beneficial in many applications where different color distribution or color patterns are desired — such as in display or architectural lighting — or where a uniform color distribution is desired.


The light emitted from a multicolor LED array produces a color pattern that is difficult to compute using traditional methods.

The fact that LEDs are tunable without filters increases their applicability; however, the typical methods used for computing the color distribution are complex. Researchers at Universidad Autonoma de Zacatecas in Mexico have developed an analytical method to compute the color pattern of light emitted from multicolor LEDs.

Measuring patterns

For demonstration purposes, they assembled a linear array of five red, five green and five blue LEDs from Lumileds of San Jose, Calif. They measured the viewing angle for each color and simulated the spectral distribution. The LEDs were assembled over an aluminum plate to dissipate heat and to minimize the formation of hot regions throughout the array.

The three-dimensional radiation pattern of well-known LEDs is shown on the left. The analytically simulated color patterns, Δ uv, from an RGB LED assembly indicate different distances from the array. X90 and Y90 are the Cartesian coordinates that delimit a representative area of the screen that collects more than 90 percent of the energy radiated by the LED array. Parameter d is the spacing between adjacent LEDs along X or Y. Cartesian coordinate Z is the spacing between target and array and is the location (with respect to the LED array) of the plane where the color pattern is calculated.

The LEDs operated at 145 mA (red), 130 mA (green) and 200 mA (blue). The center point of the array was aligned with the optical axis. The researchers positioned a fiber optic spectrometer from Ocean Optics of Dunedin, Fla., in front of the LED panel, and measured the color coordinates of the LED array at nine equally spaced points in a horizontal direction through the center of the optical axis.

This analytical method can be used for quick estimation of the color distribution or as a starting point for the analysis that is performed with optical software. The angular distribution of color can be calculated by means of relative intensity of each color, according to researcher Ivan Moreno. He added that the color angular distribution of an LED array makes sense only in far field, and in such a case, the angular variation of color results from the spatial and spectral differences between the radiation patterns of each single LED. The new method also can be used to compute color distribution as a function of several parameters; for example, viewing angle, the number of LEDs and the color temperature.

The next step is to develop a model to analytically represent both radiant intensity and irradiance for any LED available. According to Moreno, the researchers expect to incorporate these general equations into their theory of color distribution to develop a set of tools for designing multicolor LED arrays.

Optics Express, March 19, 2007, pp. 3607-3618.

Published: June 2007
ConsumerFeaturesincandescent lampssolid-state lightingspectroscopyLEDs

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