116 TECHNOLOGY / LED


Figure 1: The 14 CRI values for two typical PC white LEDs.


The lack of photons being emitted by traditional phosphor converted white LEDs in the red R9 region gave rise to lighting systems where the addition of red LEDs provide a high R9 value that “trick” the CRI calculations to enable manufacturers to claim CRI values >90. It is important to note that although the CRI calculations for such systems are indeed >90 the SPD of the resulting wavelength does not mean objects underneath such lighting system will look good to the eye! What can be shown is that red objects will look significantly better being lit by such a hybrid lighting system but other objects may actually look poorer depending on the rendering at other test colours.


Colour Temperature (CT) and Correlated Colour Temperature (CCT) Colour temperature is a characteristic of visible light that has important applications in lighting. The colour temperature of a light source is the temperature of an ideal black body radiator that radiates light of comparable hue to that of the light source. Colour temperature is conventionally stated in the unit of absolute temperature, the kelvin, having the unit symbol K. Figure 2 shows the CIE chromaticity coordinate colour space with the black body curve (Planckian locus) superimposed for various colour temperatures.


Figure 3: CIE approximation equations put forward by Kim et al.


Colour temperatures over 5000K are called cool colours while lower colour tempera- tures (2700–3000K) are called warm colours. The colour temperature of the electromag- netic radiation emitted from an ideal black body is defined as its surface temperature in kelvins which permits the definition of a standard by which light sources can be compared. The Planckian locus in CIE XYZ colour space can be defined by


, where T is the


temperature to provide the CIE chromatic- ity coordinates:


While it is possible to compute the CIE xy co-ordinates exactly given the above for- mulas, it is faster to use approximations as proposed by Kim et al using the equations in Figure 3. An incandescent lamp’s light is thermal ra- diation and the bulb approximates an ideal black body radiator, so its colour tempera- ture is essentially the temperature of the filament and follows the black body locus. However, many other light sources, such as fluorescent lamps and LEDs, emit light primarily by processes other than thermal radiation. This means the emitted radiation does not follow the form of a black body spectrum. These sources are assigned what is known as a correlated colour temperature


(CCT). CCT is the colour temperature of a black body radiator which, to human colour perception, most closely matches the light from the lamp. Because such an approxima- tion is not required for incandescent light, the CCT for an incandescent light is simply its unadjusted temperature, derived from the comparison to a black body radiator. In order to calculate CCT accurately one should use the CIE 1960 colour space as shown in figure 4 where isotherms are drawn perpendicular to the Planckian locus to indicate the maximum distance from the locus that the CIE considers the correlated colour temperature to be meaningful. The distance from the planckian locus (i.e., degree of departure from a black body) is traditionally indicated in units of Δuv and is positive for points above the locus. This concept of distance has evolved to become Delta E, which continues to be used today. A transformation matrix can be used to convert X,Y,Z tristimulus values to R,G,B coordinates by the following:


From this formula, one can find the chroma- ticities:


Figure 2: The CIE 1931 x,y chromaticity space, also showing the chromaticities of black body light sources of various temperatures (Planckian locus), and lines of constant correlated colour temperature.


Figure 4: The CIE 1960 colour space with blackbody curve and CCT isotherms.


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