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Defining Colour Tunability - Part 2

Issue 69 Oct / Nov 2012

In his last article, Dr. Geoff Archenhold introduced the concepts of human colour perception, spectral power density, luminosity and CIE functions. In part two he covers the definitions of CCT and CRI and also addresses some issues that future vCCT fixture manufacturers will need to take into account to achieve replicable CCT luminaires.

The number of LED emitters being introduced into the market by LED manufacturers to enable variable CCT products are set to explode over the next twelve months and a raft of new vCCT LED solutions will find their way to lighting designers’ doorsteps. Therefore, it is ever more important for designers to understand how the various systems will stack up in application and what issues they need to be aware of.
However, I shall continue with the description of Colour Rendering Index (CRI), Correlated Colour Temperature (CCT) and the two methods used to create colours.

Colour Rendering Index (CRI)
Colour Rendering Index is a quantitative measure of the ability of a light source to reproduce the colours of various objects faithfully in comparison with an ideal or natural light source. Light sources with a high CRI are desirable in colour-critical applications such as photography, retail, surgical and cinematography.

The CIE developed CRI to indicate how colours appear under different light sources, particularly fluorescent and high-intensity discharge lamps, and to best correspond them to a human’s perception of colour quality. Because most objects are not a single colour but a combination of several, light sources lacking in certain colours can change the apparent colour of an object which is also known as colour shift.
Specifically, CRI measures on a scale of 0 to 100 how a light source shifts the location of eight specified pastel colours compared to the same colours lit by a light source of the same CCT. A CRI of 100, or perfect colour rendering, means the light source renders the eight colours exactly how the reference light source renders them. A light source with a CRI of 80 or higher is considered by the lighting industry to provide excellent colour rendering for most indoor applications. The CRI values of typical light sources are shown in table 1.

The original method of CRI representation has been found to be an inaccurate, unreliable predictor of colour preference of solid-state lighting products such as LEDs or OLEDs, which emit different light Spectral Power Densities (SPDs) than fluorescent or HID lamps, and can result in lower or even negative CRI values. For instance, some LED products with a CRI as low as 25 can produce white light that actually make object colours appear more vivid. The CRI metric only evaluates colour rendering as it ignores other aspects of colour quality, such as chromatic discrimination and observer preferences.

Recently a new method, Colour Quality Scale (CQS), for providing colour quality has been proposed which overcomes issues found with the CRI measurement but unfortunately this has not replaced CRI as the common method of colour quality as yet. CRI suffers from some of the following issues:

•    Calculating the arithmetic mean of the errors diminishes the contribution of     any single large deviation. Two light sources with similar CRI may perform significantly differently if one has a particularly low CRI in a spectral band that is important for the application.
•    The CRI is equally weighted, whereas humans favour certain errors over others. A colour can be more saturated or less saturated without a change in the numerical value, while in general a saturated colour is experienced as being more attractive.
•    A negative CRI is difficult to interpret.
•    The CRI cannot be calculated for light sources that do not have a CCT (ie; non white light).
•    Eight samples are not enough since manufacturers can optimise the emission spectra of their lamps to reproduce them faithfully, but otherwise perform poorly.
•    The samples used to calculate the CRI are not saturated enough to pose difficulty for reproduction.
•    CRI merely measures the faithfulness of any illuminant to an ideal source with the same CCT, but the ideal source itself may not render colours well if it has an extreme colour temperature, due to a lack of energy at either short or long wavelengths (i.e., it may be excessively blue or red).
•    CRI is discontinuous at 5000K, because the chromaticity of the reference moves from the Planckian locus to the CIE  daylight locus.

The CRI may be theoretically derived from the SPD of the illuminant. However care should be taken to use a wavelength sampling resolution fine enough to capture spikes in the SPD of the light source.
In order to improve the CRI metric an enhancement was suggested in 1995 by the CIE that extended the number of test colour samples to fourteen where the last six samples provide supplementary information about the colour rendering properties of the light source; the first four for high saturation, and the last two as representatives of well-known objects to provide a CRI value known as R14. Figure 1 shows the typical output of two white phosphor converted LEDs across the R14 values with one LED (in blue) having a much higher CRI and a positive R9 value showing a much improved SPD in the red colour wavelength region.

Table 1: Various CCT and CRI values for traditional light sources.

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.

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

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 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.

Colour temperatures over 5000K are called cool colours while lower colour temperatures (2700–3000K) are called warm colours. The colour temperature of the electromagnetic 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 XT, YT, ZT, where T is the temperature to provide the CIE chromaticity coordinates:

While it is possible to compute the CIE xy co-ordinates exactly given the above formulas, 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 radiation and the bulb approximates an ideal black body radiator, so its colour temperature is essentially the temperature of the filament and follows the black body locus.

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

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 approximation 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.

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

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 chromaticities:

This was later revised for the CIE 1960 colour space system by MacAdam to:

Although the CCT can be calculated for any chromaticity coordinate, the result is meaningful only if the light sources are nearly white. The CIE recommends that: “The concept of correlated colour temperature should not be used if the chromaticity of the test source differs more than Δuv = 5x10-2 from the Planckian radiator.” Beyond a certain value of Δuv, a chromaticity coordinate may be equidistant to two points on the locus, causing ambiguity in the CCT.
One can approximate the Planckian locus in order to calculate the CCT in terms of chromaticity coordinates using the McCamy equation outlined below providing a narrow range of colour temperatures is considered between 2856K and 6504K.

CCT(x,y) = -449n3 + 3525n2 - 6823.3n + 5520.33

where n = (x - xe)/(y - ye) is the inverse slope line and (xe = 0.3320, ye = 0.1858) is the ‘epicentre’. The maximum absolute error for the colour temperature range is under 2K from the equation calculation.

A more recent proposal, using exponential terms, considerably extends the applicable range for high colour temperatures:

CCT(x,y) = A0 + A1exp(-n/t1) + A2exp(-n/t2) + A3exp(-n/t3)

where n is as before and the other constants are defined below for 3000 to 50,000K:

Your head may be spinning by the mathematics by now but don’t get too hung up on this and just remember the following:

1.    The RGB coordinates are really obtained from standard colour sensors to allow CIE x,y and z parameters to be easily calculated. It also means that if you have Red, Green, Blue LEDs it is possible to predict the CIE x,y and z parameters.
2.    It is possible to calculate CCT values based on CIE x,y values which can be derived from RGB values or a colour sensor.
The mathematic calculations also bring the first source of error for any LED lighting control system. The mathematics used to derive the CCT have conversion errors due to the equations and constant terms and these errors are shown in figure 5.

Although the CCT calculation errors can be as high as 1.5% this occurs for very warm 1700K light sources and from CCT values between 2700K and 8000K the maximum errors are less than 0.5% but remember this still can represent a calculation error of more than 35K!

There are many other types of CCT and CRI errors that one needs to take into account to ensure vCCT colour systems provide the most accurate colour rendition possible. I will discuss these errors in much more detail in part three of this series early next year but needless to say I will also attempt to show you what needs to be done to ensure many of the errors are mitigated using closed loop feedback control from intelligent LED driver systems and how to minimise costs and complexities of such systems to enable low cost, highly flexible solutions.

However, I would like to round off this edition by explaining the final concept of colour mixing which are vital in order for LED systems to create vCCT systems.

Colour Mixing
There are two ways to create colour mixing:
1)    Additive
2)    Subtractive

In both cases there are three primary colours, three secondary colours (colours made from two of the three primary colours in equal amounts), and one tertiary colour made from all three primary colours.   
Additive mixing of colours generally involves mixing colours of light. In additive mixing of colours there are three primary colours: red, green and blue. In the absence of colour or, when no colours are showing, the result is black. If all three primary colours are showing, the result is white. The use of additive colour mixing is the key method for developing quality white light but it can utilise two or more colours to achieve a result and this includes adding shades of white SPDs together to create vCCT systems.

Figure 5: The Error between real and McCamy calculated CCT for various colour temperatures.

Subtractive mixing is done by selectively removing certain colours, for instance with optical filters in front of a white light source. The three primary colours in subtractive mixing are yellow, magenta and cyan. In subtractive mixing of colour, the absence of colour is white and the presence of all three primary colours is black. This was the commonly used method for creating colours using white broadband light sources with optical filters to provide specific colours.

The human eye perceives colour according to a wide range of factors that have been modelled for nearly a century and have been shown to approximate three distinct colour functions approximated by the CIE as standard observer functions.

These functions can be used to model the human eye response to artificial light and can be transformed into a variety of mathematical spaces using simple calculations. These calculations can then be used as the basis to calculate CCT and CRI of a light source.

The majority of LED lighting fixtures can utilise additive lighting techniques to create an artificial light source with high CRI, for example the use of combining white LEDs with red LEDs to create a CRI greater than 90. However, the current definition of CRI does not work well for artificial light sources such as LEDs so it isn’t a good metric to utilise for quality of light with LED light sources.

The next edition (Dec/Jan) will focus on the annual LED roundup of LED innovations and what happened during 2012 but I will continue to explain how to specify vCCT based lighting fixtures and determine the advantages and disadvantages of various ways of implementing such systems in early 2013.

In the meantime, if you are impatient and want to know more please join the mondo*arc Linked In group and I will be happy to respond to any questions you may have.

Dr. Geoff Archenhold is an active investor in LED driver and fixture manufacturers and a lighting energy consultant.


Dr Geoff Archenhold
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