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Defining Colour Tunability

Issue 68 Aug / Sep 2012

Lighting fixture companies are in the process of developing variable CCT LED fixtures but many of them will not meet lighting designers’ specifications. In the first of a two-part article, Geoff Archenhold reports on what is needed to develop a quality lighting system that can vary CCT.

After my presentation for the IALD at Light + Building it was evident from a series of Q&As with over 20 designers that many still had reservations about colour quality and consistency with standard and variable CCT LED fixtures. Interestingly, I picked up that colour consistency is still an issue for large installations using many LED fixtures even though the reputable LED manufacturers use ANSI binning. When I broached the subject of variable colour temperature white lighting it provoked a mixed bag of emotions and reservations from those that don’t see the point to those that do but doubt if fixture manufacturers have the skills and knowledge to deliver perfectly consistent colour tuneable LED fixtures with high quality light at reasonable prices.

Interestingly, the feedback consistently mentioned that all units seen so far would look great in demonstration with one or two fixtures however in an installation the units would not be consistent with strange lighting/colouring effects occurring between them. These comments made me wonder as most companies that demonstrate such units only use one or two lighting fixtures and not 10’s or 100’s in an installation.

I have been experimenting with LED lighting systems for well over fifteen years and in the process have even developed colour tuneable LED fixture prototypes back beyond 2000 so I thought it would be interesting to create a series of articles to explain the do’s and don’ts of system design as well as how to specify colour tuneable lighting in your applications.

In this first part I will cover the fundamentals of light and colour so that the reader is able to understand the limitations of colour tuneable lighting fixtures and what is needed in order to be able to provide consistency of colour.

In order to create a variable CCT LED system we need to define the challenges that have to be overcome to create a “near” perfect system.

The first challenge is the human eye and its perception of colour which is the ability of the eye to distinguish objects based on the wavelengths (or frequencies) of the light they reflect, emit, or transmit. Indeed, a colour can be measured and quantified in various ways but within humans it is a subjective process whereby the brain responds to the stimuli that are produced when incoming light reacts with the several types of cone photoreceptors in the eye.

In humans, there are three types of cones sensitive to three different spectra, resulting in trichromatic colour vision as shown by the models in figure 1.



Two complementary theories of colour vision are the trichromatic theory and the opponent process theory. The trichromatic theory states that the retina’s three types of cones are preferentially sensitive to blue, green and red. However the opponent process theory states that the visual system interprets colour in an antagonistic way: red vs. green, blue vs. yellow, black vs. white. Both theories are actually correct and describe different stages in visual physiology.

The cones are conventionally labelled according to the ordering of the wavelengths of the peaks of their spectral sensitivities: short (S), medium (M), and long (L) cone types whose spectral sensitivities are shown in figure 2.



Unfortunately, these three cone types do not correspond well to particular colours as we know them as the perception of colour is achieved by a complex process that starts with the differential output of these cells in the retina and it will be finalised in the visual cortex and associative areas of the brain. This differential effect may be one reason why having two or more v-CCT light fixtures appear different especially if the LEDs are pulsed as that also adds the further dimensional complexity of time!

It is also important to remember that the peak response of human cone cells varies, even among individuals with ‘normal’ colour vision so what looks acceptable to one person may not be for another.

Therefore, referring to figure 2, a range of wavelengths of light stimulates each of these receptor types to varying degrees. Yellowish-green light, for example, stimulates both L and M cones equally strongly, but only stimulates S-cones weakly. Red light, on the other hand, stimulates L cones much more than M cones, and S cones hardly at all; blue-green light stimulates M cones more than L cones, and S cones a bit more strongly, and is also the peak stimulant for rod cells; and blue light stimulates S cones more strongly than red or green light, but L and M cones more weakly. The brain combines the information from each type of receptor to give rise to different perceptions of different wavelengths of light.

The Luminosity function
The luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It should not be considered perfectly accurate in every case, but it is a very good representation of visual sensitivity of the human eye and it is valuable as a baseline for experimental purposes and is used heavily for computing various efficacy and colour metrics in lighting.

The CIE luminosity function V(λ) is a standard function established by the Commission Internationale de l’Éclairage (CIE) and is used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central colour matching function in the CIE 1931 colour space.
In essence there are two main luminosity functions in common use. For everyday light levels, the photopic luminosity function best approximates the response of the human eye. For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the violet, peaking around 507 nm for young eyes; the sensitivity is equivalent to 1699 lm/W or 1700 lm/W at this peak. Recently, a third luminosity function has been proposed called Mesopic vision which is a combination of photopic vision and scotopic vision in low but not quite dark lighting situations. Mesopic light levels range from luminances of approximately 0.001 to 3 cd m-2. Most night-time outdoor and traffic lighting scenarios are in the mesopic range.

The luminous flux (or visible energy) in a light source is defined by the photopic luminosity function. The following equation calculates the total luminous flux in a source of light.

F is the luminous flux in lumens.
J (λ) is the spectral power distribution of the radiation (power per unit         wavelength), in watts per metre.
y(λ) (also known as V(λ)) is the standard luminosity function (which is dimensionless).
λ is wavelength in metres.

The standard luminosity function is normalized to a peak value of unity at 555 nm and the maximum efficacy of 683 lm/W is achieved according to human vision characteristics.

CIE 1931 colour space

In the study of colour perception, one of the first mathematically defined colour spaces is the CIE 1931 XYZ colour space derived from a series of experiments done in the late 1920s. The results were combined into the specification of the CIE RGB colour space, from which the CIE XYZ colour space was derived.

The tristimulus values of any particular colour can be conceptualised as the amounts of three primary colours in a tri-chromatic additive colour model.

Due to the distribution of cones in the eye, the tristimulus values depend on the observer’s field of view. To eliminate this variable, the CIE defined the standard (colourimetric) observer. Originally this was taken to be the chromatic response of the average human viewing through a 2° angle, due to the belief that the colour-sensitive cones resided within a 2° arc of the fovea. The standard observer is characterised by three colour matching functions as shown in figure 3.


The CIE has defined a set of three colour-matching functions, called x (λ), y (λ), and z (λ), which can be thought of as the spectral sensitivity curves of three linear light detectors that yield the CIE XYZ tristimulus values X, Y, and Z.

The tristimulus values for a colour with a spectral power distribution I (λ)  are given in terms of the standard observer by:

where λ is the wavelength of the equivalent monochromatic light (measured in nanometers).

Since the human eye has three types of colour sensors that respond to different ranges of wavelengths, a full plot of all visible colours is possible however the concept of colour can be divided into two parts: brightness and chromaticity.

The CIE XYZ colour space was deliberately designed so that the Y parameter was a measure of the brightness or luminance of a colour. The chromaticity of a colour was then specified by the two derived parameters x and y, two of the three normalised values which are functions of all three tristimulus values X, Y, and Z:

It is also possible to transform from the CIE XYZ to the CIE RGB space using the equation seen in figure 4.



Spectral Power Distribution (SPD)
In colour science and radiometry, a spectral power distribution (SPD) describes the power per unit area per unit wavelength of an illumination, or more generally, the per-wavelength contribution to any radiometric quantity and as we have seen it is crucial for calculating the luminous flux. The SPD of an incandescent lamp and a fluorescent is shown in figure 5.



The relative SPD is often calculated because the luminance of lighting fixtures and other light sources are handled separately and so a spectral power distribution is often normalized to unity at 555 or 560 nanometers, coinciding with the peak of the eye’s luminosity function.

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.

The human eye varies its spectral sensitivity response according to the ambient light conditions so the eye has three defined vision states including photopic, scotopic and Mesopic.

Finally, the perceived colour from an object to the human eye can be defined by several processes as follows:
1) The characteristic spectral power density of the light source being emitted
2) The surface and material characteristics of the object being illuminated
3) The spectral and intensity response of the human eye observing the light being emitted from the surface of the illuminated object.

In the next issue I will cover the definition of CCT and CRI as well as how to mathematically calculate CCT using the chromaticity coordinates of LED lighting sources.


Dr Geoff Archenhold
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