118 TECHNOLOGY / LED
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 tempera- ture 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 coor- dinate 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
5520.33 where n = (x - xe
+ 3525n2 )/(y - ye - 6823.3n + ) 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 + A1 + A3
exp(-n/t3 )
where n is as before and the other con- stants are defined below for 3000 to 50,000K:
Xe Ye A0 A1 t1
A2 t2
A3 t3
0.3366 0.1735
-949.86315 6253.80338 0.92159 28.70599 0.20039 0.00004 0.07125
Your head may be spinning by the mathe- matics 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 calcu-
exp(-n/t1 ) + A2 exp(-n/t2 )
lated. 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 de- rived 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. Subtractive mixing is done by selectively removing certain colours, for instance with optical filters in front of a white
Figure 5: The Error between real and McCamy calculated CCT for various colour temperatures.
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 pres- ence 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.
Overview 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 calcula- tions. 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 cre- ate 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 con- tinue to explain how to specify vCCT based lighting fixtures and determine the advan- tages 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.
g.archenhold@
mondiale.co.uk
Dr. Geoff Archenhold is an active investor in LED driver and fixture manufacturers and a lighting energy consultant.
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