Hi Andrew!
Am 2011-12-29 00:36, schrieb Andrew Gabriel:
Can anyone tell me what colour temperature X=0.45, Y=0.41 equates to?
(It comes from the specification of a warm white LED).
The short answer is: About 2840 K +/-40 K (assuming that the x,y are
rounded and thus accurate within +/-0.005 each), i.e. slightly higher
than a standard incandescent lamp (about 2700 K). The point is pretty
close to the blackbody curve, maybe very slightly green-shifted.
The long answer is how to calculate this. I taught myself with the
relating Wikipedia articles:
http://en.wikipedia.org/wiki/Color_temperature
http://en.wikipedia.org/wiki/CIE_1960_color_space
Given the x-y coordinates (lower-case, where x+y+z=1 per definition, and
x,y define the chromaticity. The upper-case XYZ are also scaled by
luminance), first the CIE 1960 u-v coordinates have to be calculated:
u = 4x / (-2x+12y+3)
v = 6y / (-2x+12y+3)
In these coordinates, the correlated color temperature can be calculated
as the closest-match Planckian locus (the x-y chromaticity of a
blackbody at this temperature) to the given colour. In the CIE 1960
color space an Euklidian metric can be assumed (which is not the case in
x-y). The closest distance can be approximated by linear interpolation
between equal-temperature lines in the mired scale (mired =
10^6/Kelvin), but the most precise solution is probably a simple
numerical solver to minimize the u-v distance. The value of this
distance is a rough measure of the color rendering properties (but NOT
equal to the CRI, which is more complex). As a rule of the thumb: For
good light quality, the u-v distance should be negligible for color
temperatures below about 4000 K and should be about 0.003 towards the
green area for temps higher than 5000 K to match the D standard
illuminants (daylight, for example, is slightly green-shifted relative
to pure blackbody radiation, AFAIK mainly due to the effects of the
atmosphere, but also the Sun is not a perfect blackbody).
One might also discuss whether the CIE 1976 or the CIELAB color space
would be more precise in terms of perceived color differences, but the
choice of the 1960 space is sort of historical standard. Human
perception is never really precise, als probably differs between
individuals.
HTH
Ingo
