Is there a way to convert Chromaticity Coordinates to Color Temperature and vice-versa?
J81
can use to convert back and forth between the two measurements? Some
lamp manufacturers give Color Temperature in their technical datasheets
but not Chromaticity Coordinates, but I've also found instances where
the opposite is true. I want a simple way to convert back and forth
between the two measurements so that I can understand the relationship
of the two measurements to one-another and be able to use them
interchangeably as necessary to assist in the comparison of one kind of
lamp to another, when trying to compensate for lack of
manufacturer-supplied data.
And if there's a complicated solution to this problem, I'm interested in
that one too if anybody's willing to explain it and/or point me in the
proper direction.
J
J
John D. Bullough, Gurley Building
>can use to convert back and forth between the two measurements? Some
>lamp manufacturers give Color Temperature in their technical datasheets
>but not Chromaticity Coordinates, but I've also found instances where
>the opposite is true. I want a simple way to convert back and forth
>between the two measurements so that I can understand the relationship
>of the two measurements to one-another and be able to use them
>interchangeably as necessary to assist in the comparison of one kind of
>lamp to another, when trying to compensate for lack of
>manufacturer-supplied data.
The procedure for calculating correlated color temperature (CCT)
of a lamp from its chromaticity coordinates is given in the book
COLOR SCIENCE: CONCEPTS AND METHODS, QUANTITATIVE DATA AND FORMULAE,
2nd ed., by Wyszecki and Stiles, pp. 224-228. Many university
libraries will have this book and Wiley sells a paperback version
at a reasonable cost.
But you cannot go back and forth between CCT and chromaticity
coordinates - you can determine the CCT from a given pair of
chromaticity coordinates but you cannot determine the chromaticity
coordinates from a given CCT, because lamps with the same CCT
can plot on the blackbody locus in the chromaticity diagram,
below it (toward the purple side) or above it (toward the green
side), so that two lamps, one being slightly purplish and one being
slightly greenish can have the same CCT even though they won't
look the same. Two sources with the same chromaticity coordinates
will match exactly.
If you're not looking for ultra precision, a convenient chart
that shows lines of constant CCT for chromaticity coordiates near
the blackbody locus is on p. 225 of COLOR SCIENCE, or p. 4-14 of
the IESNA LIGHTING HANDBOOK, 9th ed.
JB
Ian Ashdown
> of a lamp from its chromaticity coordinates is given in the book
> COLOR SCIENCE: CONCEPTS AND METHODS,
> QUANTITATIVE DATA AND FORMULAE, 2nd ed., by
> Wyszecki and Stiles, pp. 224-228. Many university libraries will
> have this book and Wiley sells a paperback version
> at a reasonable cost.
>
computer program but not for quick hand calculations. An alternative is
McCamy's equation:
n = (x - xe) / (ye - y)
CCT = 449.0 * n^3 + 3525.0 * n^2 + 6823.3 * n + 5520.33
where xe = 0.3320 and ye = 0.1858.
This equation has a maximum error of 2 Kelvin from 2,856 to 6,500 Kelvin,
corresponding to CIE illuminants A (an incandescent lamp) througfh D65
(daylight).
The original paper by McCamy is very difficult to locate outside of major
university libraries, but his equation is documented in the SPIE paper
"Chromaticity and Color Temperature for Architectural Lighting" that is
available from http://www.tirsys.com/gl-technology/b_ssl2p.html.
Ian Ashdown, P. Eng. LC, FIES
Senior Research Scientist
TIR Systems Limited
http://www.tirsys.com