Jim Worthey •
Lighting
& Color Research • jim@jimworthey.com
• 301-977-3551 • 11 Rye Court, Gaithersburg, MD 20878-1901, USA

Why
do Color Matching
Experiments use Red, Green, and Blue primaries? What wavelengths are
best?

Color Matching
Functions In a visual colorimetry
experiment, a human sets a mixture of 3 primaries to match a test
color. For example, a narrow band Test Light has unit power (1 watt,
for
example), and its power is held constant while its wavelength is varied
through the visible spectrum. At each setting of the test light, the
observer adjusts the 3 primary lights so that their mixture matches the
test light. In
quasi-algebraic terms, the observer's setting can be written:

test = Rred
+ Ggreen + Bblue
.

The words in bold
face indicate narrow-band lights, not algebraic variables. Variables R, G, B will be the power
settings of the so-called primary lights. For most settings of the test
wavelength, one of the power settings will be a negative number. In the
laboratory, if R <0, it means that
red light is added to test , rather than combining with
the mixture of Ggreen
+ Bblue . Now when test is varied through the spectrum
and R, G, Bare graphed, the 3
settings are called color matching
functions. The graph below shows a set of color matching
functions, or cmf's. But why is the graph moving?

Animated Color Matching Functions

If you have
the Flash plug-in in your browser, you should see moving graphs above.
Starting with the usual 2-degree observer of the CIE, color-matching
functions were calculated for 37 unique combinations of primary
wavelengths. The 37 graphs are then combined to make a 75-frame
animation. The
diamond shapes mark the wavelengths of the primary lights. From
starting values of 603, 538, and 446 nm, the primary wavelengths are
varied one at a time, first decreasing, then increasing, then
decreasing back to the starting value. Then the next primary is varied,
and so forth. The dashed lines are set at the same wavelengths as those
starting values. The numbers, 603, 538,
and 446,
are the Prime Colors, so named by Thornton. When the primaries are set
to these wavelengths, then the primary and the peak are at the same
wavelength, and the peak heights are 1.0, the lowest possible value.

So Far, So Good. But why are the
primary lights always red, green and blue?

The method by
which the graphs are calculated is right
out of the textbooks. There is nothing new or speculative in computing
the color matching functions for a set of 3 primary wavelengths.
Similar methods were used in comparing data from different
laboratories when the CIE 1931 system was first developed.

The traditional textbook discussion teaches that alternate sets of
primaries may be used, but leaves some questions unanswered. Why are
the primaries always red, green, and blue? Are there 3 wavelengths that
work the best?

The animation,
based on
detailed calculations, teaches two interesting lessons:
1. The peaks of the cmf's occur at certain wavelengths that are innate,
and are not particularly dependent on the choice of primaries. [If the
primaries were changed sufficiently, two of them could
be interchanged, upsetting this simple observation. The animation looks
at a more limited perturbation of
the primaries.]
2. When the primaries are set to the prime colors, 603, 538,
and 446 nm, then the cmf's peak at unit power. When one primary
wavelength is perturbed from its prime color, the maximum power needed
in that primary increases a little or a lot.

These are
not new
observations. They have been published by William A. Thornton and by
Jozef Cohen, and a related theorem was published by Michael H. Brill.
My goal here is to let you observe these facts for yourself, with the
aid of computer animation.

The same
ideas can
be re-stated in a more intuitive way. Suppose
that a child asks what the color matching functions mean. Keep
in mind there is only one test light, varying through the entire
spectrum. Therefore, the three humps in the color matching functions
show the 3 wavelength regions where the test light acts most strongly in mixtures.
There are 3 humps because color is 3-dimensional, and they denote the
regions where the test light acts strongly in the independent blue,
green, and red directions in color space.

The demo
shows that the functions peak at wavelengths that change little when
the primary
wavelengths are perturbed. We note that "certain wavelengths act
strongly in mixtures." After staring at the animation for a short time,
you can make a stronger statement. There are 3 well-defined wavelengths that act
most strongly in mixtures. They are a red, a green, and a blue, at 603, 538,
and 446 nm.

How can
there be
three "most important" wavelengths? That's simple. Color is a vector
and the full use of color vision calls for stimulation in 3 independent
dimensions. Illuminating engineers are taught that 555 nm is the one
important wavelength. The lighting textbooks are wrong.