Basic Color-Matching Experiment

The most fundamental experiment in color science entails
the determination of whether two fields of light such as
those that might be produced on a screen with two slide
projectors, appear the same or different. If such fields are
abutted and the division between them disappears to form
a single, homogeneous field, the fields are said to match. A
match will, of course, occur if there is no physical differ-
ence between the fields, and in special cases color matches
are also possible when substantial physical differences ex-
ist between the fields. An understanding of how this can
happen provides an opening to a scientific understanding
of this subject.
Given an initial physical match, a difference in color
can be introduced by either of two procedures, which are
often carried out in combination. In the first instance, the
radiance of one part of a homogeneous field is altered
without any change in its relative spectral distribution.
This produces an achromatic color difference. In the sec-
ond case, the relative spectral distribution of one field is
changed such that, for all possible relative radiances of the
two fields, no match is possible. This is called a chromatic
color difference.
When fields of different spectral distributions can be ad-
justed in relative radiance to eliminate all color difference,
the result is termed a metameric color match. In a color-
matching experiment, a test field is presented next to a
comparison field and the observer causes the two fields to
match exactly by manipulating the radiances of so-called
primaries provided to the comparison field. Such primaries
are said to be added; this can be accomplished by superpo-
sition with a half-silvered mirror, by superimposed images
projected onto a screen, by very rapid temporal alternation
of fields at a rate above the fusion frequency for vision,
or by the use of pixels too small and closely packed to be
discriminated (as in color television). If the primaries are
suitably chosen (no one of them should be matched by any
possible mixture of the other two), a human observer with
normal color vision can uniquely match any test color by
adjusting the radiances of three monochromatic primaries.
To accomplish this, it sometimes proves necessary to shift
one of the primaries so that it is added to the color being
matched; it is useful to treat this as a negative radiance
of that primary in the test field. The choice of exactly
three primaries is by no means arbitrary: If only one or
two primaries are used, matches are generally impossible,
whereas if four or more primaries are allowed, matches
are not uniquely determined.
The result of the color-matching experiment can be rep-
resented mathematically as t(T ) =r(R) + g(G) + b(B),
meaning that t units of test field T produce a color that
is matched by an additive combination of r units of pri-
mary R, g units of primary G, and b units of primary
B, where one or two of the quantities r, g, or b may be
negative. Thus any color can be represented as a vector
in R, G, B space. For small, centrally fixated fields, ex-
periment shows that the transitive, reflexive, linear, and
associative properties of algebra apply also to their empir-
ical counterparts, so that color-matching equations can be
manipulated to predict matches that would be made with achange in the choice of primaries. These simple relations
break down for very low levels of illumination and also
with higher levels if the fields are large enough to permit
significant contributions by rod photoreceptors or if the
fields are so bright as to bleach a significant fraction of
cone photopigments, thus altering their action spectra.
Matches are usually made by a method of adjustment, an
iterative, trial-and-error procedure whereby the observer
manipulates three controls, each of which monotonically
varies the radiance of one primary. Although such set-
tings at the match point may be somewhat more variable
than most purely physical measurements, reliable data re-
sult from the means of several settings for each condition
tested. A more serious problem, which will not be treated
in this article, results from differences among observers.
Although not great among those with normal color vi-
sion, such differences are by no means negligible. (For
those with abnormal color vision, they can be very large.)
To achieve a useful standardization—one that is unlikely
to apply exactly to any particular individual—averages of
normal observers are used, leading to the concept of a
standard observer.
FIGURE 1 Experimental color-matching data for primaries at 435.8, 546.1, and 700.0 nm. [From Billmeyer, F. W.,
Jr., and Saltzmann, M. (1981). “Principles of Color Technology,” 2nd ed. Copyright ©1981 John Wiley & Sons, Inc.
Reprinted by permission of John Wiley & Sons, Inc.]
In the color-matching experiment, an observer is in ef-
fect acting as an analog computer, solving three simulta-
neous equations by iteration, using his or her sensations as
a guide. Although activity in the brain underlies the expe-
rience of color, the initial encoding of information related
to wavelength is in terms of the ratios of excitations of
three different classes of cone photoreceptors in the retina
of the eye, whose spectral sensitivities overlap. Any two
physical fields, whether of the same or different spectral
composition, whose images on the retina excite each of
the three classes of cones in the same way will be indis-
criminable. The action spectra of the three classes of cones
in the normal eye are such that no two wavelengths in the
spectrum produce exactly the same ratios of excitations
among them.