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Section 3.1 Human Color Perception 71

then
T a = T b .

Finally, matching is linear: if
T a = w 1 P 1 + w 2 P 2 + w 3 P 3 ,

then
kT a =(kw 1 )P 1 +(kw 2 )P 2 +(kw 3 )P 3
for non-negative k.
Given the same test light and set of primaries, most people use the same set of
weights to match the test light. This, trichromacy, and Grassman’s laws are about
as true as any law covering biological systems can be. The exceptions include the
following:
• people with too few kinds of color receptor as a result of genetic ill fortune
(who may be able to match everything with fewer primaries);
• people with neural problems (who may display all sorts of effects, including
a complete absence of the sensation of color);
• some elderly people (whose choice of weights differ from the norm because of
the development of macular pigment in the eye);
• very bright lights (whose hue and saturation look different from less bright
versions of the same light);
• and very dark conditions (where the mechanism of color transduction is some-
what different than in brighter conditions).

3.1.2 Color Receptors
Trichromacy occurs because there are (usually!) three distinct types of receptor in
the eye that mediate color perception. Each of these receptors turns incident light
into neural signals. The principle of univariance states that the activity of these
receptors is of one kind (i.e., they respond strongly or weakly, but do not signal the
wavelength of the light falling on them). Experimental evidence can be obtained
by carefully dissecting light-sensitive cells and measuring their responses to light at
different wavelengths or by reasoning backward from color matches. Univariance is
a powerful idea because it gives us a good and simple model of human reaction to
colored light: two lights will match if they produce the same receptor responses,
whatever their spectral energy densities.
Because the system of matching is linear, the receptors must be linear. Write
p k for the response of the kth type of receptor, σ k (λ) for its sensitivity, E(λ)for
the light arriving at the receptor, and Λ for the range of visible wavelengths. We
can obtain the overall response of a receptor by adding up the response to each
separate wavelength in the incoming spectrum so that

p k = σ k (λ)E(λ)dλ.
Λ