
Light and color 13
X =
Z
740
380
¯x(λ)E(λ)dλ
Y =
Z
740
380
¯y(λ)E(λ)dλ
Z =
Z
740
380
¯z(λ)E(λ)dλ. (1.16)
The color matching functions ¯x(λ), ¯y(λ), ¯z(λ) are obtained as a linear com-
bination of ¯r(λ), ¯g(λ),
¯
b(λ) by imposing certain criteria, chiefly among them:
– ¯x(λ), ¯y(λ), ¯z(λ) must always be positive;
– ¯y(λ) is identical to the standard luminosity function V (λ), which is a
dimension-less function describing the sensitivity to light as a function
of wavelength; therefore, Y =
R
¯y(λ)E(λ)dλ would correspond to the
luminance or perceived brightness of the color stimulus;
– ¯x(λ), ¯y(λ), ¯z(λ) are normalized so that they produce equal tristimulus
values X = Y