How can tristimulus values be calculated?

Tristimulus values can be calculated if the reflectance spectrum of a sample is known. The reflectance spectrum can be measured using a reflectance spectrophotometer.

CIE XYZ tristimulus values can be calculated by the integration of the reflectance values R(l), the relative spectral energy distributions of the illuminant E(l), and the standard observer functions x(l), y(l), and z(l). The integration is appoximated by summation, thus:

X = 1/k S R(l) E(l) x(l),

Y = 1/k S R(l) E(l) y(l),

Z = 1/k S R(l) E(l) z(l),

where k = S E(l) y(l) and l = wavelength.

The normalizing factor 1/k is introduced such that Y = 100 for a sample that reflects 100% at all wavelengths: recall that Y is proportional to the luminance of the stimulus. The introduction of this normalization is convenient since it means that relative, rather than absolute, spectral energy distributions for the illuminant can be used (thus the units in which they are expressed are unimportant).