Tristimulus

Tristimulus is the term given to the perception of colour from three different sensors.

Tristimulus values are the resultant excitation of each sensor for a light of any given wavelength in relation to the other sensors.

Tristimulus value for each sensor is calculated as the sum of the product of Spectral Power Distribution (SPD) of the colour with the colour matching functions or Spectral Sensitivity of the sensor for each wavelength.

That is, for example:
Assuming an RGB system, if \(S(\lambda)\) is the SPD function of a light source and \(\bar{r}(\lambda)\) is the spectral sensitivity of the red sensor, the tristimulus value R of the sensor would be:

\(R=\int_{\lambda}S(\lambda)\bar{r}(\lambda)d\lambda\), where normally \(\lambda\in [380, 780]\)

Generally the radiometric value used in the SPD is spectral radiance for emitting sources, but for reflected light it can be SPD of Reflectance or (transmittance) multiplied by the SPD of the illuminant factor.