Spectral Power Distribution§

Spectral Power Distribution (SPD)

Any patch of light can be completely described by its spectrum, a SPD is represented as a plot of energy of photons per unit time for each wavelength, typically between 400 - 700 nm.

Light Detectors§

The capture of a light detector may be modelled with the following equation,

$$ X = \int n(\lambda) p(\lambda) d\lambda, $$


  • $n(\lambda)$ is the count of incident photons at wavelength $\lambda$,
  • $p(\lambda)$ is the efficiency of the detector at wavelength $\lambda$.

We again have a dimensional reduction, the SPD is a function of wavelength which is $\infty$-dimensional whereas the output of the detector is 1-dimensional.

Psychophysical Correspondence§

Color is not an intrinsic value of light; it is a result of human perception. Color arises from sensing light with different SPDs, as such different wavelengths of light are not colors.

There is no function that describes the perceived color, but it is helpful to consider only physical spectra that are distributed normally.

Under the normal distribution,

  • the mean, $\mu$, can be interpreted as hue,
  • variance, $\sigma^2$, as the saturation,
  • and the area as brightness.

The Eye§

The human eye is essentially a biological camera,