Spectral power distribution

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Not to be confused with Power spectral density.

In color science, a spectral power distribution describes the power per unit area per unit wavelength of an illumination (radiant exitance), or more generally, the per-wavelength contribution to any radiometric quantity (radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, or radiosity).[1]

Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:

M_\lambda=\frac{\partial^2\Phi}{\partial A\partial\lambda}\approx\frac{\Phi}{A \Delta\lambda}

where M(λ) is the spectral irradiance (or exitance) of the light (SI units: watt meter–3); Φ is the radiant flux of the source (SI units: watt); A is the area over which the radiant flux is integrated (SI units: meter2); and λ is the wavelength (SI unit: meter). (Note that it is more convenient to express the wavelength of light in terms of nanometers; spectral exitance would then be expressed in units of watt meter–2 nanometer–1.) The approximation is valid when the area and wavelength interval are small.

Relative SPD

The relative SPD of two light sources. The numbers indicate the wavelength in nanometers.
The relative SPD of two light sources. The numbers indicate the wavelength in nanometers.

Because the luminance of lighting fixtures and other light sources are handled separately, a spectral power distribution may be normalized in some manner, often to unity at 560 nanometers, coinciding with the peak of the eye's luminosity function.[2]

References

  1. ^ Mark D. Fairchild (2005). Color Appearance Models. John Wiley and Sons. ISBN 0470012161. 
  2. ^ Wyszecki, Günter; Stiles, Walter Stanley (1982). Color Science: Concepts and Methods; Quantitative Data and Formulae, second edition, New York: Wiley. ISBN 978-0-471-39918-6. 

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