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.

[edit] Relative SPD

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]

[edit] References

^ Mark D. Fairchild (2005). Color Appearance Models. John Wiley and Sons. ISBN 0470012161.
^ 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.