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Spectral power distribution

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In color science a spectral power distribution (SPD) 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][2]

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(\lambda) is the spectral irradiance (or exitance) of the light (SI units: W/m3 = kg/(m·s3)); \Phi is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m2); and \lambda is the wavelength (SI unit: meter, m). (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 W·m−2·nm−1.) The approximation is valid when the area and wavelength interval are small.

Relative SPDEdit

File:Spectral Power Distributions.png
Characteristic spectral power distributions (SPDs) for an incandescent lamp (left) and a fluorescent lamp (right). The horizontal axes are in nanometers and the vertical axes show relative intensity in arbitrary units.

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 555 or 560 nanometers, coinciding with the peak of the eye's luminosity function.[2][3]


  1. Mark D. Fairchild (2005). Color Appearance Models, John Wiley and Sons.
  2. 2.0 2.1 Michael R. Peres (2007). The Focal Encyclopedia of Photography, Focal Press.
  3. Wyszecki, Günter; Stiles, Walter Stanley (1982). Color Science: Concepts and Methods; Quantitative Data and Formulae, second edition, New York: Wiley.

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