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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

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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