distribution temperature (of a source in a given wavelength range, *λ*_{1} to *λ*_{2}) [*T*_{D}]

temperature of the Planckian radiator whose relative spectral distribution *S*(*λ*) is the same or nearly the same as that of the radiation considered in the spectral range of interest for which the following integral is minimized by adjustment of *a* and *T*:

where *λ *is the wavelength, *S*_{t}(*λ*) is the relative spectral distribution of the radiation being considered, *S*_{b}(*λ*, *T*) is the relative spectral distribution of the Planckian radiator at temperature *T*, and *a* is a scaling factor

Unit: K

NOTE 1 Planck's radiation formula:

where *c*_{2} is the second radiation constant.

NOTE 2 Distribution temperature is a meaningful characteristic for radiators having a relative spectral distribution similar to that of a Planckian radiator, but only if calculated for an extended wavelength range and for radiation whose spectral power distribution is a continuous function of wavelength in that range.

NOTE 3 In photometry and colorimetry this wavelength range, *λ*_{1}, *λ*_{2}, is the visible spectral region and in these cases the range from *λ*_{1} = 400 nm to *λ*_{2} = 750 nm is recommended.

NOTE 4 In practice, the integral is replaced by a summation. For incandescent lamps, equally spaced wavelength intervals of 10 nm will usually suffice. All values in the summation are treated with equal weight.

See also CIE 114-1994 *CIE Collection in Photometry and Radiometry - 114/4 Distribution Temperature and Ratio Temperature*

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