distribution temperature, <of a source in a given wavelength range, λ₁ to λ₂>

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

Note 1 to entry: The scaling factor a is chosen to make the quotient equal to unity at a convenient wavelength which, in photometry and colorimetry is typically 560 nm.
with , where c₂ is the second radiation constant.

Note 2 to entry: 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 expanded wavelength range and for radiation whose spectral distribution of radiant flux is a continuous function of wavelength in that range.

Note 3 to entry: In photometry and colorimetry the wavelength range set by λ₁ and λ₂ is the visible spectral range, and in these cases the range from at least λ₁ = 400 nm to λ₂ = 750 nm is recommended.

Note 4 to entry: 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.

Note 5 to entry: The distribution temperature is expressed in kelvin (K).

Note 6 to entry: For further information, see CIE 114-1994 CIE Collection in Photometry and Radiometry – 114/4 Distribution Temperature and Ratio Temperature.

Note 7 to entry: This entry was numbered 845-04-14 in IEC 60050-845:1987.

Note 8 to entry: This entry was numbered 17-341 in CIE S 017:2011.