The centre wavelength is the power-weighted mean wavelength:

${\displaystyle \lambda _{\text{c}}={\frac {1}{P_{\text{total}}}}\int p(\lambda )\lambda \,d\lambda ,}$

and the total power is

${\displaystyle P_{\text{total}}=\int p(\lambda )\,d\lambda ,}$

where ${\displaystyle p(\lambda )}$ is the power spectral density, for example in W/nm.

The above integrals theoretically extend over the entire spectrum, however, it is usually sufficient to perform the integral over the spectrum where the spectral density ${\displaystyle p(\lambda )}$ is higher than a fraction of its maximum.

See also

• Dominant wavelength

References