Centre wavelength

The centre wavelength is the power-weighted mean wavelength:

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

And the total power is:

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

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.