Centre wavelength

The centre wavelength is the power-weighted mean wavelength:

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

And the total power is:

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

where $p(\lambda)$ 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 $p(\lambda)$ is higher than a fraction of its maximum.

See also

• peak wavelength
• dominant wavelength