Centre wavelength

The centre wavelength is the power-weighted mean wavelength:


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

and the total power is


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

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.