Centre wavelength

Short description: Power-weighted mean wavelength

The centre wavelength is the power-weighted mean wavelength:

[math]\displaystyle{ \lambda_\text{c} = \frac{1}{P_\text{total}} \int p(\lambda) \lambda\, d\lambda, }[/math]

and the total power is

[math]\displaystyle{ P_\text{total} = \int p(\lambda) \,d\lambda, }[/math]

where [math]\displaystyle{ p(\lambda) }[/math] 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 [math]\displaystyle{ p(\lambda) }[/math] is higher than a fraction of its maximum.

See also

• Dominant wavelength