The centre wavelength is the power-

weighted mean The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

: :

\lambda_\text = \frac \int p(\lambda) \lambda\, d\lambda,

and the total power is :

P_\text = \int p(\lambda) \,d\lambda,

where

p(\lambda)

is the power

spectral density The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, o ...

, 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.

References

Waves {{optics-stub

See also

References