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The centroid wavelength is the power-weighted mean wavelength:

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

and the total power is

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

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.

See also

• Dominant wavelength

References

1. Hieda, Keisuke; Maruyama, Tomoyuki; Narusawa, Fumio (2019-10-04). "The Importance of Centroid Wavelength for the Image Quality Evaluation of Laser Displays". SID Symposium Digest of Technical Papers. 50 (S1): 1002–1004. doi:10.1002/sdtp.13724. ISSN 0097-966X.

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