# Centroid wavelength

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{{short description|Power-weighted mean wavelength}}

The '''centroid wavelength''' is the power-[weighted mean](/source/weighted_mean) [wavelength](/source/wavelength):<ref>{{Cite journal |last=Hieda |first=Keisuke |last2=Maruyama |first2=Tomoyuki |last3=Narusawa |first3=Fumio |date=2019-10-04 |title=The Importance of Centroid Wavelength for the Image Quality Evaluation of Laser Displays |url=https://sid.onlinelibrary.wiley.com/doi/10.1002/sdtp.13724 |journal=SID Symposium Digest of Technical Papers |language=en |volume=50 |issue=S1 |pages=1002–1004 |doi=10.1002/sdtp.13724 |issn=0097-966X|url-access=subscription }}</ref>

: <math>\lambda_\text{c} = \frac{1}{P_\text{total}} \int p(\lambda) \lambda\, d\lambda,</math>

and the total power is

: <math>P_\text{total} = \int p(\lambda) \,d\lambda,</math>

where <math>p(\lambda)</math> is the power [spectral density](/source/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>p(\lambda)</math> is higher than a fraction of its maximum.

==See also==
<!--* [Peak wavelength](/source/Peak_wavelength) -->
* [Dominant wavelength](/source/Dominant_wavelength)

==References==
{{reflist}}

Category:Waves

{{optics-stub}}

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Adapted from the Wikipedia article [Centroid wavelength](https://en.wikipedia.org/wiki/Centroid_wavelength) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Centroid_wavelength?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.