View source for Radiant flux

{{Short description|Measure of radiant energy over time}}
{{distinguish|text=[[Radiation flux]]}}
{{Redirect-distinguish|Spectral power|Spectral power density}}
{{More citations needed|auto=yes|date=December 2009}}
[[File:Flow chart inspired by Lillesand, Kiefer, Chipman.. Remote Sensing and Image Interpretation, 7th Edition Appendix A.. Radiometric Concepts, Terminology, and Units.png|alt=A flow chart describing the relationship of various physical quantities, including radiant flux and exitance.|thumb|A flow chart describing the relationship of various physical quantities, including radiant flux and exitance.]]

In [[radiometry]], '''radiant flux''' or '''radiant power''' is the [[radiant energy]] emitted, reflected, transmitted, or received per unit time, and '''spectral flux''' or '''spectral power''' is the radiant flux per unit [[frequency]] or [[wavelength]], depending on whether the [[Spectral radiometric quantity|spectrum]] is taken as a function of frequency or of wavelength. The [[International System of Units|SI unit]] of radiant flux is the [[watt]] (W), one [[joule]] per second ({{nobreak|J/s}}), while that of spectral flux in frequency is the watt per [[hertz]] ({{nobreak|W/Hz}}) and that of spectral flux in wavelength is the watt per metre ({{nobreak|W/m}})—commonly the watt per nanometre ({{nobreak|W/nm}}).

==Mathematical definitions==
===Radiant flux===
'''Radiant flux''', denoted {{math|Φ<sub>e</sub>}} ('e' for "energetic", to avoid confusion with [[Photometry (optics)|photometric]] quantities), is defined as<ref name="ISO_9288-1989" />
<math display="block">\begin{align}
\Phi_\mathrm{e} &= \frac{d Q_\mathrm{e}}{d t} \\[2pt]
Q_\mathrm{e} &= \int_{\Sigma} \mathbf{S}\cdot \hat\mathbf{n}\, dA 
\end{align}</math>
where
*{{mvar|t}} is the time;
*{{math|''Q''<sub>e</sub>}} is the [[radiant energy]] flux of the [[Electromagnetic field|field]] out of a [[closed surface]] {{math|&Sigma;}};
*{{math|'''S'''}} is the [[Poynting vector]], representing the [[current density]] of radiant energy;
*{{math|'''n'''}} is the [[normal vector]] of a point on {{math|&Sigma;}};
*{{math|'''A'''}} represents the area of {{math|&Sigma;}}.
But the time-average of the norm of the Poynting vector is used instead, because in radiometry it is the only quantity that radiation detectors are able to measure:
<math display="block">\Phi_\mathrm{e} \approx \int_\Sigma \langle|\mathbf{S}|\rangle \cos \alpha\ dA ,</math>
where {{math|{{angle brackets|-}}}} is the time-average, and {{mvar|α}} is the angle between {{math|'''n'''}} and <math>\langle|\mathbf{S}|\rangle.</math>

===Spectral flux===
'''Spectral flux in frequency''', denoted Φ<sub>e,''ν''</sub>, is defined as<ref name="ISO_9288-1989" />
<math display="block">\Phi_{\mathrm{e},\nu} = \frac{\partial \Phi_\mathrm{e}}{\partial \nu} ,</math>
where {{mvar|ν}} is the frequency.

'''Spectral flux in wavelength''', denoted {{math|Φ<sub>e,''λ''</sub>}}, is defined as<ref name="ISO_9288-1989" />
<math display="block">\Phi_{\mathrm{e},\lambda} = \frac{\partial \Phi_\mathrm{e}}{\partial \lambda} ,</math>
where {{mvar|λ}} is the wavelength.

=={{anchor|units}}SI radiometry units==
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|Comparison of photometric and radiometric quantities]]
{{SI radiometry units}}

==See also==
*[[Luminous flux]]
*[[Heat flux]]
*[[Power (physics)]]
*[[Radiosity (heat transfer)]]

==References==
{{Reflist|refs=
<ref name="ISO_9288-1989">{{cite web|url=http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=16943 |title=Thermal insulation — Heat transfer by radiation — Physical quantities and definitions|work=ISO 9288:1989|publisher=[[International Organization for Standardization|ISO]] catalogue|year=1989|access-date=2015-03-15}}</ref>
}}

==Further reading==
*{{cite book 
|title= Radiometry and the Detection of Optical Radiation (Pure & Applied Optics Series)
|last = Boyd
|first = Robert
|author-link = Robert W. Boyd (physicist)
|year = 1983
|publisher = Wiley-Interscience
|isbn = 978-0-471-86188-1
}}

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[[Category:Power (physics)]]
[[Category:Physical quantities]]
[[Category:Radiometry]]
[[Category:Temporal rates]]