{{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}}). Radiant flux is sometimes called '''[[luminosity]]''', especially in astronomy contexts.
==Mathematical definitions== ===Radiant flux=== Radiant flux, denoted [[Phi|{{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_{T} \int_{\Sigma} \mathbf{S}\cdot \hat\mathbf{n}\, dA dt \end{align}</math> where *{{math|''Q''<sub>e</sub>}} is the [[radiant energy]] passing out of a [[closed surface]] {{math|Σ}} in time interval {{mvar|T}}; *{{mvar|t}} is time; *{{mvar|A}} is the area of the surface {{math|Σ}}; *{{math|'''S'''}} is the [[Poynting vector]], representing the ''directional'' flow of energy per unit time, per unit area; *{{math|'''n'''}} is the unit [[normal vector]] to the differential area element {{math|''dA''}}. The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, giving <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|'''S'''}}.
===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]]