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'{{Refimprove|auto=yes|date=December 2009}} (deez nutz) 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), that is the [[joule]] per second ({{nobreak|J/s}}) in SI base units, 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 Φ_e ("e" for "energetic", to avoid confusion with [[Photometry (optics)|photometric]] quantities), is defined as<ref name="ISO_9288-1989" /> :<math>\Phi_\mathrm{e} = \frac{\partial Q_\mathrm{e}}{\partial t},</math> where *∂ is the [[partial derivative]] symbol; *''Q''_e is the radiant energy emitted, reflected, transmitted or received; *''t'' is the time. ===Spectral flux=== '''Spectral flux in frequency''', denoted Φ_e,ν, is defined as<ref name="ISO_9288-1989" /> :<math>\Phi_{\mathrm{e},\nu} = \frac{\partial \Phi_\mathrm{e}}{\partial \nu},</math> where ''ν'' is the frequency. '''Spectral flux in wavelength''', denoted Φ_e,λ, is defined as<ref name="ISO_9288-1989" /> :<math>\Phi_{\mathrm{e},\lambda} = \frac{\partial \Phi_\mathrm{e}}{\partial \lambda},</math> where ''λ'' is the wavelength. ==Relationship with the Poynting vector== One can show that the radiant flux of a ''surface'' is the [[flux]] of the [[Poynting vector]] through this surface, hence the name "radiant flux": :<math>\Phi_\mathrm{e} = \oint_\Sigma \mathbf{S} \cdot \mathbf{\hat{n}}\, \mathrm{d}A = \oint_\Sigma |\mathbf{S}| \cos \alpha\, \mathrm{d}A,</math> where *''Σ'' is the surface; *'''S''' is the Poynting vector; *'''n''' is a unit [[Normal (geometry)|normal vector]] to that surface; *''A'' is the area of that surface; *''α'' is the angle between '''n''' and '''S'''. 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 measure: :<math>\Phi_\mathrm{e} = \oint_\Sigma \langle|\mathbf{S}|\rangle \cos \alpha\, \mathrm{d}A,</math> where < • > is the time-average. ==SI radiometry units== {{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|accessdate=2015-03-15}}</ref> }} ==Further reading== *{{cite book |title= Radiometry and the Detection of Optical Radiation (Pure & Applied Optics Series) |last = Boyd |first = Robert |authorlink = Robert W. Boyd (physicist) |year = 1983 |publisher = Wiley-Interscience |isbn = 978-0-471-86188-1 |url = http://www.amazon.com/Radiometry-Detection-Optical-Radiation-Applied/dp/047186188X/ref=sr_1_1?s=books&ie=UTF8&qid=1313084491&sr=1-1}} [[Category:Power (physics)]] [[Category:Physical quantities]] [[Category:Radiometry]]'