Editing Radiant intensity

{{Short description|Intensity of electromagnetic radiation}}
{{Redirect|Radiation intensity|ionizing radiation|Radiation flux|other measures of electromagnetic radiation|Light intensity (disambiguation)}}
<!--Do NOT redirect this page to "Intensity". Radiant intensity is a different quantity, with different units!-->

In [[radiometry]], '''radiant intensity'''<!--DO NOT LINK: general use of term--> is the [[radiant flux]] emitted, reflected, transmitted or received, per unit [[solid angle]], and '''spectral intensity''' is the radiant intensity per unit [[frequency]] or [[wavelength]], depending on whether the [[Spectral radiometric quantity|spectrum]] is taken as a function of frequency or of wavelength. These are ''directional'' quantities. The [[International System of Units|SI unit]] of radiant intensity is the [[watt]] per [[steradian]] ({{nobreak|W/sr}}), while that of spectral intensity in frequency is the watt per steradian per [[hertz]] ({{nobreak|W·sr<sup>−1</sup>·Hz<sup>−1</sup>}}) and that of spectral intensity in wavelength is the watt per steradian per metre ({{nobreak|W·sr<sup>−1</sup>·m<sup>−1</sup>}})—commonly the watt per steradian per nanometre ({{nobreak|W·sr<sup>−1</sup>·nm<sup>−1</sup>}}). Radiant intensity is distinct from [[irradiance]] and [[radiant exitance]], which are often called ''[[intensity (physics)|intensity]]'' in branches of [[physics]] other than radiometry. In [[radio-frequency engineering]], radiant intensity is sometimes called '''radiation intensity'''.

==Mathematical definitions==
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|Comparison of photometric and radiometric quantities]]
===Radiant intensity===
'''Radiant intensity''', denoted ''I''<sub>e,Ω</sub> ("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this is a ''directional'' quantity), is defined as<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>
:<math>I_{\mathrm{e},\Omega} = \frac{\partial \Phi_\mathrm{e}}{\partial \Omega},</math>
where
*∂ is the [[partial derivative]] symbol;
*Φ<sub>e</sub> is the [[radiant flux]] emitted, reflected, transmitted or received;
*''Ω'' is the [[solid angle]].

In general, ''I''<sub>e,Ω</sub> is a function of viewing angle ''θ'' and potentially [[azimuth angle]]. For the special case of a [[Lambertian reflectance|Lambertian surface]], ''I''<sub>e,Ω</sub> follows the [[Lambert's cosine law]] ''I''<sub>e,Ω</sub> = ''I''<sub>0</sub> cos ''θ''.

When calculating the radiant intensity emitted by a source, ''Ω'' refers to the solid angle into which the light is emitted. When calculating radiance received by a detector, ''Ω'' refers to the solid angle subtended by the source as viewed from that detector.

===Spectral intensity===
'''Spectral intensity in frequency''', denoted ''I''<sub>e,Ω,ν</sub>, is defined as<ref name="ISO_9288-1989" />
:<math>I_{\mathrm{e},\Omega,\nu} = \frac{\partial I_{\mathrm{e},\Omega}}{\partial \nu},</math>
where ''ν'' is the frequency.

'''Spectral intensity in wavelength''', denoted ''I''<sub>e,Ω,λ</sub>, is defined as<ref name="ISO_9288-1989" />
:<math>I_{\mathrm{e},\Omega,\lambda} = \frac{\partial I_{\mathrm{e},\Omega}}{\partial \lambda},</math>
where ''λ'' is the wavelength.

==Radio-frequency engineering==
Radiant intensity is used to characterize the emission of radiation by an [[Antenna (radio)|antenna]]:<ref name="Antennas_for_all_applications">{{cite book|title=Antennas for all applications|edition=3rd|first1=John|last1=de Kraus|first2=Ronald J.|last2=Marhefka|date=2002|publisher=McGraw-Hill |isbn=0-07-232103-2}}</ref>
:<math>I_{\mathrm{e},\Omega} = E_\mathrm{e}(r) \, r^2,</math>
where
*''E''<sub>e</sub> is the [[irradiance]] of the antenna;
*''r'' is the distance from the antenna.

Unlike power density, radiant intensity does not depend on distance: because radiant intensity is defined as the power through a solid angle, the decreasing power density over distance due to the [[inverse-square law]] is offset by the increase in area with distance.

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

==See also==
*[[Candela]]
*[[Luminous intensity]]

==References==
{{Reflist}}

==External links==
*[http://www.ndt-ed.org/EducationResources/CommunityCollege/RadiationSafety/theory/activity.htm Radiation: Activity and Intensity] NDE/NDT Resource Center

{{Authority control}}

[[Category:Physical quantities]]
[[Category:Radiometry]]