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 spectrum is taken as a function of frequency or of wavelength. These are ''directional'' quantities. The 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⁻¹·Hz⁻¹}}) and that of spectral intensity in wavelength is the watt per steradian per metre ({{nobreak|W·sr⁻¹·m⁻¹}})—commonly the watt per steradian per nanometre ({{nobreak|W·sr⁻¹·nm⁻¹}}). Radiant intensity is distinct from irradiance and radiant exitance, which are often called ''intensity'' in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called '''radiation intensity'''.

==Mathematical definitions== thumb|upright=1.5|Comparison of photometric and radiometric quantities ===Radiant intensity=== '''Radiant intensity''', denoted ''I''_e,Ω ("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=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_e is the radiant flux emitted, reflected, transmitted or received; *''Ω'' is the solid angle.

In general, ''I''_e,Ω is a function of viewing angle ''θ'' and potentially azimuth angle. For the special case of a Lambertian surface, ''I''_e,Ω follows the Lambert's cosine law ''I''_e,Ω = ''I''₀ 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''_e,Ω,ν, 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''_e,Ω,λ, 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:<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''_e 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}} 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