Radiant flux
This article needs additional citations for verification. (December 2009) |
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 spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second (J/s), while that of spectral flux in frequency is the watt per hertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly the watt per nanometre (W/nm).
Mathematical definitions
Radiant flux
Radiant flux, denoted Φe ('e' for "energetic", to avoid confusion with 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
- t is the time;
- Qe is the radiant energy flux of the field out of a closed surface Σ;
- S is the Poynting vector, representing the current density of radiant energy;
- n is the normal vector of a point on Σ;
- A represents the area of Σ.
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 ⟨-⟩ is the time-average, and α is the angle between n and <math>\langle|\mathbf{S}|\rangle.</math>
Spectral flux
Spectral flux in frequency, denoted Φe,ν, is defined as<ref name="ISO_9288-1989" /> <math display="block">\Phi_{\mathrm{e},\nu} = \frac{\partial \Phi_\mathrm{e}}{\partial \nu} ,</math> where ν is the frequency.
Spectral flux in wavelength, denoted Φe,λ, is defined as<ref name="ISO_9288-1989" /> <math display="block">\Phi_{\mathrm{e},\lambda} = \frac{\partial \Phi_\mathrm{e}}{\partial \lambda} ,</math> where λ is the wavelength.
SI radiometry units
Quantity | Unit | Dimension | Notes | ||
---|---|---|---|---|---|
Name | Symbol<ref group="nb" name="note-suffix-e">Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.</ref> | Name | Symbol | ||
Radiant energy | Qe<ref group="nb" name="note-alternative-symbol-radiometric">Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.</ref> | joule | J | M⋅L2⋅T−2 | Energy of electromagnetic radiation. |
Radiant energy density | we | joule per cubic metre | J/m3 | M⋅L−1⋅T−2 | Radiant energy per unit volume. |
Radiant flux | Φe<ref group="nb" name="note-alternative-symbol-radiometric"></ref> | watt | W = J/s | M⋅L2⋅T−3 | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy. |
Spectral flux | Φe,ν<ref group="nb" name="note-suffix-nu">Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)</ref> | watt per hertz | W/Hz | M⋅L2⋅T −2 | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1. |
Φe,λ<ref group="nb" name="note-suffix-lambda">Spectral quantities given per unit wavelength are denoted with suffix "λ".</ref> | watt per metre | W/m | M⋅L⋅T−3 | ||
Radiant intensity | Ie,Ω<ref group="nb" name="note-suffix-omega">Directional quantities are denoted with suffix "Ω".</ref> | watt per steradian | W/sr | M⋅L2⋅T−3 | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. |
Spectral intensity | Ie,Ω,ν<ref group="nb" name="note-suffix-nu"></ref> | watt per steradian per hertz | W⋅sr−1⋅Hz−1 | M⋅L2⋅T−2 | Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity. |
Ie,Ω,λ<ref group="nb" name="note-suffix-lambda"></ref> | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | ||
Radiance | Le,Ω<ref group="nb" name="note-suffix-omega"></ref> | watt per steradian per square metre | W⋅sr−1⋅m−2 | M⋅T−3 | Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". |
Spectral radiance Specific intensity |
Le,Ω,ν<ref group="nb" name="note-suffix-nu"></ref> | watt per steradian per square metre per hertz | W⋅sr−1⋅m−2⋅Hz−1 | M⋅T−2 | Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". |
Le,Ω,λ<ref group="nb" name="note-suffix-lambda"></ref> | watt per steradian per square metre, per metre | W⋅sr−1⋅m−3 | M⋅L−1⋅T−3 | ||
Irradiance Flux density |
Ee<ref group="nb" name="note-alternative-symbol-radiometric"></ref> | watt per square metre | W/m2 | M⋅T−3 | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral irradiance Spectral flux density |
Ee,ν<ref group="nb" name="note-suffix-nu"></ref> | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy). |
Ee,λ<ref group="nb" name="note-suffix-lambda"></ref> | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiosity | Je<ref group="nb" name="note-alternative-symbol-radiometric"></ref> | watt per square metre | W/m2 | M⋅T−3 | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral radiosity | Je,ν<ref group="nb" name="note-suffix-nu"></ref> | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity". |
Je,λ<ref group="nb" name="note-suffix-lambda"></ref> | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exitance | Me<ref group="nb" name="note-alternative-symbol-radiometric"></ref> | watt per square metre | W/m2 | M⋅T−3 | Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity". |
Spectral exitance | Me,ν<ref group="nb" name="note-suffix-nu"></ref> | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". |
Me,λ<ref group="nb" name="note-suffix-lambda"></ref> | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exposure | He | joule per square metre | J/m2 | M⋅T−2 | Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence". |
Spectral exposure | He,ν<ref group="nb" name="note-suffix-nu"></ref> | joule per square metre per hertz | J⋅m−2⋅Hz−1 | M⋅T−1 | Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence". |
He,λ<ref group="nb" name="note-suffix-lambda"></ref> | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | ||
See also: |
See also
References
Further reading
- Boyd, Robert (1983). Radiometry and the Detection of Optical Radiation (Pure & Applied Optics Series). Wiley-Interscience. ISBN 978-0-471-86188-1.
Lua error in Module:Authority_control at line 181: attempt to index field 'wikibase' (a nil value).