Radiant_flux

Radiant flux

Measure of radiant energy over time

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 Φ_e ('e' for "energetic", to avoid confusion with photometric quantities), is defined as^[1]

{\begin{aligned}\Phi _{\mathrm {e} }&={\frac {dQ_{\mathrm {e} }}{dt}}\\[2pt]Q_{\mathrm {e} }&=\int _{\Sigma }\mathbf {S} \cdot {\hat {\mathbf {n} }}\,dA\end{aligned}}

where

t is the time;
Q_e 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:

\Phi _{\mathrm {e} }\approx \int _{\Sigma }\langle |\mathbf {S} |\rangle \cos \alpha \ dA,

where ⟨-⟩ is the time-average, and α is the angle between n and $\langle |\mathbf {S} |\rangle .$

Spectral flux

Spectral flux in frequency, denoted Φ_e,ν, is defined as^[1]

\Phi _{\mathrm {e} ,\nu }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \nu }},

where ν is the frequency.

Spectral flux in wavelength, denoted Φ_e,λ, is defined as^[1]

\Phi _{\mathrm {e} ,\lambda }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \lambda }},

where λ is the wavelength.

SI radiometry units

Comparison of photometric and radiometric quantities

More information Quantity, Unit ...

SI radiometry units
v
t
e
Quantity		Unit		Dimension	Notes
Name	Symbol^{[nb 1]}	Name	Symbol	Dimension	Notes
Radiant energy	Q_e^{[nb 2]}	joule	J	M⋅L²⋅T⁻²	Energy of electromagnetic radiation.
Radiant energy density	w_e	joule per cubic metre	J/m³	M⋅L⁻¹⋅T⁻²	Radiant energy per unit volume.
Radiant flux	Φ_e^{[nb 2]}	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	Φ_e,ν^{[nb 3]}	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.
Spectral flux	Φ_e,λ^{[nb 4]}	watt per metre	W/m	M⋅L⋅T⁻³
Radiant intensity	I_e,Ω^{[nb 5]}	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	I_e,Ω,ν^{[nb 3]}	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.
Spectral intensity	I_e,Ω,λ^{[nb 4]}	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³
Radiance	L_e,Ω^{[nb 5]}	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	L_e,Ω,ν^{[nb 3]}	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".
Spectral radiance Specific intensity	L_e,Ω,λ^{[nb 4]}	watt per steradian per square metre, per metre	W⋅sr⁻¹⋅m⁻³	M⋅L⁻¹⋅T⁻³
Irradiance Flux density	E_e^{[nb 2]}	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	E_e,ν^{[nb 3]}	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).
Spectral irradiance Spectral flux density	E_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiosity	J_e^{[nb 2]}	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	J_e,ν^{[nb 3]}	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".
Spectral radiosity	J_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exitance	M_e^{[nb 2]}	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	M_e,ν^{[nb 3]}	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".
Spectral exitance	M_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exposure	H_e	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	H_e,ν^{[nb 3]}	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".
Spectral exposure	H_e,λ^{[nb 4]}	joule per square metre, per metre	J/m³	M⋅L⁻¹⋅T⁻²
See also: SI Radiometry Photometry

[N 1]
Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
[N 2]
Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
[N 3]
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.)
[N 4]
Spectral quantities given per unit wavelength are denoted with suffix "λ".
[N 5]
Directional quantities are denoted with suffix "Ω".

Share this article:

This article uses material from the Wikipedia article Radiant_flux, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.

[note-suffix-e-2] [N 1]
Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.

[note-alternative-symbol-radiometric-3] [N 2]
Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.

[note-suffix-nu-4] [N 3]
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.)

[note-suffix-lambda-5] [N 4]
Spectral quantities given per unit wavelength are denoted with suffix "λ".

[note-suffix-omega-6] [N 5]
Directional quantities are denoted with suffix "Ω".

[ISO_9288-1989-1] [1]
"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

[1]

[nb 1]

[nb 2]

[nb 3]

[nb 4]

[nb 5]

Radiant_flux

Radiant flux

Mathematical definitions

Radiant flux

Spectral flux

SI radiometry units

See also

References

Further reading

Share this article: