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Radiant flux

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(Redirected from Stellar flux) Measure of radiant energy over time Not to be confused with Radiation flux. "Spectral power" redirects here. Not to be confused with Spectral power density.
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A flow chart describing the relationship of various physical quantities, including radiant flux and exitance.
A flow chart describing the relationship of various physical quantities, including radiant flux and exitance.

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 Φ e = d Q e d t Q e = ∫ T ∫ Σ S ⋅ n ^ d A d t {\displaystyle {\begin{aligned}\Phi _{\mathrm {e} }&={\frac {dQ_{\mathrm {e} }}{dt}}\\Q_{\mathrm {e} }&=\int _{T}\int _{\Sigma }\mathbf {S} \cdot {\hat {\mathbf {n} }}\,dAdt\end{aligned}}} where

The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, giving Φ e ≈ ∫ Σ ⟨ | S | ⟩ cos ⁡ α   d A , {\displaystyle \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 ⟨ | S | ⟩ . {\displaystyle \langle |\mathbf {S} |\rangle .}

Spectral flux

Spectral flux in frequency, denoted Φe,ν, is defined as Φ e , ν = ∂ Φ e ∂ ν , {\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \nu }},} where ν is the frequency.

Spectral flux in wavelength, denoted Φe,λ, is defined as Φ e , λ = ∂ Φ e ∂ λ , {\displaystyle \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

SI radiometry units
Quantity Unit Dimension Notes
Name Symbol Name Symbol
Radiant energy Qe joule J M⋅L⋅T Energy of electromagnetic radiation.
Radiant energy density we joule per cubic metre J/m M⋅L⋅T Radiant energy per unit volume.
Radiant flux Φe watt W = J/s M⋅L⋅T 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 watt per hertz W/Hz M⋅L⋅T Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm.
Φe,λ watt per metre W/m M⋅L⋅T
Radiant intensity Ie,Ω watt per steradian W/sr M⋅L⋅T Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity Ie,Ω,ν watt per steradian per hertz W⋅sr⋅Hz M⋅L⋅T Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅nm. This is a directional quantity.
Ie,Ω,λ watt per steradian per metre W⋅sr⋅m M⋅L⋅T
Radiance Le,Ω watt per steradian per square metre W⋅sr⋅m M⋅T 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 watt per steradian per square metre per hertz W⋅sr⋅m⋅Hz M⋅T Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅m⋅nm. This is a directional quantity. This is sometimes also confusingly called "spectral intensity".
Le,Ω,λ watt per steradian per square metre, per metre W⋅sr⋅m M⋅L⋅T
Irradiance
Flux density 		Ee watt per square metre W/m M⋅T Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance
Spectral flux density 		Ee,ν watt per square metre per hertz W⋅m⋅Hz M⋅T 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 W⋅m⋅Hz) and solar flux unit (1 sfu = 10 W⋅m⋅Hz = 10 Jy).
Ee,λ watt per square metre, per metre W/m M⋅L⋅T
Radiosity Je watt per square metre W/m M⋅T Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosity Je,ν watt per square metre per hertz W⋅m⋅Hz M⋅T Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. This is sometimes also confusingly called "spectral intensity".
Je,λ watt per square metre, per metre W/m M⋅L⋅T
Radiant exitance Me watt per square metre W/m M⋅T 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 watt per square metre per hertz W⋅m⋅Hz M⋅T Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity".
Me,λ watt per square metre, per metre W/m M⋅L⋅T
Radiant exposure He joule per square metre J/m M⋅T 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 joule per square metre per hertz J⋅m⋅Hz M⋅T Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m⋅nm. This is sometimes also called "spectral fluence".
He,λ joule per square metre, per metre J/m M⋅L⋅T
See also:
  1. Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
  2. ^ Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
  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.)
  4. ^ Spectral quantities given per unit wavelength are denoted with suffix "λ".
  5. ^ Directional quantities are denoted with suffix "Ω".

See also

References

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

Further reading

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