Radiant exposure

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In radiometry, radiant exposure or fluence is the radiant energy received by a surface per unit area, or equivalently the irradiance of a surface, integrated over time of irradiation, and spectral exposure is the radiant exposure 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 exposure is the joule per square metre (J/m2), while that of spectral exposure in frequency is the joule per square metre per hertz (J⋅m−2⋅Hz−1) and that of spectral exposure in wavelength is the joule per square metre per metre (J/m3)—commonly the joule per square metre per nanometre (J⋅m−2⋅nm−1).

Mathematical definitions

Radiant exposure

Radiant exposure of a surface, denoted He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as<ref name="GoldBook">IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Radiant exposure". doi:10.1351/goldbook.R05042</ref> <math display="block">H_\mathrm{e} = \frac{\partial Q_\mathrm{e}}{\partial A} = \int_0^T E_\mathrm{e}(t)\, \mathrm{d}t,</math> where

  • ∂ is the partial derivative symbol;
  • Qe is the radiant energy;
  • A is the area;
  • T is the duration of irradiation;
  • Ee is the irradiance.

Spectral exposure

Spectral exposure in frequency of a surface, denoted He,ν, is defined as<ref name="GoldBook" /> <math display="block">H_{\mathrm{e},\nu} = \frac{\partial H_\mathrm{e}}{\partial \nu},</math> where ν is the frequency.

Spectral exposure in wavelength of a surface, denoted He,λ, is defined as<ref name="GoldBook" /> <math display="block">H_{\mathrm{e},\lambda} = \frac{\partial H_\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 ML2T−2 Energy of electromagnetic radiation.
Radiant energy density we joule per cubic metre J/m3 ML−1T−2 Radiant energy per unit volume.
Radiant flux Φe<ref group="nb" name="note-alternative-symbol-radiometric"></ref> watt W = J/s ML2T−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 ML2T −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 MLT−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 ML2T−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 ML2T−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 MLT−3
Radiance Le,Ω<ref group="nb" name="note-suffix-omega"></ref> watt per steradian per square metre W⋅sr−1⋅m−2 MT−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 MT−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 ML−1T−3
Irradiance
Flux density
Ee<ref group="nb" name="note-alternative-symbol-radiometric"></ref> watt per square metre W/m2 MT−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 MT−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 ML−1T−3
Radiosity Je<ref group="nb" name="note-alternative-symbol-radiometric"></ref> watt per square metre W/m2 MT−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 MT−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 ML−1T−3
Radiant exitance Me<ref group="nb" name="note-alternative-symbol-radiometric"></ref> watt per square metre W/m2 MT−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 MT−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 ML−1T−3
Radiant exposure He joule per square metre J/m2 MT−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 MT−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 ML−1T−2
See also:
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See also

References

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