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).

Contents

Mathematical definitions

Radiant exposure

Radiant exposure of a surface, denoted He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as [1] where

Spectral exposure

Spectral exposure in frequency of a surface, denoted He,ν, is defined as [1] where ν is the frequency.

Spectral exposure in wavelength of a surface, denoted He,λ, is defined as [1] where λ is the wavelength.

SI radiometry units

QuantityUnitDimensionNotes
NameSymbol [nb 1] NameSymbol
Radiant energy Qe [nb 2] joule J ML2T−2Energy of electromagnetic radiation.
Radiant energy density wejoule per cubic metreJ/m3ML−1T−2Radiant energy per unit volume.
Radiant flux Φe [nb 2] watt W = J/sML2T−3Radiant 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 [nb 3] watt per hertz W/Hz ML2T −2Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1.
Φe,λ [nb 4] watt per metreW/mMLT−3
Radiant intensity Ie,Ω [nb 5] watt per steradian W/sr ML2T−3Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity Ie,Ω,ν [nb 3] watt per steradian per hertzW⋅sr−1⋅Hz−1ML2T−2Radiant 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 [nb 4] watt per steradian per metreW⋅sr−1⋅m−1MLT−3
Radiance Le,Ω [nb 5] watt per steradian per square metreW⋅sr−1⋅m−2MT−3Radiant 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 [nb 3] watt per steradian per square metre per hertzW⋅sr−1⋅m−2⋅Hz−1MT−2Radiance 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 [nb 4] watt per steradian per square metre, per metreW⋅sr−1⋅m−3ML−1T−3
Irradiance
Flux density
Ee [nb 2] watt per square metreW/m2MT−3Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance
Spectral flux density
Ee,ν [nb 3] watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Irradiance 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 [nb 4] watt per square metre, per metreW/m3ML−1T−3
Radiosity Je [nb 2] watt per square metreW/m2MT−3Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosity Je,ν [nb 3] watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Radiosity 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 [nb 4] watt per square metre, per metreW/m3ML−1T−3
Radiant exitance Me [nb 2] watt per square metreW/m2MT−3Radiant 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 [nb 3] watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Radiant 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 [nb 4] watt per square metre, per metreW/m3ML−1T−3
Radiant exposure Hejoule per square metreJ/m2MT−2Radiant 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 [nb 3] joule per square metre per hertzJ⋅m−2⋅Hz−1MT−1Radiant 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 [nb 4] joule per square metre, per metreJ/m3ML−1T−2
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. 1 2 3 4 5 Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
  3. 1 2 3 4 5 6 7 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. 1 2 3 4 5 6 7 Spectral quantities given per unit wavelength are denoted with suffix " λ ".
  5. 1 2 Directional quantities are denoted with suffix "Ω".

See also

References

  1. 1 2 3 IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006) " Radiant exposure ". doi : 10.1351/goldbook.R05042