Radiant exposure

"Fluence" redirects here. For the car produced by Renault, see Renault Fluence.

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 H_e ("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;
• Q_e is the radiant energy;
• A is the area;
• T is the duration of irradiation;
• E_e is the irradiance.

Spectral exposure

Spectral exposure in frequency of a surface, denoted H_e,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 H_e,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

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: SI Radiometry Photometry

See also

• Exposure (photography)
• Irradiance
• Radiant energy