In radiometry, radiant energy density is the measure of the amount of radiant energy per unit volume at a given location and time.[1] Its SI unit is joule per cubic metre (J/m3).

It is defined by

${\displaystyle w={\frac {{\mathrm {d} }W}{{\mathrm {d} }V}},}$[2]

where

${\displaystyle w}$ is the radiant energy density,
${\displaystyle W}$ is the amount of radiant energy in some volume,
${\displaystyle V}$ is the volume.

Relation to other radiometric quantities

Because radiation always transmits the energy,[2] it is useful to wonder what the speed of the transmission is. If all the radiation at given location propagates in the same direction, then the radiant flux through a unit area perpendicular to the propagation direction is expressed by radiant flux density, whose value is

${\displaystyle I_{\mathrm {e} }=cw,}$[2]

where

${\displaystyle I_{\mathrm {e} }}$ is the radiant flux density (i.e. radiant flux per unit area),
${\displaystyle c}$ is the speed of light (generally radiation propagation speed),
${\displaystyle w}$ is the radiant energy density.

Contrarily if the radiation intensity is equal in all directions, like in a cavity in a thermodynamic equilibrium, then the energy transmition is best described by radiance (i.e. radiant flux per unit area and unit solid angle), whose value is

${\displaystyle L_{\mathrm {e} }={\frac {c}{4\pi }}w.}$[3]

Radiant exitance through a small opening from such cavity is ${\displaystyle M_{\mathrm {e} }=\pi L_{\mathrm {e} }}$.[4] These relations can be used for example in the black body radiation equations derivation.

References

1. IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Radiant energy density. Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.R05040. Last update: 2012-08-19; version: 2.3.2. Visited 2013-10-07.
2. Karel Rusňák. Přenos energie elektromagnetickým vlněním. Department of Physics, Faculty of Applied Sciences, University of West Bohemia. 2005-11. Visited 2013-10-06
3. Max Plack. The Theory of Heat Radiation. Equation 21. 1914.
4. Max Plack. The Theory of Heat Radiation. Equation 7. 1914.

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Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy Qe[nb 2] joule J ML2T−2 energy
Radiant flux Φe[nb 2] watt W or J/s ML2T−3 radiant energy per unit time, also called radiant power.
Spectral power Φ[nb 2][nb 3] watt per metre W⋅m−1 MLT−3 radiant power per wavelength.
Radiant intensity Ie watt per steradian W⋅sr−1 ML2T−3 power per unit solid angle.
Spectral intensity I[nb 3] watt per steradian per metre W⋅sr−1⋅m−1 MLT−3 radiant intensity per wavelength.
Radiance Le watt per steradian per square metre W⋅sr−1m−2 MT−3 power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

Spectral radiance L[nb 3]
or
L[nb 4]
watt per steradian per metre3
or

watt per steradian per square
metre per hertz

W⋅sr−1m−3
or
W⋅sr−1⋅m−2Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.

Irradiance Ee[nb 2] watt per square metre W⋅m−2 MT−3 power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

Spectral irradiance E[nb 3]
or
E[nb 4]
watt per metre3
or
watt per square metre per hertz
W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅m−2nm−1
or 10−22 W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]

Me[nb 2] watt per square metre W⋅m−2 MT−3 power emitted from a surface.
Spectral radiant exitance /
M[nb 3]
or
M[nb 4]
watt per metre3
or

watt per square
metre per hertz

W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
power emitted from a surface per unit wavelength or frequency.

Radiosity Je watt per square metre W⋅m−2 MT−3 emitted plus reflected power leaving a surface.
Spectral radiosity J[nb 3] watt per metre3 W⋅m−3 ML−1T−3 emitted plus reflected power leaving a surface per unit wavelength
Radiant exposure He joule per square metre J⋅m−2 MT−2 also referred to as fluence
Radiant energy density ωe joule per metre3 J⋅m−3 ML−1T−2