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Radiometry

## Summary

Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct from quantum techniques such as photon counting.

Comparison of photometric and radiometric quantities

The use of radiometers to determine the temperature of objects and gasses by measuring radiation flux is called pyrometry. Handheld pyrometer devices are often marketed as infrared thermometers.

Radiometry is important in astronomy, especially radio astronomy, and plays a significant role in Earth remote sensing. The measurement techniques categorized as radiometry in optics are called photometry in some astronomical applications, contrary to the optics usage of the term.

Spectroradiometry is the measurement of absolute radiometric quantities in narrow bands of wavelength.[1]

## Radiometric quantities

Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy Qe[nb 2] 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[nb 2] 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[nb 3] 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[nb 4] watt per metre W/m MLT−3
Radiant intensity Ie,Ω[nb 5] 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[nb 3] 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[nb 4] watt per steradian per metre W⋅sr−1⋅m−1 MLT−3
Radiance Le,Ω[nb 5] 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[nb 3] 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[nb 4] watt per steradian per square metre, per metre W⋅sr−1⋅m−3 ML−1T−3
Irradiance
Flux density
Ee[nb 2] 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[nb 3] 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[nb 4] watt per square metre, per metre W/m3 ML−1T−3
Radiosity Je[nb 2] 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[nb 3] 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[nb 4] watt per square metre, per metre W/m3 ML−1T−3
Radiant exitance Me[nb 2] 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[nb 3] 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[nb 4] 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[nb 3] 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[nb 4] joule per square metre, per metre J/m3 ML−1T−2
See also: SI · Radiometry · Photometry
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. ^ a b Directional quantities are denoted with suffix "Ω".
Quantity SI units Notes
Name Sym.
Hemispherical emissivity ε Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.
Spectral hemispherical emissivity εν
or
ελ
Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity εΩ Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.
Spectral directional emissivity εΩ,ν
or
εΩ,λ
Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance A Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance Aν
or
Aλ
Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance AΩ Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance AΩ,ν
or
AΩ,λ
Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance".
Hemispherical reflectance R Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance Rν
or
Rλ
Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance RΩ Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance RΩ,ν
or
RΩ,λ
Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance T Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance Tν
or
Tλ
Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance TΩ Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance TΩ,ν
or
TΩ,λ
Spectral radiance transmitted by a surface, divided by that received by that surface.
Hemispherical attenuation coefficient μ m−1 Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient μν
or
μλ
m−1 Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient μΩ m−1 Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient μΩ,ν
or
μΩ,λ
m−1 Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

## Integral and spectral radiometric quantities

Integral quantities (like radiant flux) describe the total effect of radiation of all wavelengths or frequencies, while spectral quantities (like spectral power) describe the effect of radiation of a single wavelength λ or frequency ν. To each integral quantity there are corresponding spectral quantities, for example the radiant flux Φe corresponds to the spectral power Φe,λ and Φe,ν.

Getting an integral quantity's spectral counterpart requires a limit transition. This comes from the idea that the precisely requested wavelength photon existence probability is zero. Let us show the relation between them using the radiant flux as an example:

Integral flux, whose unit is W:

${\displaystyle \Phi _{\mathrm {e} }.}$

Spectral flux by wavelength, whose unit is W/m:

${\displaystyle \Phi _{\mathrm {e} ,\lambda }={\mathrm {d} \Phi _{\mathrm {e} } \over \mathrm {d} \lambda },}$

where ${\displaystyle \mathrm {d} \Phi _{\mathrm {e} }}$  is the radiant flux of the radiation in a small wavelength interval ${\displaystyle [\lambda -{\mathrm {d} \lambda \over 2},\lambda +{\mathrm {d} \lambda \over 2}]}$ . The area under a plot with wavelength horizontal axis equals to the total radiant flux.

Spectral flux by frequency, whose unit is W/Hz:

${\displaystyle \Phi _{\mathrm {e} ,\nu }={\mathrm {d} \Phi _{\mathrm {e} } \over \mathrm {d} \nu },}$

where ${\displaystyle \mathrm {d} \Phi _{\mathrm {e} }}$  is the radiant flux of the radiation in a small frequency interval ${\displaystyle [\nu -{\mathrm {d} \nu \over 2},\nu +{\mathrm {d} \nu \over 2}]}$ . The area under a plot with frequency horizontal axis equals to the total radiant flux.

The spectral quantities by wavelength λ and frequency ν are related to each other, since the product of the two variables is the speed of light (${\displaystyle \lambda \cdot \nu =c}$ ):

${\displaystyle \Phi _{\mathrm {e} ,\lambda }={c \over \lambda ^{2}}\Phi _{\mathrm {e} ,\nu },}$  or ${\displaystyle \Phi _{\mathrm {e} ,\nu }={c \over \nu ^{2}}\Phi _{\mathrm {e} ,\lambda },}$  or ${\displaystyle \lambda \Phi _{\mathrm {e} ,\lambda }=\nu \Phi _{\mathrm {e} ,\nu }.}$

The integral quantity can be obtained by the spectral quantity's integration:

${\displaystyle \Phi _{\mathrm {e} }=\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda =\int _{0}^{\infty }\Phi _{\mathrm {e} ,\nu }\,\mathrm {d} \nu =\int _{0}^{\infty }\lambda \Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \ln \lambda =\int _{0}^{\infty }\nu \Phi _{\mathrm {e} ,\nu }\,\mathrm {d} \ln \nu .}$

## References

1. ^ Leslie D. Stroebel & Richard D. Zakia (1993). Focal Encyclopedia of Photography (3rd ed.). Focal Press. p. 115. ISBN 0-240-51417-3. spectroradiometry Focal Encyclopedia of Photography.