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 Title: Radiometry Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

In optics, radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques 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. Radiometry is distinct from quantum techniques such as photon counting.

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]

## Contents

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.

or
L[nb 4]
or

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.

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.
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
1. ^ quantities should be denoted with a 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 emittance.
3. Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
4. ^ a b c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
5. ^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).

## 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 Φeλ and Φeν.

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 quantity – radiant flux, whose unit is W:
\Phi_\mathrm{e}
• Spectral power by wavelength, whose unit is W/m:
\Phi_{\mathrm{e}\lambda} = {\mathrm{d}\Phi_\mathrm{e} \over \mathrm{d}\lambda},   where \mathrm{d}\Phi_\mathrm{e} is the radiant flux of the radiation in a small wavelength interval \lang \lambda, \lambda + \mathrm{d}\lambda \rang
The area under a plot with wavelength horizontal axis equals to the total radiant flux.
• Spectral power by frequency, whose unit is W/Hz:
\Phi_{\mathrm{e}\nu} = {\mathrm{d}\Phi_\mathrm{e} \over \mathrm{d}\nu},   where \mathrm{d}\Phi_\mathrm{e} is the radiant flux of the radiation in a small frequency interval \lang \nu, \nu + \mathrm{d}\nu \rang
The area under a plot with frequency horizontal axis equals to the total radiant flux.
• Spectral power multiplied by wavelength or frequency, whose unit is W, i.e. the same as the integral quantity:
\lambda \Phi_{\mathrm{e}\lambda} = \nu \Phi_{\mathrm{e}\nu}
The area under a plot with logarithmic wavelength or frequency horizontal axis equals to the total radiant flux.

The spectral quantities by wavelength λ and frequency ν are related by equations featuring the speed of light c:

\Phi_{\mathrm{e}\lambda} = {c \over \lambda^2} \Phi_{\mathrm{e}\nu}
\Phi_{\mathrm{e}\nu} = {c \over \nu^2} \Phi_{\mathrm{e}\lambda}
\lambda = {c \over \nu}

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

\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 and Richard D. Zakia (1993). Focal Encyclopedia of Photography (3rd ed. ed.).
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