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Inradiometry,radiant flux orradiant power is theradiant energy emitted, reflected, transmitted, or received per unit time, andspectral flux orspectral power is the radiant flux per unitfrequency orwavelength, depending on whether thespectrum is taken as a function of frequency or of wavelength. TheSI unit of radiant flux is thewatt (W), onejoule per second (J/s), while that of spectral flux in frequency is the watt perhertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly the watt per nanometre (W/nm).
Radiant flux, denotedΦe ('e' for "energetic", to avoid confusion withphotometric quantities), is defined as[1]where
The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, givingwhere⟨-⟩ is the time average, andα is the angle betweenn andS.
Spectral flux in frequency, denoted Φe,ν, is defined as[1]whereν is the frequency.
Spectral flux in wavelength, denotedΦe,λ, is defined as[1]whereλ is the wavelength.
| Quantity | Unit | Dimension | Notes | ||
|---|---|---|---|---|---|
| Name | Symbol[nb 1] | Name | Symbol | ||
| Radiant energy | Qe[nb 2] | 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[nb 2] | 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 calledluminosity in astronomy. |
| Spectral flux | Φe,ν[nb 3] | watt perhertz | W/Hz | M⋅L2⋅T −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 | M⋅L⋅T−3 | ||
| Radiant intensity | Ie,Ω[nb 5] | watt persteradian | W/sr | M⋅L2⋅T−3 | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is adirectional quantity. |
| Spectral intensity | Ie,Ω,ν[nb 3] | 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 adirectional quantity. |
| Ie,Ω,λ[nb 4] | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | ||
| Radiance | Le,Ω[nb 5] | watt per steradian per square metre | W⋅sr−1⋅m−2 | M⋅T−3 | Radiant flux emitted, reflected, transmitted or received by asurface, per unit solid angle per unit projected area. This is adirectional 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 | M⋅T−2 | Radiance of asurface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is adirectional 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 | M⋅L−1⋅T−3 | ||
| Irradiance Flux density | Ee[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant fluxreceived by asurface 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 | M⋅T−2 | Irradiance of asurface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density includejansky (1 Jy =10−26 W⋅m−2⋅Hz−1) andsolar 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 | M⋅L−1⋅T−3 | ||
| Radiosity | Je[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant fluxleaving (emitted, reflected and transmitted by) asurface 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 | M⋅T−2 | Radiosity of asurface 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 | M⋅L−1⋅T−3 | ||
| Radiant exitance | Me[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant fluxemitted by asurface 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 | M⋅T−2 | Radiant exitance of asurface 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 | M⋅L−1⋅T−3 | ||
| Radiant exposure | He | joule per square metre | J/m2 | M⋅T−2 | Radiant energy received by asurface per unit area, or equivalently irradiance of asurface 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 | M⋅T−1 | Radiant exposure of asurface 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 | M⋅L−1⋅T−2 | ||
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