Radiant exposure
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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 He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as H e = ∂ Q e ∂ A = ∫ 0 T E e ( t ) d t , {\displaystyle H_{\mathrm {e} }={\frac {\partial Q_{\mathrm {e} }}{\partial A}}=\int _{0}^{T}E_{\mathrm {e} }(t)\,\mathrm {d} t,} where
- ∂ is the partial derivative symbol;
- Qe is the radiant energy;
- A is the area;
- T is the duration of irradiation;
- Ee is the irradiance.
Spectral exposure
Spectral exposure in frequency of a surface, denoted He,ν, is defined as H e , ν = ∂ H e ∂ ν , {\displaystyle H_{\mathrm {e} ,\nu }={\frac {\partial H_{\mathrm {e} }}{\partial \nu }},} where ν is the frequency.
Spectral exposure in wavelength of a surface, denoted He,λ, is defined as H e , λ = ∂ H e ∂ λ , {\displaystyle H_{\mathrm {e} ,\lambda }={\frac {\partial H_{\mathrm {e} }}{\partial \lambda }},} where λ is the wavelength.
SI radiometry units
| Quantity | Unit | Dimension | Notes | ||
|---|---|---|---|---|---|
| Name | Symbol | Name | Symbol | ||
| Radiant energy | Qe | 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 | 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 | 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 | watt per metre | W/m | M⋅L⋅T−3 | ||
| Radiant intensity | Ie,Ω | 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 | 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 | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | ||
| Radiance | Le,Ω | 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 called "intensity". |
| Spectral radiance Specific intensity | Le,Ω,ν | 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 called "spectral intensity". |
| Le,Ω,λ | watt per steradian per square metre, per metre | W⋅sr−1⋅m−3 | M⋅L−1⋅T−3 | ||
| Irradiance Flux density | Ee | watt per square metre | W/m2 | M⋅T−3 | Radiant flux received by a surface per unit area. This is sometimes also called "intensity". |
| Spectral irradiance Spectral flux density | Ee,ν | 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 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 | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
| Radiosity | Je | 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 called "intensity". |
| Spectral radiosity | Je,ν | 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 called "spectral intensity". |
| Je,λ | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
| Radiant exitance | Me | 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 called "intensity". |
| Spectral exitance | Me,ν | 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 called "spectral intensity". |
| Me,λ | 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 | 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 | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | ||
| See also: SIRadiometryPhotometry |