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/m), while that of spectral exposure in frequency is the joule per square metre per hertz (J⋅m⋅Hz) and that of spectral exposure in wavelength is the joule per square metre per metre (J/m)—commonly the joule per square metre per nanometre (J⋅m⋅nm).
Mathematical definitions
Radiant exposure
Radiant exposure of a surface, denoted He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as where
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 where ν is the frequency.
where ν is the frequency.
Spectral exposure in wavelength of a surface, denoted He,λ, is defined as where λ is the wavelength.
where λ is the wavelength.
SI radiometry units
| Quantity | Unit | Dimension | Notes | ||
|---|---|---|---|---|---|
| Name | Symbol | Name | Symbol | ||
| Radiant energy | Qe | joule | J | M⋅L⋅T | Energy of electromagnetic radiation. |
| Radiant energy density | we | joule per cubic metre | J/m | M⋅L⋅T | Radiant energy per unit volume. |
| Radiant flux | Φe | watt | W = J/s | M⋅L⋅T | 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⋅L⋅T | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm. |
| Φe,λ | watt per metre | W/m | M⋅L⋅T | ||
| Radiant intensity | Ie,Ω | watt per steradian | W/sr | M⋅L⋅T | 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⋅Hz | M⋅L⋅T | Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅nm. This is a directional quantity. |
| Ie,Ω,λ | watt per steradian per metre | W⋅sr⋅m | M⋅L⋅T | ||
| Radiance | Le,Ω | watt per steradian per square metre | W⋅sr⋅m | M⋅T | 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 | watt per steradian per square metre per hertz | W⋅sr⋅m⋅Hz | M⋅T | Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅m⋅nm. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". |
| Le,Ω,λ | watt per steradian per square metre, per metre | W⋅sr⋅m | M⋅L⋅T | ||
| Irradiance Flux density |
Ee | watt per square metre | W/m | M⋅T | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". |
| Spectral irradiance Spectral flux density |
Ee,ν | watt per square metre per hertz | W⋅m⋅Hz | M⋅T | 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 W⋅m⋅Hz) and solar flux unit (1 sfu = 10 W⋅m⋅Hz = 10 Jy). |
| Ee,λ | watt per square metre, per metre | W/m | M⋅L⋅T | ||
| Radiosity | Je | watt per square metre | W/m | M⋅T | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". |
| Spectral radiosity | Je,ν | watt per square metre per hertz | W⋅m⋅Hz | M⋅T | Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. This is sometimes also confusingly called "spectral intensity". |
| Je,λ | watt per square metre, per metre | W/m | M⋅L⋅T | ||
| Radiant exitance | Me | watt per square metre | W/m | M⋅T | 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 | watt per square metre per hertz | W⋅m⋅Hz | M⋅T | Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". |
| Me,λ | watt per square metre, per metre | W/m | M⋅L⋅T | ||
| Radiant exposure | He | joule per square metre | J/m | M⋅T | 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⋅Hz | M⋅T | Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m⋅nm. This is sometimes also called "spectral fluence". |
| He,λ | joule per square metre, per metre | J/m | M⋅L⋅T | ||
| See also: | |||||
- Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ 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.)
- ^ Spectral quantities given per unit wavelength are denoted with suffix "λ".
- ^ Directional quantities are denoted with suffix "Ω".
See also
References
- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Radiant exposure". doi:10.1351/goldbook.R05042