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 or 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^{2}), 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/m^{3})—commonly the joule per square metre per nanometre (J⋅m^{−2}⋅nm^{−1}).
Contents
Mathematical definitionsEdit
Radiant exposureEdit
Radiant exposure of a surface, denoted H_{e} ("e" for "energetic", to avoid confusion with photometric quantities), is defined as^{[1]}
where
- ∂ is the partial derivative symbol;
- Q_{e} is the radiant energy;
- A is the area;
- T is the duration of irradiation;
- E_{e} is the irradiance.
Spectral exposureEdit
Spectral exposure in frequency of a surface, denoted H_{e,ν}, is defined as^{[1]}
where ν is the frequency.
Spectral exposure in wavelength of a surface, denoted H_{e,λ}, is defined as^{[1]}
where λ is the wavelength.
SI radiometry unitsEdit
Quantity | Unit | Dimension | Notes | |||||
---|---|---|---|---|---|---|---|---|
Name | Symbol^{[nb 1]} | Name | Symbol | Symbol | ||||
Radiant energy | Q_{e}^{[nb 2]} | joule | J | M⋅L^{2}⋅T^{−2} | Energy of electromagnetic radiation. | |||
Radiant energy density | w_{e} | joule per cubic metre | J/m^{3} | M⋅L^{−1}⋅T^{−2} | Radiant energy per unit volume. | |||
Radiant flux | Φ_{e}^{[nb 2]} | watt | W = J/s | M⋅L^{2}⋅T^{−3} | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power". | |||
Spectral flux | Φ_{e,ν}^{[nb 3]} or Φ_{e,λ}^{[nb 4]} |
watt per hertz or watt per metre |
W/Hz or W/m |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm^{−1}. | |||
Radiant intensity | I_{e,Ω}^{[nb 5]} | watt per steradian | W/sr | M⋅L^{2}⋅T^{−3} | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. | |||
Spectral intensity | I_{e,Ω,ν}^{[nb 3]} or I_{e,Ω,λ}^{[nb 4]} |
watt per steradian per hertz or watt per steradian per metre |
W⋅sr^{−1}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−1} |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr^{−1}⋅nm^{−1}. This is a directional quantity. | |||
Radiance | L_{e,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 a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". | |||
Spectral radiance | L_{e,Ω,ν}^{[nb 3]} or L_{e,Ω,λ}^{[nb 4]} |
watt per steradian per square metre per hertz or watt per steradian per square metre, per metre |
W⋅sr^{−1}⋅m^{−2}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Irradiance Flux density |
E_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral irradiance Spectral flux density |
E_{e,ν}^{[nb 3]} or E_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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} = 10^{4} Jy). | |||
Radiosity | J_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral radiosity | J_{e,ν}^{[nb 3]} or J_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Radiant exitance | M_{e}^{[nb 2]} | watt per square metre | W/m^{2} | 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 confusingly called "intensity". | |||
Spectral exitance | M_{e,ν}^{[nb 3]} or M_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Radiant exposure | H_{e} | joule per square metre | J/m^{2} | 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 | H_{e,ν}^{[nb 3]} or H_{e,λ}^{[nb 4]} |
joule per square metre per hertz or joule per square metre, per metre |
J⋅m^{−2}⋅Hz^{−1} or J/m^{3} |
M⋅T^{−1} or M⋅L^{−1}⋅T^{−2} |
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". | |||
Hemispherical emissivity | ε | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Spectral hemispherical emissivity | ε_{ν} or ε_{λ} |
1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Directional emissivity | ε_{Ω} | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | |||||
Spectral directional emissivity | ε_{Ω,ν} or ε_{Ω,λ} |
1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | |||||
Hemispherical absorptance | A | 1 | Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance". | |||||
Spectral hemispherical absorptance | A_{ν} or A_{λ} |
1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | |||||
Directional absorptance | A_{Ω} | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | |||||
Spectral directional absorptance | A_{Ω,ν} or A_{Ω,λ} |
1 | 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 | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | |||||
Spectral hemispherical reflectance | R_{ν} or R_{λ} |
1 | Spectral flux reflected by a surface, divided by that received by that surface. | |||||
Directional reflectance | R_{Ω} | 1 | Radiance reflected by a surface, divided by that received by that surface. | |||||
Spectral directional reflectance | R_{Ω,ν} or R_{Ω,λ} |
1 | Spectral radiance reflected by a surface, divided by that received by that surface. | |||||
Hemispherical transmittance | T | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | |||||
Spectral hemispherical transmittance | T_{ν} or T_{λ} |
1 | Spectral flux transmitted by a surface, divided by that received by that surface. | |||||
Directional transmittance | T_{Ω} | 1 | Radiance transmitted by a surface, divided by that received by that surface. | |||||
Spectral directional transmittance | T_{Ω,ν} or T_{Ω,λ} |
1 | Spectral radiance transmitted by a surface, divided by that received by that surface. | |||||
Hemispherical attenuation coefficient | μ | reciprocal metre | m^{−1} | L^{−1} | Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral hemispherical attenuation coefficient | μ_{ν} or μ_{λ} |
reciprocal metre | m^{−1} | L^{−1} | Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Directional attenuation coefficient | μ_{Ω} | reciprocal metre | m^{−1} | L^{−1} | Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral directional attenuation coefficient | μ_{Ω,ν} or μ_{Ω,λ} |
reciprocal metre | m^{−1} | L^{−1} | Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
See also: SI · Radiometry · Photometry |
- ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
- ^ ^{a} ^{b} Directional quantities are denoted with suffix "Ω" (Greek).
See alsoEdit
ReferencesEdit
- ^ ^{a} ^{b} ^{c} IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Radiant exposure". doi:10.1351/goldbook.R05042