Radiometry

Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics 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.

The use of radiometers to determine the temperature of objects and gasses by measuring radiation flux is called pyrometry. Handheld pyrometer devices are often marketed as infrared thermometers.

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]

Radiometric quantities

**SI radiometry units**
Quantity		Unit		Dimension	Notes
Name	Symbol^{[nb 1]}	Name	Symbol	Symbol	Notes
Radiant energy	Q_e^{[nb 2]}	joule	J	M⋅L²⋅T⁻²	Energy of electromagnetic radiation.
Radiant energy density	w_e	joule per cubic metre	J/m³	M⋅L⁻¹⋅T⁻²	Radiant energy per unit volume.
Radiant flux	Φ_e^{[nb 2]}	watt	W or J/s	M⋅L²⋅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⋅L²⋅T⁻² or M⋅L⋅T⁻³	Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅sr⁻¹⋅m⁻²⋅nm⁻¹.
Radiant intensity	I_e,Ω^{[nb 5]}	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	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⋅L²⋅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/m²	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/m³	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 = 10⁻²⁶ W⋅m⁻²⋅Hz⁻¹ and solar flux unit (1SFU = 10⁻²² W⋅m⁻²⋅Hz⁻¹=10⁴Jy).
Radiosity	J_e^{[nb 2]}	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 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/m³	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/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 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/m³	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/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	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/m³	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.
1 2 3 4 5 Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
1 2 3 4 5 6 7 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.
1 2 3 4 5 6 7 Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
1 2 Directional quantities are denoted with suffix "Ω" (Greek).

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 Φ_e corresponds to the spectral power Φ_e,λ and Φ_e,ν.

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 flux, whose unit is W:

\Phi _{{\mathrm {e}}}.

Spectral flux 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 [λ, λ + dλ]. The area under a plot with wavelength horizontal axis equals to the total radiant flux.

Spectral flux 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 [ν, ν + dν]. The area under a plot with frequency horizontal axis equals to the total radiant flux.

Spectral flux 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

↑ Leslie D. Stroebel & Richard D. Zakia (1993). Focal Encyclopedia of Photography (3rd ed.). Focal Press. p. 115. ISBN 0-240-51417-3.

External links

Radiometry and photometry FAQ Professor Jim Palmer's Radiometry FAQ page (The University of Arizona College of Optical Sciences).

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Radiometry

Radiometric quantities

Integral and spectral radiometric quantities

See also

References

External links