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Radiometry

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Techniques for measuring electromagnetic radiation

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Comparison of photometric and radiometric quantities

Radiometry is a set of techniques formeasuring electromagnetic radiation, includingvisible light. Radiometric techniques inoptics characterize the distribution of the radiation'spower in space, as opposed tophotometric techniques, which characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct fromquantum techniques such asphoton counting.

The use ofradiometers to determine the temperature of objects and gasses by measuring radiation flux is calledpyrometry. Handheld pyrometer devices are often marketed asinfrared thermometers.

Radiometry is important inastronomy, especiallyradio astronomy, and plays a significant role inEarth remote sensing. The measurement techniques categorized asradiometry in optics are calledphotometry 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

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SI radiometry units
v
t
e
Quantity		Unit		Dimension	Notes
Name	Symbol^{[nb 1]}	Name	Symbol	Dimension	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 = 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	Φ_e,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.
Spectral flux	Φ_e,λ^{[nb 4]}	watt per metre	W/m	M⋅L⋅T⁻³
Radiant intensity	I_e,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	I_e,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.
Spectral intensity	I_e,Ω,λ^{[nb 4]}	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³
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 asurface, per unit solid angle per unit projected area. This is adirectional quantity. This is sometimes also confusingly called "intensity".
Spectral radiance Specific intensity	L_e,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".
Spectral radiance Specific intensity	L_e,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	E_e^{[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	E_e,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).
Spectral irradiance Spectral flux density	E_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiosity	J_e^{[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	J_e,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".
Spectral radiosity	J_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exitance	M_e^{[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	M_e,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".
Spectral exitance	M_e,λ^{[nb 4]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exposure	H_e	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	H_e,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".
Spectral exposure	H_e,λ^{[nb 4]}	joule per square metre, per metre	J/m³	M⋅L⁻¹⋅T⁻²
See also: SI Radiometry Photometry

^Standards organizations recommend that radiometricquantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric orphoton quantities.
^^a ^b ^c ^d ^eAlternative symbols sometimes seen:W orE for radiant energy,P orF for radiant flux,I for irradiance,W for radiant exitance.
^^a ^b ^c ^d ^e ^f ^gSpectral quantities given per unitfrequency are denoted with suffix "ν" (Greek letternu, not to be confused with a letter "v", indicating a photometric quantity.)
^^a ^b ^c ^d ^e ^f ^gSpectral quantities given per unitwavelength are denoted with suffix "λ".
^^a ^bDirectional quantities are denoted with suffix "Ω".

Radiometry coefficients
v
t
e
Quantity		SI units	Notes
Name	Sym.	SI units	Notes
Hemispherical emissivity	ε	—	Radiant exitance of asurface, divided by that of ablack body at the same temperature as that surface.
Spectral hemispherical emissivity	ε_ν ε_λ	—	Spectral exitance of asurface, divided by that of ablack body at the same temperature as that surface.
Directional emissivity	ε_Ω	—	Radianceemitted by asurface, divided by that emitted by ablack body at the same temperature as that surface.
Spectral directional emissivity	ε_Ω,ν ε_Ω,λ	—	Spectral radianceemitted by asurface, divided by that of ablack body at the same temperature as that surface.
Hemispherical absorptance	A	—	Radiant fluxabsorbed by asurface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance	A_ν A_λ	—	Spectral fluxabsorbed by asurface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	A_Ω	—	Radianceabsorbed by asurface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".
Spectral directional absorptance	A_Ω,ν A_Ω,λ	—	Spectral radianceabsorbed by asurface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance".
Hemispherical reflectance	R	—	Radiant fluxreflected by asurface, divided by that received by that surface.
Spectral hemispherical reflectance	R_ν R_λ	—	Spectral fluxreflected by asurface, divided by that received by that surface.
Directional reflectance	R_Ω	—	Radiancereflected by asurface, divided by that received by that surface.
Spectral directional reflectance	R_Ω,ν R_Ω,λ	—	Spectral radiancereflected by asurface, divided by that received by that surface.
Hemispherical transmittance	T	—	Radiant fluxtransmitted by asurface, divided by that received by that surface.
Spectral hemispherical transmittance	T_ν T_λ	—	Spectral fluxtransmitted by asurface, divided by that received by that surface.
Directional transmittance	T_Ω	—	Radiancetransmitted by asurface, divided by that received by that surface.
Spectral directional transmittance	T_Ω,ν T_Ω,λ	—	Spectral radiancetransmitted by asurface, divided by that received by that surface.
Hemispherical attenuation coefficient	μ	m⁻¹	Radiant fluxabsorbed andscattered by avolume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient	μ_ν μ_λ	m⁻¹	Spectral radiant fluxabsorbed andscattered by avolume per unit length, divided by that received by that volume.
Directional attenuation coefficient	μ_Ω	m⁻¹	Radianceabsorbed andscattered by avolume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	μ_Ω,ν μ_Ω,λ	m⁻¹	Spectral radianceabsorbed andscattered by avolume per unit length, divided by that received by that volume.

Integral and spectral radiometric quantities

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Integral quantities (likeradiant flux) describe the total effect of radiation of allwavelengths orfrequencies, whilespectral quantities (likespectral power) describe the effect of radiation of a single wavelengthλ or frequencyν. To eachintegral quantity there are correspondingspectral quantities, defined as the quotient of the integrated quantity by the range of frequency or wavelength considered.^[2] 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 alimit transition. This comes from the idea that the precisely requested wavelengthphoton existence probability is zero. Let us show the relation between them using the radiant flux as an example:

Integral flux, whose unit isW: $\Phi _{\mathrm {e} }.$ Spectral flux by wavelength, whose unit isW/m: $\Phi _{\mathrm {e} ,\lambda }={d\Phi _{\mathrm {e} } \over d\lambda },$ where $d\Phi _{\mathrm {e} }$ is the radiant flux of the radiation in a small wavelength interval $[\lambda -{d\lambda \over 2},\lambda +{d\lambda \over 2}]$ .The area under a plot with wavelength horizontal axis equals to the total radiant flux.

Spectral flux by frequency, whose unit isW/Hz: $\Phi _{\mathrm {e} ,\nu }={d\Phi _{\mathrm {e} } \over d\nu },$ where $d\Phi _{\mathrm {e} }$ is the radiant flux of the radiation in a small frequency interval $[\nu -{d\nu \over 2},\nu +{d\nu \over 2}]$ .The area under a plot with frequency horizontal axis equals to the total radiant flux.

The spectral quantities by wavelengthλ and frequencyν are related to each other, since the product of the two variables is thespeed of light ( $\lambda \cdot \nu =c$ ):