Radiometry

File:Photometry radiometry units.svg

Comparison of photometric and radiometric quantities

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. 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 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.

Radiometric quantities

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Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Radiant energy	Template:Math	joule	J	M⋅L2⋅T−2	Energy of electromagnetic radiation.
Radiant energy density	Template:Math	joule per cubic metre	J/m3	M⋅L−1⋅T−2	Radiant energy per unit volume.
Radiant flux	Template:Math	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	Template:Math	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.
	Template:Math	watt per metre	W/m	M⋅L⋅T−3
Radiant intensity	Template:Math	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	Template:Math	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.
	Template:Math	watt per steradian per metre	W⋅sr−1⋅m−1	M⋅L⋅T−3
Radiance	Template:Math	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 Specific intensity	Template:Math	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 confusingly called "spectral intensity".
	Template:Math	watt per steradian per square metre, per metre	W⋅sr−1⋅m−3	M⋅L−1⋅T−3
Irradiance Flux density	Template:Math	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	Template:Math	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 confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (Template:Val = Template:Val) and solar flux unit (Template:Val = Template:Val = Template:Val).
	Template:Math	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiosity	Template:Math	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	Template:Math	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 confusingly called "spectral intensity".
	Template:Math	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiant exitance	Template:Math	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	Template:Math	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 confusingly called "spectral intensity".
	Template:Math	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiant exposure	Template:Math	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	Template:Math	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".
	Template:Math	joule per square metre, per metre	J/m3	M⋅L−1⋅T−2
See also: Template:Hlist

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 Template:Mvar or frequency Template:Mvar. To each integral quantity there are corresponding spectral quantities, defined as the quotient of the integrated quantity by the range of frequency or wavelength considered. For example, the radiant flux Φ_e corresponds to the spectral power Φ_{e,Template:Mvar} and Φ_{e,Template:Mvar}.

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

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

The spectral quantities by wavelength Template:Mvar and frequency Template:Mvar are related to each other, since the product of the two variables is the speed of light ($\lambda \cdot \nu =c$):

${\mathrm{\Phi }}_{\mathrm{e},\lambda }=\frac{c}{{\lambda }^2}{\mathrm{\Phi }}_{\mathrm{e},\nu },$ or ${\mathrm{\Phi }}_{\mathrm{e},\nu }=\frac{c}{{\nu }^2}{\mathrm{\Phi }}_{\mathrm{e},\lambda },$ or $\lambda {\mathrm{\Phi }}_{\mathrm{e},\lambda }=\nu {\mathrm{\Phi }}_{\mathrm{e},\nu }.$

The integral quantity can be obtained by the spectral quantity's integration:

$${\mathrm{\Phi }}_{\mathrm{e}}=\underset{0}{\overset{\mathrm{\infty }}{\int }}{\mathrm{\Phi }}_{\mathrm{e},\lambda }d\lambda =\underset{0}{\overset{\mathrm{\infty }}{\int }}{\mathrm{\Phi }}_{\mathrm{e},\nu }d\nu =\underset{0}{\overset{\mathrm{\infty }}{\int }}\lambda {\mathrm{\Phi }}_{\mathrm{e},\lambda }d\ln \lambda =\underset{0}{\overset{\mathrm{\infty }}{\int }}\nu {\mathrm{\Phi }}_{\mathrm{e},\nu }d\ln \nu .$$

See also

• Reflectivity
• Microwave radiometer
• Measurement of ionizing radiation
• Radiometric calibration
• Radiometric resolution

External links

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