Mathematical definition
Radiant energy density, denoted we ("e" for "energetic", to avoid confusion with photometric quantities), is defined as [2]
where
- ∂ is the partial derivative symbol;
- Qe is the radiant energy;
- V is the volume.
In radiometry, radiant energy density is the radiant energy per unit volume. [1] The SI unit of radiant energy density is the joule per cubic metre (J/m3).
Radiant energy density, denoted we ("e" for "energetic", to avoid confusion with photometric quantities), is defined as [2]
where
Because radiation always transmits the energy, [2] it is useful to wonder what the speed of the transmission is. If all the radiation at given location propagates in the same direction, then the radiant flux through a unit area perpendicular to the propagation direction is given by the irradiance: [2]
where c is the radiation propagation speed.
Contrarily if the radiation intensity is equal in all directions, like in a cavity in a thermodynamic equilibrium, then the energy transmission is best described by radiance: [3]
Radiant exitance through a small opening from such a cavity is: [4]
These relations can be used for example in the black-body radiation equation's derivation.
| Quantity | Unit | Dimension | Notes | |||||
|---|---|---|---|---|---|---|---|---|
| Name | Symbol [nb 1] | Name | Symbol | Symbol | ||||
| Radiant energy | Qe [nb 2] | joule | J | M⋅L2⋅T−2 | Energy of electromagnetic radiation. | |||
| Radiant energy density | we | joule per cubic metre | J/m3 | M⋅L−1⋅T−2 | Radiant energy per unit volume. | |||
| Radiant flux | Φe [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". | |||
| Spectral flux | Φe,ν [nb 3] | 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. | |||
| Φe,λ [nb 4] | watt per metre | W/m | M⋅L⋅T−3 | |||||
| Radiant intensity | Ie,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 | Ie,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 a directional quantity. | |||
| Ie,Ω,λ [nb 4] | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | |||||
| Radiance | Le,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 | Le,Ω,ν [nb 3] | 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". | |||
| Le,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 | Ee [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 | Ee,ν [nb 3] | 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 (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy). | |||
| Ee,λ [nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
| Radiosity | Je [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 | Je,ν [nb 3] | 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". | |||
| Je,λ [nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
| Radiant exitance | Me [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 | Me,ν [nb 3] | 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". | |||
| Me,λ [nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | |||||
| Radiant exposure | He | 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 | He,ν [nb 3] | 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". | |||
| He,λ [nb 4] | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | |||||
| Hemispherical emissivity | ε | N/A | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Spectral hemispherical emissivity | εν or ελ | N/A | 1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Directional emissivity | εΩ | N/A | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | ||||
| Spectral directional emissivity | εΩ,ν or εΩ,λ | N/A | 1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Hemispherical absorptance | A | N/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 | Aν or Aλ | N/A | 1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | ||||
| Directional absorptance | AΩ | N/A | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | ||||
| Spectral directional absorptance | AΩ,ν or AΩ,λ | N/A | 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 | N/A | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | ||||
| Spectral hemispherical reflectance | Rν or Rλ | N/A | 1 | Spectral flux reflected by a surface, divided by that received by that surface. | ||||
| Directional reflectance | RΩ | N/A | 1 | Radiance reflected by a surface, divided by that received by that surface. | ||||
| Spectral directional reflectance | RΩ,ν or RΩ,λ | N/A | 1 | Spectral radiance reflected by a surface, divided by that received by that surface. | ||||
| Hemispherical transmittance | T | N/A | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | ||||
| Spectral hemispherical transmittance | Tν or Tλ | N/A | 1 | Spectral flux transmitted by a surface, divided by that received by that surface. | ||||
| Directional transmittance | TΩ | N/A | 1 | Radiance transmitted by a surface, divided by that received by that surface. | ||||
| Spectral directional transmittance | TΩ,ν or TΩ,λ | N/A | 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 | μν or μλ | 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 | μΩ | 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 | μΩ,ν or μΩ,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 | ||||||||
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material, and spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.
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 reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic structure of the material to the electromagnetic field of light, and is in general a function of the frequency, or wavelength, of the light, its polarization, and the angle of incidence. The dependence of reflectance on the wavelength is called a reflectance spectrum or spectral reflectance curve.
In physics, intensity of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kg⋅s−3 in base units. Intensity is used most frequently with waves such as acoustic waves (sound) or electromagnetic waves such as light or radio waves, in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.
Flux describes any effect that appears to pass or travel through a surface or substance. A flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.
The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body's thermodynamic temperature T:
Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.
Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.
In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Spectral radiance is the radiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiance is the watt per steradian per square metre, while that of spectral radiance in frequency is the watt per steradian per square metre per hertz and that of spectral radiance in wavelength is the watt per steradian per square metre per metre —commonly the watt per steradian per square metre per nanometre. The microflick is also used to measure spectral radiance in some fields. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation, or to quantify emission of neutrinos and other particles. Historically, radiance is called "intensity" and spectral radiance is called "specific intensity". Many fields still use this nomenclature. It is especially dominant in heat transfer, astrophysics and astronomy. "Intensity" has many other meanings in physics, with the most common being power per unit area.
In radiometry, irradiance is the radiant flux (power) received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.
The emissivity of the surface of a material is its effectiveness in emitting energy as thermal radiation. Thermal radiation is electromagnetic radiation that may include both visible radiation (light) and infrared radiation, which is not visible to human eyes. The thermal radiation from very hot objects is easily visible to the eye. Quantitatively, emissivity is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. The ratio varies from 0 to 1. The surface of a perfect black body emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature ; all real objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates.
In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiant intensity is the watt per steradian, while that of spectral intensity in frequency is the watt per steradian per hertz and that of spectral intensity in wavelength is the watt per steradian per metre —commonly the watt per steradian per nanometre. Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity.
In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.
In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted or received, per unit time, and spectral flux or spectral power is the radiant flux 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 flux is the watt (W), that is the joule per second in SI base units, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.
In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre, while that of spectral exitance in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.
In radiometry, radiosity is the radiant flux leaving a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiosity is the watt per square metre, while that of spectral radiosity in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral radiosity in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiosity is often called intensity in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam. The SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is an old term for this quantity but is still used in meteorology and climatology. Most commonly, the quantity measures the value of downward e-folding distance of the original intensity as the energy of the intensity passes through a unit thickness of material, so that an attenuation coefficient of 1 m−1 means that after passing through 1 metre, the radiation will be reduced by a factor of e, and for material with a coefficient of 2 m−1, it will be reduced twice by e, or e2. Other measures may use a different factor than e, such as the decadic attenuation coefficient below. The broad-beam attenuation coefficient counts forward-scattered radiation as transmitted rather than attenuated, and is more applicable to radiation shielding.
Radiative flux, also known as radiative flux density or radiation flux, is the amount of power radiated through a given area, in the form of photons or other elementary particles, typically measured in W/m2. It is used in astronomy to determine the magnitude and spectral class of a star and in meteorology to determine the intensity of the convection in the planetary boundary layer. Radiative flux also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the infrared spectrum.
Absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power. This should not be confused with absorbance and absorption coefficient.
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, while that of spectral exposure in frequency is the joule per square metre per hertz and that of spectral exposure in wavelength is the joule per square metre per metre —commonly the joule per square metre per nanometre.
