In
radiometry, irradiance is the
radiant flux ''received'' by a ''surface'' per unit area. The
SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
of irradiance is the
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
per square metre (W⋅m
−2). The
CGS unit erg
The erg is a unit of energy equal to 10−7joules (100 nJ). It originated in the Centimetre–gram–second system of units (CGS). It has the symbol ''erg''. The erg is not an SI unit. Its name is derived from (), a Greek word meaning 'work' o ...
per square centimetre per second (erg⋅cm
−2⋅s
−1) is often used in
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
. Irradiance is often called
intensity, but this term is avoided in radiometry where such usage leads to confusion with
radiant intensity
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 ...
. In astrophysics, irradiance is called ''radiant flux''.
Spectral irradiance is the irradiance of a surface per unit
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
or
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, depending on whether the
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
is taken as a function of frequency or of wavelength. The two forms have different
dimensions
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordin ...
and units: spectral irradiance of a frequency spectrum is measured in watts per square metre per
hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
(W⋅m
−2⋅Hz
−1), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W⋅m
−3), or more commonly watts per square metre per nanometre (W⋅m
−2⋅nm
−1).
Mathematical definitions
Irradiance
Irradiance of a surface, denoted ''E''
e ("e" for "energetic", to avoid confusion with
photometric quantities), is defined as
:
where
*∂ is the
partial derivative symbol;
*Φ
e is the radiant flux received;
*''A'' is the area.
If we want to talk about the radiant flux ''emitted'' by a surface, we speak of
radiant exitance
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 wheth ...
.
Spectral irradiance
Spectral irradiance in frequency of a surface, denoted ''E''
e,ν, is defined as
:
where ''ν'' is the frequency.
Spectral irradiance in wavelength of a surface, denoted ''E''
e,λ, is defined as
:
where ''λ'' is the wavelength.
Property
Irradiance of a surface is also, according to the definition of
radiant flux, equal to the time-average of the component of the
Poynting vector perpendicular to the surface:
:
where
* is the time-average;
*S is the Poynting vector;
*''α'' is the angle between a unit vector
normal Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
to the surface and S.
For a propagating ''sinusoidal''
linearly polarized electromagnetic
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, ...
, the Poynting vector always points to the direction of propagation while oscillating in magnitude. The irradiance of a surface is then given by
:
where
*''E''
m is the amplitude of the wave's electric field;
*''n'' is the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
of the medium of propagation;
*''c'' is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
;
*μ
0 is the
vacuum permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
;
*ε
0 is the
vacuum permittivity.
This formula assumes that the
magnetic susceptibility is negligible, i.e. that ''μ''
r ≈ 1 where ''μ''
r is the
magnetic permeability of the propagation medium. This assumption is typically valid in transparent media in the
optical frequency range.
Point source
A
point source
A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can ...
of light produces spherical wavefronts. The irradiance in this case varies inversely with the square of the distance from the source.
:
where
* is the distance;
* is the radiant power;
* is the surface area of a sphere of radius .
For quick approximations, this equation indicates that doubling the distance reduces irradiation to one quarter; or similarly, to double irradiation, reduce the distance to 0.7. When it is not a point source, for real light sources, the irradiance profile may be obtained by the image convolution of a picture of the light source.
Solar irradiance
The global irradiance on a horizontal surface on Earth consists of the direct irradiance ''E''
e,dir and diffuse irradiance ''E''
e,diff. On a tilted plane, there is another irradiance component, ''E''
e,refl, which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance ''E''
e on a tilted plane consists of three components:
:
The
integral
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
of solar irradiance over a time period is called "
solar exposure" or "
insolation".
SI radiometry units
See also
*Albedo
Albedo (; ) is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that refl ...
*Fluence
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 un ...
*Illuminance
In photometry (optics), photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate w ...
* Insolation
*Light diffusion
Photon diffusion is a situation where photons travel through a material without being absorbed, but rather undergoing repeated scattering events which change the direction of their path. The path of any given photon is then effectively a random wal ...
* PI curve (photosynthesis-irradiance curve)
*Solar azimuth angle
The solar azimuth angle is the azimuth (horizontal angle with respect to north) of the Sun's position. This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary ...
* Solar irradiance
*Solar noon
Noon (or midday) is 12 o'clock in the daytime. It is written as 12 noon, 12:00 m. (for meridiem, literally 12:00 noon), 12 p.m. (for post meridiem, literally "after noon"), 12 pm, or 12:00 (using a 24-hour clock) or 1200 ( military time).
Sola ...
*Spectral flux density
In spectroscopy, spectral flux density is the quantity that describes the rate at which energy is transferred by electromagnetic radiation through a real or virtual surface, per unit surface area and per unit wavelength (or, equivalently, per un ...
*Stefan–Boltzmann law
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 ...
References
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Physical quantities
Radiometry