In
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 ch ...
, irradiance is the
radiant flux ''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
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 celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galax ...
. Irradiance is often called
intensity
Intensity may refer to:
In colloquial use
*Strength (disambiguation)
*Amplitude
* Level (disambiguation)
* Magnitude (disambiguation)
In physical sciences
Physics
*Intensity (physics), power per unit area (W/m2)
*Field strength of electric, ma ...
, but this term is avoided in radiometry where such usage leads to confusion with
radiant intensity. In astrophysics, irradiance is called ''radiant flux''.
Spectral irradiance is the irradiance of a surface per unit
frequency or
wavelength, 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 ...
is taken as a function of frequency or of wavelength. The two forms have different
dimensions and units: spectral irradiance of a frequency spectrum is measured in watts per square metre per
hertz (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.
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 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, th ...
, 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 of the medium of propagation;
*''c'' is the
speed of light in
vacuum;
*μ
0 is the
vacuum permeability;
*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 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 of solar irradiance over a time period is called "
solar exposure" or "
insolation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/ ...
".
SI radiometry units
See also
*Albedo
Albedo (; ) is the measure of the diffuse reflection of sunlight, 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 ...
* Fluence
* Illuminance
*Insolation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/ ...
*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 a ...
* Solar irradiance
* Solar noon
* Spectral flux density
* Stefan–Boltzmann law
References
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Physical quantities
Radiometry