In ^{−2}). The CGS unit ^{−2}⋅s^{−1}) is often used in ^{−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}).

_{e} ("e" for "energetic", to avoid confusion with _{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

_{e,ν}, is defined as
:$E\_\; =\; \backslash frac,$
where ''ν'' is the frequency.
Spectral irradiance in wavelength of a surface, denoted ''E''_{e,λ}, is defined as
:$E\_\; =\; \backslash frac,$
where ''λ'' is the wavelength.

_{m} is the amplitude of the wave's electric field;
*''n'' is the _{0} is the _{0} is the _{r} ≈ 1 where ''μ''_{r} is the

_{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:
:$E\_\backslash mathrm\; =\; E\_\; +\; E\_\; +\; E\_.$
The

radiometry
Radiometry is a set of techniques for measuring
'
Measurement is the numerical quantification of the attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are depen ...

, irradiance is the radiant flux
In radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as op ...

''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
The metric system is a system of measurement
A syste ...

of irradiance is the watt
The watt (symbol: W) is a unit of power
Power typically refers to:
* Power (physics)
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal ...

per square metre (W⋅merg
The erg is a unit of energy equal to 10−7joule
The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an object ...

per square centimetre per second (erg⋅cmastronomy
Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...

. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity
In radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as op ...

. 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
A unit of time is any particular time
Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

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 (waves), phase on the wave, such as two adja ...

, 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 (theory), continuum. The word was first used scientifically in optics to describe the ...

is taken as a function of frequency or of wavelength. The two forms have different dimensions
thumb
, 236px
, The first four spatial dimensions, represented in a two-dimensional picture.
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature ...

: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz
The hertz (symbol: Hz) is the unit
Unit may refer to:
Arts and entertainment
* UNIT
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action ...

(W⋅mMathematical definitions

Irradiance

Irradiance of a surface, denoted ''E''photometricPhotometry can refer to:
* Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision
* Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electroma ...

quantities), is defined as
:$E\_\backslash mathrm\; =\; \backslash frac,$
where
*∂ is the partial derivative
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

symbol;
*Φradiant 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 whether ...

.
Spectral irradiance

Spectral irradiance in frequency of a surface, denoted ''E''Property

Irradiance of a surface is also, according to the definition ofradiant flux
In radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as op ...

, equal to the time-average of the component of the Poynting vector
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

perpendicular to the surface:
:$E\_\backslash mathrm\; =\; \backslash langle,\; \backslash mathbf,\; \backslash rangle\; \backslash cos\; \backslash alpha,$
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
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Ph ...

, the Poynting vector always points to the direction of propagation while oscillating in magnitude. The irradiance of a surface is then given by
:$E\_\backslash mathrm\; =\; \backslash frac\; E\_\backslash mathrm^2\; \backslash cos\; \backslash alpha\; =\; \backslash frac\; E\_\backslash mathrm^2\; \backslash cos\; \backslash alpha,$
where
*''E''refractive index
In optics, the refractive index (also known as refraction index or index of refraction) of a optical medium, material is a dimensionless number that describes how fast EM radiation, light travels through the material. It is defined as
:n = \frac ...

of the medium of propagation;
*''c'' is the speed of light
The speed of light in vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...

in vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter
A parameter (from the Ancient Gree ...

;
*μvacuum permeability
Vacuum permeability is the magnetic permeability in a classical vacuum. ''Vacuum permeability'' is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field prod ...

;
*εvacuum permittivity
Vacuum permittivity, commonly denoted (pronounced as "epsilon nought" or "epsilon zero") is the value of the absolute dielectric permittivity of classical vacuum. Alternatively may be referred to as the permittivity of free space, the electr ...

.
This formula assumes that the magnetic susceptibility
In electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carr ...

is negligible, i.e. that ''μ''magnetic permeability
In electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ...

of the propagation medium. This assumption is typically valid in transparent media in the optical frequency range.
Point source

Apoint 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 us ...

of light produces spherical wavefronts. The irradiance in this case varies inversely with the square of the distance from the source.
:$E\; =\; \backslash frac\; P\; A\; =\; \backslash frac\; P\; .\; \backslash ,$
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 energy

The global irradiance on a horizontal surface on Earth consists of the direct irradiance ''E''integral
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

of solar irradiance over a time period is called " solar exposure" or "insolation
Solar irradiance is the power
Power typically refers to:
* Power (physics)
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one j ...

".
SI radiometry units

See also

*Albedo
Albedo (prounounced ; la, albedo, meaning 'whiteness') 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 radiat ...

*Fluence
In radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as oppo ...

*Illuminance
In photometryPhotometry can refer to:
* Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision
* Photometry (astronomy), the measurement of the flux or intensity of an astronomical ob ...

*Insolation
Solar irradiance is the power
Power typically refers to:
* Power (physics)
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one j ...

*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 walk ...

*PI curve
The PI (or photosynthesis-irradiance) curve is a graphical representation of the empirical relationship between solar irradiance
Solar irradiance is the power
Power typically refers to:
* Power (physics)
In physics, power is the amount of ene ...

(photosynthesis-irradiance curve)
* Solar azimuth angle
*Solar irradiance
Solar irradiance is the power (physics), power per unit area received from the Sun in the form of electromagnetic radiation as measured in the wavelength range of the measuring instrument.
The solar irradiance is measured in watt per square met ...

*Solar noon
Noon (or midday) is 12 12-hour clock, o'clock in the daytime. It is written as 12 noon, 12:00 m. (for 12-hour clock, meridiem, literally 12:00 noon), 12 p.m. (for 12-hour clock, post meridiem, literally "after noon"), 12 pm, or 12:00 (using a 2 ...

*Spectral flux density
In spectroscopy
Spectroscopy is the study of the interaction between matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ...

*Stefan–Boltzmann law
The Stefan–Boltzmann law describes the power radiated from a black body in terms of its thermodynamic temperature, temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit area, surface area of a bl ...

References

{{Authority control Physical quantities Radiometry