Irradiance

Irradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m²), while the cgs units are ergs per square centimeter per second (erg·cm⁻²·s⁻¹, often used in astronomy). These quantities are sometimes called intensity, but this usage leads to confusion with radiant intensity, which has different units.

All of these quantities characterize the total amount of radiation present, at all frequencies. It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m³, or commonly W·m⁻²·nm⁻¹.

If a point source radiates light uniformly in all directions through a non-absorptive medium, then the irradiance decreases in proportion to the square of the distance from the object.

1 Technical details
2 Solar energy
3 See also
4 References

Technical details

The irradiance of a monochromatic light wave in matter is given in terms of its electric field by ^[1]

$I \approx \frac{c \, n \, \epsilon_0}{2} |E|^2$ ,

where E is the complex amplitude of the wave's electric field, n is the refractive index of the medium, $c$ is the speed of light in vacuum, and ϵ₀ is the vacuum permittivity. (This formula assumes that the magnetic susceptibility is negligible, i.e. $\mu_r \approx 1$ where $\mu_r$ is the magnetic permeability of the light transmitting media. This assumption is typically valid in transparent media in the optical frequency range.)

Irradiance is also the time average of the component of the Poynting vector perpendicular to the surface.

Solar energy

Irradiance due to solar radiation is also called insolation. The global irradiance on a horizontal surface on Earth consists of the direct irradiance E_dir and diffuse irradiance E_dif. On a tilted plane, there is another irradiance component: E_ref, 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_tilt on a tilted plane consists of three components: E_tilt = E_dir + E_dif + E_ref.^[2]

The integral of solar irradiance over a time period is solar irradiation. Irradiation is measured in J/m² and is represented by the symbol H.^[2]

'
Quantity	Symbol^{[nb 1]}	SI unit	Symbol	Dimension	Notes
Radiant energy	Q_e^{[nb 2]}	joule	J	M⋅L²⋅T⁻²	energy
Radiant flux	Φ_e^{[nb 2]}	watt	W	M⋅L²⋅T⁻³	radiant energy per unit time, also called radiant power.
Spectral power	Φ_eλ^{[nb 2]}^{[nb 3]}	watt per metre	W⋅m⁻¹	M⋅L⋅T⁻³	radiant power per wavelength.
Radiant intensity	I_e	watt per steradian	W⋅sr⁻¹	M⋅L²⋅T⁻³	power per unit solid angle.
Spectral intensity	I_eλ^{[nb 3]}	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³	radiant intensity per wavelength.
Radiance	L_e	watt per steradian per square metre	W⋅sr⁻¹⋅m⁻²	M⋅T⁻³	power per unit solid angle per unit projected source area. confusingly called "intensity" in some other fields of study.
Spectral radiance	L_eλ^{[nb 3]} or L_eν^{[nb 4]}	watt per steradian per metre³ or watt per steradian per square metre per hertz	W⋅sr⁻¹⋅m⁻³ or W⋅sr⁻¹⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	commonly measured in W⋅sr⁻¹⋅m⁻²⋅nm⁻¹ with surface area and either wavelength or frequency.
Irradiance	E_e^{[nb 2]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	power incident on a surface, also called radiant flux density. sometimes confusingly called "intensity" as well.
Spectral irradiance	E_eλ^{[nb 3]} or E_eν^{[nb 4]}	watt per metre³ or watt per square metre per hertz	W⋅m⁻³ or W⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	commonly measured in W⋅m⁻²⋅nm⁻¹ or 10⁻²²W⋅m⁻²⋅Hz⁻¹, known as solar flux unit.^{[nb 5]}
Radiant exitance / Radiant emittance	M_e^{[nb 2]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	power emitted from a surface.
Spectral radiant exitance / Spectral radiant emittance	M_eλ^{[nb 3]} or M_eν^{[nb 4]}	watt per metre³ or watt per square metre per hertz	W⋅m⁻³ or W⋅m⁻²⋅Hz⁻¹	M⋅L⁻¹⋅T⁻³ or M⋅T⁻²	power emitted from a surface per wavelength or frequency.
Radiosity	J_e or J_eλ^{[nb 3]}	watt per square metre	W⋅m⁻²	M⋅T⁻³	emitted plus reflected power leaving a surface.
Radiant exposure	H_e	joule per square metre	J⋅m⁻²	M⋅T⁻²
Radiant energy density	ω_e	joule per metre³	J⋅m⁻³	M⋅L⁻¹⋅T⁻²
See also: SI · Radiometry · Photometry

^ Standards organizations recommend that radiometric quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
^ ^a ^b ^c ^d ^e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
^ ^a ^b ^c ^d ^e ^f Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
^ ^a ^b ^c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).

References

^ Griffiths, David J. (1999). Introduction to electrodynamics (3. ed., reprint. with corr. ed.). Upper Saddle River, NJ [u.a.]: Prentice-Hall. ISBN 0-13-805326-X. http://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X.
^ ^a ^b Quaschning, Volker (2003). "Technology fundamentals—The sun as an energy resource". Renewable Energy World 6 (5): 90–93. http://www.volker-quaschning.de/articles/fundamentals1/index_e.html.

Irradiance

Contents

Technical details

Solar energy

See also

References