In optics, wall-plug efficiency or radiant efficiency is the energy conversion efficiency with which the system converts electrical power into optical power. It is defined as the ratio of the radiant flux (i.e., the total optical output power) to the input electrical power.[1]

In laser systems, this efficiency includes losses in the power supply and also the power required for a cooling system, not just the laser itself.[2]

See also

Luminous efficiency

Luminous coefficient

Luminous efficacy - Efficacy, weighted by the eye's response to light

Coefficient of utilization

Quantity | Unit | Dimension | Notes | |||||
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Name | Symbol^{[nb 1]} |
Name | Symbol | Symbol | ||||

Radiant energy | Q_{e}^{[nb 2]} |
joule | J | M⋅L^{2}⋅T^{−2} |
Energy of Electromagnetic radiation. | |||

Radiant energy density | w_{e} |
joule per cubic metre | J/m^{3} |
M⋅L^{−1}⋅T^{−2} |
Radiant energy per unit volume. | |||

Radiant flux | Φ_{e}^{[nb 2]} |
watt | W = J/s | M⋅L^{2}⋅T^{−3} |
Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power". | |||

Spectral flux | Φ_{e,ν}^{[nb 3]} |
watt per hertz | W/Hz | M⋅L^{2}⋅T^{−2} |
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm^{−1}. |
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Φ_{e,λ}^{[nb 4]} |
watt per metre | W/m | M⋅L⋅T^{−3} |
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Radiant intensity | I_{e,Ω}^{[nb 5]} |
watt per steradian | W/sr | M⋅L^{2}⋅T^{−3} |
Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. |
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Spectral intensity | I_{e,Ω,ν}^{[nb 3]} |
watt per steradian per hertz | W⋅sr^{−1}⋅Hz^{−1} |
M⋅L^{2}⋅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. |
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I_{e,Ω,λ}^{[nb 4]} |
watt per steradian per metre | W⋅sr^{−1}⋅m^{−1} |
M⋅L⋅T^{−3} |
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Radiance | L_{e,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". |
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Spectral radiance | L_{e,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". |
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L_{e,Ω,λ}^{[nb 4]} |
watt per steradian per square metre, per metre | W⋅sr^{−1}⋅m^{−3} |
M⋅L^{−1}⋅T^{−3} |
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Irradiance Flux density |
E_{e}^{[nb 2]} |
watt per square metre | W/m^{2} |
M⋅T^{−3} |
Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". |
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Spectral irradiance Spectral flux density |
E_{e,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} = 10^{4} Jy). |
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E_{e,λ}^{[nb 4]} |
watt per square metre, per metre | W/m^{3} |
M⋅L^{−1}⋅T^{−3} |
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Radiosity | J_{e}^{[nb 2]} |
watt per square metre | W/m^{2} |
M⋅T^{−3} |
Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". |
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Spectral radiosity | J_{e,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". |
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J_{e,λ}^{[nb 4]} |
watt per square metre, per metre | W/m^{3} |
M⋅L^{−1}⋅T^{−3} |
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Radiant exitance | M_{e}^{[nb 2]} |
watt per square metre | W/m^{2} |
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". |
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Spectral exitance | M_{e,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". |
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M_{e,λ}^{[nb 4]} |
watt per square metre, per metre | W/m^{3} |
M⋅L^{−1}⋅T^{−3} |
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Radiant exposure | H_{e} |
joule per square metre | J/m^{2} |
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". |
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Spectral exposure | H_{e,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". |
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H_{e,λ}^{[nb 4]} |
joule per square metre, per metre | J/m^{3} |
M⋅L^{−1}⋅T^{−2} |
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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. |
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Spectral hemispherical emissivity | ε_{ν}orε_{λ} |
N/A | 1 |
Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. |
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Directional emissivity | ε_{Ω} |
N/A | 1 |
Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. |
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Spectral directional emissivity | ε_{Ω,ν}orε_{Ω,λ} |
N/A | 1 |
Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. |
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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". |
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Spectral hemispherical absorptance | A_{ν}orA_{λ} |
N/A | 1 |
Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". |
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Directional absorptance | A_{Ω} |
N/A | 1 |
Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". |
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Spectral directional absorptance | A_{Ω,ν}orA_{Ω,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". |
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Hemispherical reflectance | R |
N/A | 1 |
Radiant flux reflected by a surface, divided by that received by that surface. |
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Spectral hemispherical reflectance | R_{ν}orR_{λ} |
N/A | 1 |
Spectral flux reflected by a surface, divided by that received by that surface. |
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Directional reflectance | R_{Ω} |
N/A | 1 |
Radiance reflected by a surface, divided by that received by that surface. |
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Spectral directional reflectance | R_{Ω,ν}orR_{Ω,λ} |
N/A | 1 |
Spectral radiance reflected by a surface, divided by that received by that surface. |
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Hemispherical transmittance | T |
N/A | 1 |
Radiant flux transmitted by a surface, divided by that received by that surface. |
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Spectral hemispherical transmittance | T_{ν}orT_{λ} |
N/A | 1 |
Spectral flux transmitted by a surface, divided by that received by that surface. |
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Directional transmittance | T_{Ω} |
N/A | 1 |
Radiance transmitted by a surface, divided by that received by that surface. |
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Spectral directional transmittance | T_{Ω,ν}orT_{Ω,λ} |
N/A | 1 |
Spectral radiance transmitted by a surface, divided by that received by that surface. |
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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. |
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Spectral hemispherical attenuation coefficient | μ_{ν}orμ_{λ} |
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. |
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Directional attenuation coefficient | μ_{Ω} |
reciprocal metre | m^{−1} |
L^{−1} |
Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. |
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Spectral directional attenuation coefficient | μ_{Ω,ν}orμ_{Ω,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. |
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See also: SI · Radiometry · Photometry |

Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.

Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.

Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.

Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).

Directional quantities are denoted with suffix "Ω" (Greek).

References

N. P. Barnes, “Solid-state lasers from an efficiency perspective”, IEEE J. Sel. Top. Quantum Electron. 13 (3), 435 (2007)

Experimental measurement of the wall-plug efficiency in THz quantum cascade lasers

Hellenica World - Scientific Library

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