Photometry (optics)

Last updated February 11, 2024

Photopic (daytime-adapted, black curve) and scotopic (darkness-adapted, green curve) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd-Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jagle 2005 data (dotted). The horizontal axis is wavelength in nm. Luminosity.png — Photopic (daytime-adapted, black curve) and scotopic (darkness-adapted, green curve) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd-Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted). The horizontal axis is wavelength in nm.

Photometry is a branch of science that deals with the measurement of light in terms of its perceived brightness to the human eye.^[1] It is concerned with quantifying the amount of light that is emitted, transmitted, or received by an object or a system.

In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this weighting function is the photopic sensitivity function, although the scotopic function or other functions may also be applied in the same way. The weightings are standardized by the CIE and ISO.^[2]

Photometry is distinct from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power.

Photometry and the eye

The human eye is not equally sensitive to all wavelengths of visible light. Photometry attempts to account for this by weighting the measured power at each wavelength with a factor that represents how sensitive the eye is at that wavelength. The standardized model of the eye's response to light as a function of wavelength is given by the luminosity function. The eye has different responses as a function of wavelength when it is adapted to light conditions (photopic vision) and dark conditions (scotopic vision). Photometry is typically based on the eye's photopic response, and so photometric measurements may not accurately indicate the perceived brightness of sources in dim lighting conditions where colors are not discernible, such as under just moonlight or starlight.^[1] Photopic vision is characteristic of the eye's response at luminance levels over three candela per square metre. Scotopic vision occurs below 2 × 10⁻⁵ cd/m². Mesopic vision occurs between these limits and is not well characterised for spectral response.^[2]^[1]

Photometric quantities

Measurement of the effects of electromagnetic radiation became a field of study as early as the end of 18th century. Measurement techniques varied depending on the effects under study and gave rise to different nomenclature. The total heating effect of infrared radiation as measured by thermometers led to development of radiometric units in terms of total energy and power. Use of the human eye as a detector led to photometric units, weighted by the eye's response characteristic. Study of the chemical effects of ultraviolet radiation led to characterization by the total dose or actinometric units expressed in photons per second.^[1]

Many different units of measure are used for photometric measurements. The adjective "bright" can refer to a light source which delivers a high luminous flux (measured in lumens), or to a light source which concentrates the luminous flux it has into a very narrow beam (candelas), or to a light source that is seen against a dark background. Because of the ways in which light propagates through three-dimensional space — spreading out, becoming concentrated, reflecting off shiny or matte surfaces — and because light consists of many different wavelengths, the number of fundamentally different kinds of light measurement that can be made is large, and so are the numbers of quantities and units that represent them.

For example, offices are typically "brightly" illuminated by an array of many recessed fluorescent lights for a combined high luminous flux. A laser pointer has very low luminous flux (it could not illuminate a room) but is blindingly bright in one direction (high luminous intensity in that direction).

Table 1. SI photometry quantities
v
t
e
Quantity		Unit		Dimension ^{[nb 1]}	Notes
Name	Symbol^{[nb 2]}	Name	Symbol	Dimension ^{[nb 1]}	Notes
Luminous energy	$Q v$ ^{[nb 3]}	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	$Φ v$ ^{[nb 3]}	lumen (= candela steradian)	lm (= cd⋅sr)	J	Luminous energy per unit time
Luminous intensity	$I v$	candela (= lumen per steradian)	cd (= lm/sr)	J	Luminous flux per unit solid angle
Luminance	$L v$	candela per square metre	cd/m² (= lm/(sr⋅m²))	L⁻²⋅J	Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit .
Illuminance	$E v$	lux (= lumen per square metre)	lx (= lm/m²)	L⁻²⋅J	Luminous flux incident on a surface
Luminous exitance, luminous emittance	$M v$	lumen per square metre	lm/m²	L⁻²⋅J	Luminous flux emitted from a surface
Luminous exposure	$H v$	lux second	lx⋅s	L⁻²⋅T⋅J	Time-integrated illuminance
Luminous energy density	$ω v$	lumen second per cubic metre	lm⋅s/m³	L⁻³⋅T⋅J
Luminous efficacy (of radiation)	$K$	lumen per watt	lm/W	M⁻¹⋅L⁻²⋅T³⋅J	Ratio of luminous flux to radiant flux
Luminous efficacy (of a source)	$η$ ^{[nb 3]}	lumen per watt	lm/W	M⁻¹⋅L⁻²⋅T³⋅J	Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient	$V$			1	Luminous efficacy normalized by the maximum possible efficacy
See also: SI Photometry Radiometry\|(Compare)

Photometric versus radiometric quantities

There are two parallel systems of quantities known as photometric and radiometric quantities. Every quantity in one system has an analogous quantity in the other system. Some examples of parallel quantities include:^[1]

Luminance (photometric) and radiance (radiometric)
Luminous flux (photometric) and radiant flux (radiometric)
Luminous intensity (photometric) and radiant intensity (radiometric)

In photometric quantities every wavelength is weighted according to how sensitive the human eye is to it, while radiometric quantities use unweighted absolute power. For example, the eye responds much more strongly to green light than to red, so a green source will have greater luminous flux than a red source with the same radiant flux would. Radiant energy outside the visible spectrum does not contribute to photometric quantities at all, so for example a 1000 watt space heater may put out a great deal of radiant flux (1000 watts, in fact), but as a light source it puts out very few lumens (because most of the energy is in the infrared, leaving only a dim red glow in the visible).

Table 2. SI radiometry units
v
t
e
Quantity		Unit		Dimension	Notes
Name	Symbol^{[nb 4]}	Name	Symbol	Dimension	Notes
Radiant energy	$Q e$ ^{[nb 5]}	joule	J	M⋅L²⋅T⁻²	Energy of electromagnetic radiation.
Radiant energy density	$w e$	joule per cubic metre	J/m³	M⋅L⁻¹⋅T⁻²	Radiant energy per unit volume.
Radiant flux	$Φ e$ ^{[nb 5]}	watt	W = J/s	M⋅L²⋅T⁻³	Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy.
Spectral flux	$Φ e, ν$ ^{[nb 6]}	watt per hertz	W/Hz	M⋅L²⋅T⁻²	Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm⁻¹.
Spectral flux	$Φ e, λ$ ^{[nb 7]}	watt per metre	W/m	M⋅L⋅T⁻³
Radiant intensity	$I e,Ω$ ^{[nb 8]}	watt per steradian	W/sr	M⋅L²⋅T⁻³	Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity	$I e,Ω, ν$ ^{[nb 6]}	watt per steradian per hertz	W⋅sr⁻¹⋅Hz⁻¹	M⋅L²⋅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.
Spectral intensity	$I e,Ω, λ$ ^{[nb 7]}	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³
Radiance	$L e,Ω$ ^{[nb 8]}	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".
Spectral radiance Specific intensity	$L e,Ω, ν$ ^{[nb 6]}	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".
Spectral radiance Specific intensity	$L e,Ω, λ$ ^{[nb 7]}	watt per steradian per square metre, per metre	W⋅sr⁻¹⋅m⁻³	M⋅L⁻¹⋅T⁻³
Irradiance Flux density	$E e$ ^{[nb 5]}	watt per square metre	W/m²	M⋅T⁻³	Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance Spectral flux density	$E e, ν$ ^{[nb 6]}	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 = 10⁴ Jy).
Spectral irradiance Spectral flux density	$E e, λ$ ^{[nb 7]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiosity	$J e$ ^{[nb 5]}	watt per square metre	W/m²	M⋅T⁻³	Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosity	$J e, ν$ ^{[nb 6]}	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".
Spectral radiosity	$J e, λ$ ^{[nb 7]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exitance	$M e$ ^{[nb 5]}	watt per square metre	W/m²	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".
Spectral exitance	$M e, ν$ ^{[nb 6]}	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".
Spectral exitance	$M e, λ$ ^{[nb 7]}	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exposure	$H e$	joule per square metre	J/m²	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".
Spectral exposure	$H e, ν$ ^{[nb 6]}	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".
Spectral exposure	$H e, λ$ ^{[nb 7]}	joule per square metre, per metre	J/m³	M⋅L⁻¹⋅T⁻²
See also: SI Radiometry Photometry\|(Compare)

Watts versus lumens

Watts are units of radiant flux while lumens are units of luminous flux. A comparison of the watt and the lumen illustrates the distinction between radiometric and photometric units.

The watt is a unit of power. We are accustomed to thinking of light bulbs in terms of power in watts. This power is not a measure of the amount of light output, but rather indicates how much energy the bulb will use. Because incandescent bulbs sold for "general service" all have fairly similar characteristics (same spectral power distribution), power consumption provides a rough guide to the light output of incandescent bulbs.

Watts can also be a direct measure of output. In a radiometric sense, an incandescent light bulb is about 80% efficient: 20% of the energy is lost (e.g. by conduction through the lamp base). The remainder is emitted as radiation, mostly in the infrared. Thus, a 60 watt light bulb emits a total radiant flux of about 45 watts. Incandescent bulbs are, in fact, sometimes used as heat sources (as in a chick incubator), but usually they are used for the purpose of providing light. As such, they are very inefficient, because most of the radiant energy they emit is invisible infrared. A compact fluorescent lamp can provide light comparable to a 60 watt incandescent while consuming as little as 15 watts of electricity.

The lumen is the photometric unit of light output. Although most consumers still think of light in terms of power consumed by the bulb, in the U.S. it has been a trade requirement for several decades that light bulb packaging give the output in lumens. The package of a 60 watt incandescent bulb indicates that it provides about 900 lumens, as does the package of the 15 watt compact fluorescent.

The lumen is defined as amount of light given into one steradian by a point source of one candela strength; while the candela, a base SI unit, is defined as the luminous intensity of a source of monochromatic radiation, of frequency 540 terahertz, and a radiant intensity of 1/683 watts per steradian. (540 THz corresponds to about 555 nanometres, the wavelength, in the green, to which the human eye is most sensitive. The number 1/683 was chosen to make the candela about equal to the standard candle, the unit which it superseded).

Combining these definitions, we see that 1/683 watt of 555 nanometre green light provides one lumen.

The relation between watts and lumens is not just a simple scaling factor. We know this already, because the 60 watt incandescent bulb and the 15 watt compact fluorescent can both provide 900 lumens.

The definition tells us that 1 watt of pure green 555 nm light is "worth" 683 lumens. It does not say anything about other wavelengths. Because lumens are photometric units, their relationship to watts depends on the wavelength according to how visible the wavelength is. Infrared and ultraviolet radiation, for example, are invisible and do not count. One watt of infrared radiation (which is where most of the radiation from an incandescent bulb falls) is worth zero lumens. Within the visible spectrum, wavelengths of light are weighted according to a function called the "photopic spectral luminous efficiency." According to this function, 700 nm red light is only about 0.4% as efficient as 555 nm green light. Thus, one watt of 700 nm red light is "worth" only 2.7 lumens.

Because of the summation over the visual portion of the EM spectrum that is part of this weighting, the unit of "lumen" is color-blind: there is no way to tell what color a lumen will appear. This is equivalent to evaluating groceries by number of bags: there is no information about the specific content, just a number that refers to the total weighted quantity.

Photometric measurement techniques

Photometric measurement is based on photodetectors, devices (of several types) that produce an electric signal when exposed to light. Simple applications of this technology include switching luminaires on and off based on ambient light conditions, and light meters, used to measure the total amount of light incident on a point.

More complex forms of photometric measurement are used frequently within the lighting industry. Spherical photometers can be used to measure the directional luminous flux produced by lamps, and consist of a large-diameter globe with a lamp mounted at its center. A photocell rotates about the lamp in three axes, measuring the output of the lamp from all sides.

Lamps and lighting fixtures are tested using goniophotometers and rotating mirror photometers, which keep the photocell stationary at a sufficient distance that the luminaire can be considered a point source. Rotating mirror photometers use a motorized system of mirrors to reflect light emanating from the luminaire in all directions to the distant photocell; goniophotometers use a rotating 2-axis table to change the orientation of the luminaire with respect to the photocell. In either case, luminous intensity is tabulated from this data and used in lighting design.

Non-SI photometry units

Illuminance

Notes

↑ The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
↑ Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
1 2 3 Alternative symbols sometimes seen: $W$ for luminous energy, $P$ or $F$ for luminous flux, and $ρ$ for luminous efficacy of a source.
↑ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
1 2 3 4 5 Alternative symbols sometimes seen: $W$ or $E$ for radiant energy, $P$ or $F$ for radiant flux, $I$ for irradiance, $W$ for radiant exitance.
1 2 3 4 5 6 7 Spectral quantities given per unit frequency are denoted with suffix " ν " (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)
1 2 3 4 5 6 7 Spectral quantities given per unit wavelength are denoted with suffix " λ ".
1 2 Directional quantities are denoted with suffix "Ω".

Related Research Articles

<span class="mw-page-title-main">Candela</span> SI unit of luminous intensity

The candela is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

<span class="mw-page-title-main">Luminance</span> Photometric measure

Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.

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 characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct from quantum techniques such as photon counting.

The lux is the unit of illuminance, or luminous flux per unit area, in the International System of Units (SI). It is equal to one lumen per square metre. In photometry, this is used as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface. It is analogous to the radiometric unit watt per square metre, but with the power at each wavelength weighted according to the luminosity function, a model of human visual brightness perception, standardized by the CIE and ISO. In English, "lux" is used as both the singular and plural form. The word is derived from the Latin word for "light", lux.

Lighting or illumination is the deliberate use of light to achieve practical or aesthetic effects. Lighting includes the use of both artificial light sources like lamps and light fixtures, as well as natural illumination by capturing daylight. Daylighting is sometimes used as the main source of light during daytime in buildings. This can save energy in place of using artificial lighting, which represents a major component of energy consumption in buildings. Proper lighting can enhance task performance, improve the appearance of an area, or have positive psychological effects on occupants.

<span class="mw-page-title-main">Luminous efficiency function</span> Description of the average spectral sensitivity of human visual perception of brightness

A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of theoretical human eye. It is valuable as a baseline for experimental purposes, and in colorimetry. Different luminous efficiency functions apply under different lighting conditions, varying from photopic in brightly lit conditions through mesopic to scotopic under low lighting conditions. When not specified, the luminous efficiency function generally refers to the photopic luminous efficiency function.

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calculated by integrating radiant flux with respect to time. The symbol Q_e is often used throughout literature to denote radiant energy. In branches of physics other than radiometry, electromagnetic energy is referred to using E or W. The term is used particularly when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be visible or invisible to the human eye.

<span class="mw-page-title-main">Foot-candle</span>

A foot-candle is a non-SI unit of illuminance or light intensity. The foot-candle is defined as one lumen per square foot. This unit is commonly used in lighting layouts in parts of the world where United States customary units are used, mainly the United States. Nearly all of the world uses the corresponding SI derived unit lux, defined as one lumen per square meter.

In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation, and to quantify emission of neutrinos and other particles. The SI unit of radiance is the watt per steradian per square metre. It is a directional quantity: the radiance of a surface depends on the direction from which it is being observed.

<span class="mw-page-title-main">Luminous flux</span> Perceived luminous power

In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of electromagnetic radiation, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.

In 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 with human brightness perception. Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.

The lumen is the unit of luminous flux, a measure of the perceived power of visible light emitted by a source, in the International System of Units (SI). Luminous flux differs from power in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model of the human eye's sensitivity to various wavelengths, this weighting is standardized by the CIE and ISO. One lux is one lumen per square metre.

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 as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiant intensity is the watt per steradian, while that of spectral intensity in frequency is the watt per steradian per hertz and that of spectral intensity in wavelength is the watt per steradian per metre —commonly the watt per steradian per nanometre. Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity.

In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.

Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux to power, measured in lumens per watt in the International System of Units (SI). Depending on context, the power can be either the radiant flux of the source's output, or it can be the total power consumed by the source. Which sense of the term is intended must usually be inferred from the context, and is sometimes unclear. The former sense is sometimes called luminous efficacy of radiation, and the latter luminous efficacy of a light source or overall luminous efficacy.

In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.

Several measures of light are commonly known as intensity:

In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.

Energy conversion efficiency (η) is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The input, as well as the useful output may be chemical, electric power, mechanical work, light (radiation), or heat. The resulting value, η (eta), ranges between 0 and 1.

References

1 2 3 4 5 Bass, Michael, ed. (1995). Handbook of Optics: Volume II –Devices, Measurements and Properties (2nd ed.). McGraw-Hill. pp. 24-40–24-47. ISBN 978-0-07-047974-6.
1 2 ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry. ISO/CIE. 2023. doi:10.25039/IS0.CIE.23539.2023.

External links

Photometry (nist.gov) (archived)
Radiometry and photometry FAQ Professor Jim Palmer's Radiometry FAQ page (University of Arizona) (archived)
Visualization and calculation of photometric quantities — Java executable JAR

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[note-dimension-symbol-3] The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.

[note-suffix-v-4] Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967

[note-alternative-symbol-photometric-5] 1 2 3 Alternative symbols sometimes seen: $W$ for luminous energy, $P$ or $F$ for luminous flux, and $ρ$ for luminous efficacy of a source.

[note-suffix-e-6] Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.

[note-alternative-symbol-radiometric-7] 1 2 3 4 5 Alternative symbols sometimes seen: $W$ or $E$ for radiant energy, $P$ or $F$ for radiant flux, $I$ for irradiance, $W$ for radiant exitance.

[note-suffix-nu-8] 1 2 3 4 5 6 7 Spectral quantities given per unit frequency are denoted with suffix " ν " (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)

[note-suffix-lambda-9] 1 2 3 4 5 6 7 Spectral quantities given per unit wavelength are denoted with suffix " λ ".

[note-suffix-omega-10] 1 2 Directional quantities are denoted with suffix "Ω".

[Bass95-1] 1 2 3 4 5 Bass, Michael, ed. (1995). Handbook of Optics: Volume II –Devices, Measurements and Properties (2nd ed.). McGraw-Hill. pp. 24-40–24-47. ISBN 978-0-07-047974-6.

[ISO_CIE_23539_2023-2] 1 2 ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry. ISO/CIE. 2023. doi:10.25039/IS0.CIE.23539.2023.

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