# Luminous flux

Luminous flux
Common symbols
Φv
SI unitlumen
In SI base unitscdsr
Dimension${\displaystyle {\mathsf {J}}}$

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 (including infrared, ultraviolet, and visible light), in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.

## Units

The SI unit of luminous flux is the lumen (lm). One lumen is defined as the luminous flux of light produced by a light source that emits one candela of luminous intensity over a solid angle of one steradian.

${\displaystyle 1\ {\text{lm}}=1\ {\text{cd}}\times 1\ {\text{sr}}}$

In other systems of units, luminous flux may have units of power.

## Weighting

The luminous flux accounts for the sensitivity of the eye by weighting the power at each wavelength with the luminosity function, which represents the eye's response to different wavelengths. The luminous flux is a weighted sum of the power at all wavelengths in the visible band. Light outside the visible band does not contribute. The ratio of the total luminous flux to the radiant flux is called the luminous efficacy. This model of the human visual brightness perception, is standardized by the CIE and ISO.[5]

## Context

Luminous flux is often used as an objective measure of the useful light emitted by a light source, and is typically reported on the packaging for light bulbs, although it is not always prominent. Consumers commonly compare the luminous flux of different light bulbs since it provides an estimate of the apparent amount of light the bulb will produce, and a lightbulb with a higher ratio of luminous flux to consumed power is more efficient.

Luminous flux is not used to compare brightness, as this is a subjective perception which varies according to the distance from the light source and the angular spread of the light from the source.

## Measurement

Luminous flux of artificial light sources is typically measured using an integrating sphere, or a goniophotometer outfitted with a photometer or a spectroradiometer. [6]

Quantity Unit Dimension
[nb 1]
Notes
Name Symbol[nb 2] Name Symbol
Luminous energy Qv[nb 3] lumen second lm⋅s TJ The lumen second is sometimes called the talbot.
Luminous flux, luminous power Φv[nb 3] lumen (= candela steradian) lm (= cd⋅sr) J Luminous energy per unit time
Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr) J Luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 (= lm/(sr⋅m2)) L−2J Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance Ev lux (= lumen per square metre) lx (= lm/m2) L−2J Luminous flux incident on a surface
Luminous exitance, luminous emittance Mv lumen per square metre lm/m2 L−2J Luminous flux emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2TJ Time-integrated illuminance
Luminous energy density ωv lumen second per cubic metre lm⋅s/m3 L−3TJ
Luminous efficacy (of radiation) K lumen per watt lm/W M−1L−2T3J Ratio of luminous flux to radiant flux
Luminous efficacy (of a source) η[nb 3] lumen per watt lm/W M−1L−2T3J Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient V 1 Luminous efficacy normalized by the maximum possible efficacy
1. ^ 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.
2. ^ 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
3. ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.

### Relationship to luminous intensity

Luminous flux (in lumens) is a measure of the total amount of light a lamp puts out. The luminous intensity (in candelas) is a measure of how bright the beam in a particular direction is. If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1 steradian beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 steradian then the source would have a luminous intensity of 2 candela. The resulting beam is narrower and brighter, however the luminous flux remains the same.

## Examples

Table of comparative luminous flux of several light sources[7][8][9]
Source Luminous flux (lumens)
37 mW "Superbright" white LED 0.20
15 mW green laser (532 nm wavelength) 8.4
1 W high-output white LED 25–120
Kerosene lantern 100
40 W incandescent lamp at 230 volts 325
7 W high-output white LED 450
6 W COB filament LED lamp 600
18 W fluorescent lamp 1250
100 W incandescent lamp 1750
40 W fluorescent lamp 2800
35 W xenon bulb 2200–3200
100 W fluorescent lamp 8000
127 W low pressure sodium vapor lamp 25,000
400 W metal-halide lamp 40,000
Values are given for newly manufactured sources. The output from many sources decreases significantly over their lifetime.

## References

1. ^ "Scotopic luminosity function".
2. ^
3. ^
4. ^ "Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function". Archived from the original on 2007-09-27. Retrieved 2007-05-10.
5. ^
6. ^ Schneider, T.; Young, R.; Bergen, T.; Dam-Hansen, C; Goodman, T.; Jordan, W.; Lee, D.-H; Okura, T.; Sperfeld, P.; Thorseth, A; Zong, Y. (2022). CIE 250:2022 Spectroradiometric Measurement of Optical Radiation Sources. Vienna: CIE - International Commission on Illumination. ISBN 978-3-902842-23-7.
7. ^ Szokolay, S. V. (2008). Introduction to Architectural Science: The Basis of Sustainable Design (Second ed.). Routledge. p. 143. ISBN 9780750687041.
8. ^ BeLight. Vol. 3. Trendforce. 2010. pp. 10–12.
9. ^ Jahne, Bernd (2004). Practical Handbook on Image Processing for Scientific and Technical Applications (Second ed.). CRC. p. 111. ISBN 9780849390302.