# Lumen (unit)

Physical unit
Unit name Lumens
Unit symbol ${\ displaystyle \ mathrm {lm}}$
Physical quantity (s) Luminous flux
Formula symbol ${\ displaystyle {\ mathit {\ Phi}} _ {\ mathrm {v}}}$
dimension ${\ displaystyle {\ mathsf {J}}}$
system International system of units
In SI units ${\ displaystyle \ mathrm {1 \, lm = 1 \; cd \ cdot sr}}$
Named after Latin lumen , "light, lamp"

The lumen ( Latin for light , lamp ) is the SI unit of luminous flux . So it indicates how much light a lamp emits per unit of time . The lumen may not use the Lux be confused, the unit of illuminance , which indicates how much light per unit time per unit area incident .

## definition

The luminous flux is a photobiological quantity. It corresponds to the radiation power , measured in watts (W), taking into account that the human eye for light of different wavelengths is different sensitivity: . The factor that describes the sensitivity of the eye is the photometric radiation equivalent . ${\ displaystyle \ Phi _ {\ mathrm {v}}}$ ${\ displaystyle \ Phi _ {\ mathrm {e}}}$${\ displaystyle \ lambda}$${\ displaystyle \ Phi _ {\ mathrm {v}} = \ Phi _ {\ mathrm {e}} \ cdot K (\ lambda)}$${\ displaystyle K (\ lambda)}$

For practical and historical reasons, the luminous flux is viewed as a quantity with its own dimension . The lumen is therefore a separate unit, but coupled to the watt via K (λ). It is

"[...] defined by specifying the numerical value 683 for the radiation equivalent K cd of the monochromatic radiation of the frequency 540 · 10 12 Hz, expressed in the unit lm W -1 [...]"

This normalization factor of 683 lm / W is an arbitrarily determined value. It was chosen so that the lumen so defined in 1979 matched its earlier definition as closely as possible. The frequency of 540 THz chosen for this definition corresponds to yellow-green light with a wavelength of 555  nanometers . The human eye is most sensitive to daytime vision at this wavelength . The value of K decreases towards the red and blue end of the color spectrum and reaches the value zero at the edge of the visible area. As a rule, the eye is offered a mixture of electromagnetic radiation of different wavelengths, which contribute to the impression of brightness to different degrees. K is then the weighted mean (“average”) of K (λ). For the wavelength mixture of daylight, K  ≈ 125 lm / W.

The sensitivity curve K ' (λ) for night vision has a different course, but happens to be almost exactly the same value at 555 nm. The definition is therefore also suitable for night vision.

A luminous flux of one lumen at a wavelength of 555 nm corresponds to a photon en rate of 4.1 · 10 15 photons per second.

## history

The lumen unit was proposed by André-Eugène Blondel in 1894 and accepted at the International Congress of Electricians in Geneva in 1896.

Photometric quantities and units were initially defined using standardized light sources such as the Hefner lamp , which emitted light in a broad frequency band. For technical reasons, luminous intensities were compared. Since 1946, the unit of light intensity, the candela , was defined by a black body (initially under the name “New Candle” and from 1948 as “Candela”).

The current definition has been valid since 1979, but in its current formulation only since the redefinition of the SI units by the 26th General Conference on Weights and Measures , which came into force on May 20, 2019. Before 2019, the rule was that all units of measurement had to be derived from the SI base units if they were not themselves such. The base unit referred to in this case was the candela. As a result, the definition of the lumen had to be formulated in a more complicated manner.

When the definition was redefined in 1979 with a connection to the tidal flats , the responsible international committee (Comité Consultatif de Photométrie et Radiométrie (CCPR)) advocated that the lumen should replace the candela as the SI base unit . However, in order not to jeopardize the approval of the redefinition of the photometric units as a whole, this was not done.

## use

### Specification for lamps

With light sources , the numerical value in lumens is a measure of how much light a lamp emits. According to EC regulation 244/2009, this information must be dominant on the lamp packaging. The numerical value in watts, on the other hand, indicates how much electrical power is consumed ("used"). The light output - the ratio of “lumens to watts” - is therefore a measure of the cost-effectiveness of a lamp.

For a list of typical luminous flux of light sources and comparing the electrical power consumed (measured in watts) see # examples luminous flux typical luminous flux and light source # examples .

### ANSI lumens

“ANSI Lumen” is a slang term in connection with the technical specification of projectors . This is not about a special lighting unit, but it says that the luminous flux (colloquially "the brightness") of the projector was determined in the unit lumen according to a measurement specification developed by the American National Standards Institute (ANSI) .

To prepare for the measurement, set the projector so that a five percent gray-tinted field can be distinguished from a ten percent gray-tinted field against a white background, i.e. two very light gray tones . The projection surface is then divided into three columns and three rows and the mean value of the illuminance (in lux) of all nine fields is determined. This mean value multiplied by the projection area results in the "ANSI lumens": ${\ displaystyle E _ {\ mathrm {v}}}$${\ displaystyle A}$

${\ displaystyle {\ mathit {\ Phi}} _ {\ mathrm {v}} = E _ {\ mathrm {v}} \ cdot A}$

Most projector manufacturers' specifications refer to the maximum settings that conform to standards, which are rarely optimal for practical use. The luminous flux achieved with the optimal setting is sometimes significantly lower.

## Individual evidence

1. New definitions in the International System of Units (SI). (pdf) PTB , September 2019, accessed on September 28, 2019 . - Excerpt from the definition of the candela
2. Directive (EU) 2019/1258 of the Commission of July 23, 2019 amending the annex to Council Directive 80/181 / EEC with regard to the definitions of the SI base units for the purpose of adapting them to technical progress , official German translation from the SI Brochure from 2019 (9th edition) - Excerpt from the definition of the candela
3. 1/683 W = · hc / λ = λ / (683 · hc ) W = 555 · 10 −9 / (683 · 6.626 · 10 −34 · 2.998 · 10 8 ) m · W / (J · s m s −1 ) = 4.09 10 15 s −1
4. a b Comité International des Poids et Mesures - Procès verbaux des séances . 2 e series . XX série, 1947, p.  119-121 ( bipm.org [PDF]). : The wording is on pages 125-127 of the PDF document.
5. ^ Resolution 7 of the 9th meeting of the CGPM (1948) ( online , accessed October 16, 2019)
6. 26th CGPM (2018) - Resolutions adopted / Résolutions adoptées. (PDF; 1.2 MB) Versailles 13–16 November 2018. In: bipm.org. Bureau International des Poids et Mesures, November 19, 2018, pp. 2–5 , accessed on May 6, 2019 (English, French).
7. ^ Resolution 1 of the 26th meeting of the CGPM (2018) ( online , accessed August 30, 2019): "[...] the International System of Units [...] is the system of units in which [...] the luminous efficacy of monochromatic radiation of frequency 540 × 10 12  Hz, K cd , is 683 lm / W [...] "
8. Minutes of the 15th General Conference on Weights and Measures , 1975, p. 77, accessed Nov. 14, 2019
9. Comité International des Poids et Mesures - Procès verbaux des séances . 66 e session. 2 e série, 1977, p.  5-6 ( bipm.org [PDF]). (7.4 MB): "Recommandation P 3 (lumen comme unité de base avec une définition en fonction du watt) est celle qui a la préférence de la majorité du CCPR." The CCPR (Comité Consultatif de Photométrie et Radiométrie) is that Competent advisory body of the International Committee for Weights and Measures (CIPM) . The wording of recommendation P 3 can be found on page 143 of the same document.
10. EC Regulation 244/2009 , Annex II Paragraph 3.1.a)
11. The corresponding standard IT7.227-1998 was withdrawn by ANSI in July 2003 and can no longer be found there. However, the practically identical standards of the International Electrotechnical Commission  (IEC) and DIN EN 61947-1 apply.
12. Description of the measurement method (section ANSI Lumen)