# Luminous flux

Physical size
Surname Luminous flux
Formula symbol ${\ displaystyle \ Phi _ {\ mathrm {v}}, F \}$
Size and
unit system
unit dimension
SI Lumen  (lm) J

Luminous flux ( English luminous flux , formula symbol ) is a photometric quantity that indicates how much light perceivable to the human eye a light source emits per unit of time. It corresponds to the physical ( radiometric ) radiation power , but also takes into account the sensitivity of the human eye. It is given in the unit of measurement lumen (lm). ${\ displaystyle \ Phi _ {\ mathrm {v}}}$

## definition

Relative brightness sensitivity curves for day vision V (λ) (red) and night vision V '(λ) (blue)

Every light source emits energy in the form of electromagnetic radiation. The energy radiated per unit of time is referred to as radiant power or radiant flux . However, only a limited spectral range is accessible to the human eye, and in the visible range too, the sensitivity of the eye strongly depends on the wavelength . To describe the impression of brightness, the visible portion of the radiation output is therefore evaluated (weighted) using the brightness sensitivity curve of the human eye. The result is the luminous flux (“v” for “visual” denotes the luminous flux as a photometric quantity). To emphasize that the luminous flux is a quantity specially tailored to the human eye, it is not specified in the unit of measurement watt (W), but has its own unit of measurement, the lumen (lm). ${\ displaystyle \ Phi _ {\ mathrm {e}}}$ ${\ displaystyle \ lambda}$${\ displaystyle \ Phi _ {\ mathrm {v}}}$

The conversion factor between radiant power and luminous flux is the spectral photometric radiation equivalent

${\ displaystyle K (\ lambda) = K _ {\ mathrm {m}} \ cdot V (\ lambda) \.}$

Here, V (λ), the luminosity curve for daylight vision . Its maximum V (λ) = 1 is at the wavelength λ = 555 nm ( yellow-green light). The scaling factor K m was set at 683 lm / W so that the lumen unit of measurement thus defined matched its earlier definition as closely as possible.

In the case of monochromatic light (only one wavelength) the luminous flux is

${\ displaystyle \ Phi _ {\ mathrm {v}} = K (\ lambda) \ cdot \ Phi _ {\ mathrm {e}} = K _ {\ mathrm {m}} \ cdot V (\ lambda) \ cdot \ Phi _ {\ mathrm {e}} \.}$

For monochromatic light with a wavelength of λ = 555 nm, a radiation power of 1 W corresponds to a luminous flux of 683 lm, at other wavelengths the luminous flux is lower for the same radiation power.

As a rule, however, light consists of a mixture of wavelengths. Then the spectral radiant power for each wavelength must be multiplied by the corresponding spectral photometric radiation equivalent, i.e. H. one calculates the integral over the wavelength: ${\ displaystyle \ textstyle {\ mathrm {d} \ Phi _ {\ mathrm {e}} (\ lambda)} / {\ mathrm {d} \ lambda}}$

${\ displaystyle \ Phi _ {\ mathrm {v}} = K _ {\ mathrm {m}} \ int V (\ lambda) \ {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {e}} ( \ lambda)} {\ mathrm {d} \ lambda}} \ \ mathrm {d} \ lambda \.}$

At low brightness (more precisely: luminance ), so-called night vision , the light in the eye is registered by other cells that have a different sensitivity. The corresponding quantities are then K ′ m  = 1699 lm / W and V ′ (λ). V ′ (λ) has its maximum at λ = 507 nm.

In an analogous manner, other photometric quantities (to light intensity , illumination intensity , luminance , ...) by measurement or by calculation directly from the corresponding radiometric quantity ( beam intensity , irradiation intensity , beam density , ...) can be derived when it is known from which wavelength mixture, the respective electromagnetic radiation composed.

The visible part of the electromagnetic radiation (“light” in the photometric sense) determined in this way represents a quantitative measure of the light stimulus that causes the eye to perceive brightness. The subjective perception of this sensation of brightness with its adaptation, contrast and other physiological effects is no longer the subject of photometry.

## Previous definition

Photometric measurements were originally carried out using standardized light sources (“standard candles”) that emitted a mixture of wavelengths. Quantities and units of photometry were separated from those of radiometry and the rest of the SI. The light intensity (luminous flux through solid angle :) was chosen as the fundamental photometric variable , because the visual comparison of light sources was in the foreground and the light intensity was the property of the sources that was easiest to compare. The unit of light intensity (since 1947 the candela ) was the basic unit. In a mathematically simplified representation, the definition of the luminous flux was (the content is still valid today): ${\ textstyle \ mathrm {d} \ Phi _ {\ mathrm {v}} / {\ mathrm {d} \ Omega}}$

If the light intensity is constant within a solid angle, then the luminous flux emitted in this solid angle is the product of the light intensity and the solid angle.

In 1979 the candela was redefined by connecting the lumen to the watt via the photometric radiation equivalent. Since the luminous flux was now the more fundamental quantity, the responsible international committee advocated in advance that the luminous flux should replace the luminous intensity as the basic quantity and the lumen should replace the candela as the basic unit. However, the application was rejected in order not to jeopardize the approval of the redefinition of the photometric units as a whole.

## Examples of typical luminous fluxes

In the following, the luminous flux of common illuminants is listed as an example.

The luminous efficacy measured here in lm / W should not be confused with the above-mentioned photometric radiation equivalent, which is also measured in lm / W. The latter describes how many lumens there are for each watt of the emitted electromagnetic power. The luminous efficacy describes how many lumens there are for each watt of the (mostly electrical) power consumed by the light source , i.e. it includes technical conversion losses.

### lightbulbs

Typical values ​​for general service lamps of the main series 230 V, lamps with double filament:

Power
W
Luminous flux
lm
Luminous efficiency
lm / W
40 430 10.8
60 730 12.2
100 1380 13.8
500 8400 16.8

Typical values ​​for low-voltage halogen lamps without reflector, color temperature 3000 K:

Power
W
Luminous flux
lm
Luminous efficiency
lm / W
10 (12 V) 140 14th
20 (12 V) 350 17.5
50 (12 V) 950 19th
50 (24 V) 850 17th
100 (12 V) 2300 23
100 (24 V) 2200 22nd

### Fluorescent lamps

Typical values ​​for fluorescent lamps with a light color of light white, rod design (diameter 26 mm):

Power
W
Pipe length
mm
Luminous flux
lm
Luminous efficiency
lm / W
Luminance
cd / m 2
15th 438 650 43 07000
30th 895 1600 53 07500
36 1200 3350 93 11400
58 1500 5200 90 14500

(Power consumption without considering the ballast)

### Other light sources

 Firefly 0.0144 lm per cm 2 illuminated area Indicator LED approx. 0.001 - 1 lm candle approx. 10 lm "High-Power" LED up to 250 lm Sun 3.7 x 10 28  lm

## Measurement method

### Integrating sphere (spherical photometer)

The common but relative measurement with the help of an integrating sphere leads to a comparatively fast result, which is available in the millisecond / second range. If the preparation times, such as controlled aging (48 h for halogen lamps) or thermal stabilization (2 h for LED lights and lamps), of the light source are observed, the time advantage is reduced. A photometer / spectrometer connected to the integrating sphere allows immediate reading of the luminous flux. Precise measurements can be carried out under three conditions:

• The (relatively) measuring sphere must have been calibrated by a suitable light source with identical spatial radiation, since the light mixing is not sufficient with the usual photometer color (inner lining of the sphere). The CIE no longer recommends increasing the degree of reflection to values ​​greater than 90%, as long-term stability cannot be guaranteed due to the inevitable dustiness of the lower half of the sphere.
• Second, the sphere must either be calibrated with a known light source of identical spectral distribution or the overall system “sphere with mounted photometer head” must have a spectral sensitivity similar to the light sensitivity function of the (human) eye. However, this requirement can only be met for photometers (can be read out quickly) with partial filtering and spectrometers (read out significantly more slowly) with integrated scattered light matrix correction.
• Third, the design (dimensions, self-absorption ) of the calibration light source must match the design of the test item. Additional calibration with a so-called auxiliary lamp is often not sufficient, especially in the case of high self-absorption.

In summary, it can be said that the sphere delivers excellent measurement results when “equal versus equal” and thus relatively measured. If the spatial or spectral radiation or the design of the calibration light source deviate from the measurement object, the measurement uncertainty is significantly increased.

### From the light intensity distribution (goniophotometer)

The much more accurate, because absolute, measurement of the luminous flux is carried out with the aid of a photometer head mounted on a goniometer. The goniometer moves the photometer head (actually the illuminance measuring head) on a virtual spherical surface around the measuring object. Depending on the distribution of the angle-dependent light intensity of the light source, the measurement time is in the range of minutes / hours. It is important that the light source to be measured works stably over the duration of the measurement. The paths traveled by the goniometer are historically based on loxodromes (spiral paths ) or simulate great circles / small circles . If the light intensity distribution (LID) is known to some extent, every conceivable grid can be scanned by CNC, thus reducing the time required for measurement considerably. If there is a sensible spatial distribution of the measured values ​​after the recording of the measured values, numerical methods can be used to calculate the luminous flux from the luminous intensity distribution. As with measurements on a spherical photometer, the spectral adaptation of the measuring head is important; according to DIN 5032 Part 7, a class L measuring head only results in a total error of less than 1.5%. The use of illuminance measuring heads with partial filtering is necessary. Furthermore, a sufficiently narrow measuring grid must be ensured.

## Relationship with other radiometric and photometric quantities

 radiometric quantity Symbol a) SI unit description photometric equivalent b) symbol SI unit Radiant flux radiant power, radiant flux, radiant power ${\ displaystyle \ Phi _ {\ mathrm {e}}}$ W ( watt ) Radiant energy through time Luminous flux luminous flux, luminous power ${\ displaystyle \ Phi _ {\ mathrm {v}}}$ lm ( lumens ) Radiant intensity irradiance, radiant intensity ${\ displaystyle I _ {\ mathrm {e}}}$ W / sr Radiation flux through solid angles Luminous intensity luminous intensity ${\ displaystyle I _ {\ mathrm {v}}}$ cd = lm / sr ( candela ) Irradiance irradiance ${\ displaystyle E _ {\ mathrm {e}}}$ W / m 2 Radiation flux through the receiver surface Illuminance illuminance ${\ displaystyle E _ {\ mathrm {v}}}$ lx = lm / m 2 ( lux ) Specific radiation emission current density, radiant exitance ${\ displaystyle M _ {\ mathrm {e}}}$ W / m 2 Radiation flux through the transmitter surface Specific light emission luminous exitance ${\ displaystyle M _ {\ mathrm {v}}}$ lm / m 2 Radiance radiance, radiance, radiance ${\ displaystyle L _ {\ mathrm {e}}}$ W / m 2 sr Radiant intensity through effective transmitter area Luminance luminance ${\ displaystyle L _ {\ mathrm {v}}}$ cd / m 2 Radiant energy amount of radiation, radiant energy ${\ displaystyle Q _ {\ mathrm {e}}}$ J ( joules ) by radiation transmitted energy Amount of light luminous energy, quantity of light ${\ displaystyle Q _ {\ mathrm {v}}}$ lm · s Irradiation irradiation, radiant exposure ${\ displaystyle H _ {\ mathrm {e}}}$ J / m 2 Radiant energy through the receiver surface Exposure luminous exposure ${\ displaystyle H _ {\ mathrm {v}}}$ lx s Radiation yield radiant efficiency ${\ displaystyle \ eta _ {\ mathrm {e}}}$ 1 Radiation flux through absorbed (mostly electrical) power Luminous efficiency (overall) luminous efficacy ${\ displaystyle \ eta _ {\ mathrm {v}}}$ lm / W
a)The index "e" is used to distinguish it from the photometric quantities. It can be omitted.
b)The photometric quantities are the radiometric quantities, weighted with the photometric radiation equivalent K , which indicates the sensitivity of the human eye.

## literature

• Hans R. Ris: Lighting technology for practitioners. 2nd Edition. VDE-Verlag, Berlin / Offenbach 1997, ISBN 3-8007-2163-5 .
• Günter Springer: Expertise in electrical engineering. (= Europa-Lehrmittel. 30318). 18th, completely revised and expanded edition. Verlag Europa-Lehrmittel, Wuppertal 1989, ISBN 3-8085-3018-9 .
• Wilhelm Gerster: Modern lighting systems for indoors and outdoors. Compact Verlag, Munich 1997, ISBN 3-8174-2395-0 .
• Horst Stöcker: Pocket book of physics. 4th edition. Verlag Harry Deutsch, Frankfurt am Main 2000, ISBN 3-8171-1628-4 .

## Remarks

1. The exact definition is K cd  = 683 lm / W for radiation with a frequency of 540 THz, which corresponds to λ = 555.016 nm in air. At λ = 555 nm, K has its maximum value K m  = 683.002 lm / W ( IEC terminology )
2. The luminous flux is an integral quantity from which all other photometric quantities can be derived through differentiation.

## Individual evidence

1. Ludwig Bergmann , Clemens Schaefer : Optics: Wave and particle optics . In: Bergmann-Schaefer textbook on experimental physics . tape 3 . Walter de Gruyter, 2004, ISBN 3-11-017081-7 , p. 637 ( limited preview in Google Book search).
2. International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-01-25, Luminous flux, (accessed February 12, 2015).
3. ^ WR Blevin, B. Steiner: Redefinition of the Candela and the Lumen. In: Metrologia . 11, 1975, pp. 97-104. doi: 10.1088 / 0026-1394 / 11/3/001
4. HAE Keitz: Light calculations and light measurements. 2nd Edition. Philips Technical Library, Eindhoven 1967, p. 25.
5. 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.
6. H.-J. Hentschel: Light and Lighting - Theory and Practice of Lighting Technology. 4th edition. Hüthig Buch, Heidelberg 1994, ISBN 3-7785-2184-5 , p. 128.
7. H.-J. Hentschel: Light and Lighting - Theory and Practice of Lighting Technology. 4th edition. Hüthig Buch, Heidelberg 1994, ISBN 3-7785-2184-5 , p. 131.
8. H.-J. Hentschel: Light and Lighting - Theory and Practice of Lighting Technology. 4th edition. Hüthig Buch, Heidelberg 1994, ISBN 3-7785-2184-5 , p. 134.
9. 15W: 650lm / 15W = 43 lm / W 30W: 1600lm / 30W = 53 lm / W ....
10. ^ HE Ives: The Fire-Fly as an Illuminant. In: Journal of the Franklin Institute. vol. 194, no. 2, August 1922, pp. 213-230. doi: 10.1016 / S0016-0032 (22) 90057-2 , "on specimens of the larva of one of the Pennsylvania varieties of fire-fly." The lumen used at the time differs slightly from today's SI lumen.
11. a b D. A. Steigerwald et al .: Illumination with solid state lighting technology. In: IEEE Journal on Selected Topics in Quantum Electronics. vol. 8, no. 2, March / April 2002, pp. 310-320. doi: 10.1109 / 2944.999186 , p. 310f.
12. Typical luminous intensity of a candle: I v ≈ 1 cd isotropic, therefore luminous flux Φ v = 4π · I v ≈ 10 lm.
13. Licht.de: Efficiency of light sources (overview without operating losses ). Retrieved January 19, 2020 .
14. Licht.de: Efficiency of light sources (graphic). Retrieved January 19, 2020 .
15. S. Darula, R. Kittler, CA Gueymard: Reference luminous solar constant and solar luminance for illuminance calculations. In: Solar Energy. Volume 79, Issue 5, November 2005, pp. 559-565. doi: 10.1016 / j.solener.2005.01.004 . For the standard brightness sensitivity curve V (λ): 3.7497438 · 10 28 lm, for the brightness sensitivity curve V M (λ) modified in 1988 : 3.7715109 · 10 28 lm.