Light efficiency

Light efficiency
Light efficiency
Dimension	J. M -1. L -2. T 3
Units
SI	lm W -1
Notes
	scalar value

The light output of a light source is the ratio of the luminous flux emitted by a source to the power it consumes ^[1] . The International System of Units (SI) is measured in lumens per watt (lm / W). It is an indicator of the effectiveness and efficiency of light sources.

The expression for light returns has the form:

\eta ={\frac {\Phi _{v}}{P}},

{\ displaystyle \ eta = {\ frac {\ Phi _ {v}} {P}},}

{\ displaystyle \ eta = {\ frac {\ Phi _ {v}} {P}},}

Where $\Phi _{v}$ ${\ displaystyle \ Phi _ {v}}$ ${\ displaystyle \ Phi _ {v}}$ - the luminous flux emitted by the source, and $P$ ${\ displaystyle P}$ $P$ - power consumption.

By introducing the amount of radiation flux $\Phi _{e}$ ${\ displaystyle \ Phi _ {e}}$ $\ Phi _ {e}$ attitude ${\frac {\Phi _{v}}{P}}$ ${\ displaystyle {\ frac {\ Phi _ {v}} {P}}}$ ${\ displaystyle {\ frac {\ Phi _ {v}} {P}}}$ can be represented as ${\frac {\Phi _{v}}{\Phi _{e}}}\cdot {\frac {\Phi _{e}}{P}}$ ${\ displaystyle {\ frac {\ Phi _ {v}} {\ Phi _ {e}}} \ cdot {\ frac {\ Phi _ {e}} {P}}}$ ${\ displaystyle {\ frac {\ Phi _ {v}} {\ Phi _ {e}}} \ cdot {\ frac {\ Phi _ {e}} {P}}}$ . In this product, the first of the factors represents the luminous efficacy of radiation $K$ ${\ displaystyle K}$ $K$ and the second is the energy efficiency of the source ^[2] $\eta _{e}$ ${\ displaystyle \ eta _ {e}}$ ${\ displaystyle \ eta _ {e}}$ . As a result, the initial expression for light recoil takes the form:

\eta =K\cdot \eta _{e}.

{\ displaystyle \ eta = K \ cdot \ eta _ {e}.}

{\ displaystyle \ eta = K \ cdot \ eta _ {e}.}

Thus, the magnitude of the light output is determined by the combined effect of two factors. One of them is the efficiency of conversion of the electric energy consumed by the source of energy into radiation energy, characterized by the value of efficiency, the other is the ability of this radiation to excite a person’s visual sensations, determined by the luminous efficiency of radiation.

Sources of monochromatic radiation

Relative spectral light efficiency of monochromatic radiation for day vision

In the case of monochromatic radiation with a wavelength $\lambda$ ${\ displaystyle \ lambda}$ $\lambda$ for $K(\lambda )$ ${\ displaystyle K (\ lambda)}$ $K(\lambda )$ in SI is performed:

K(\lambda )=K_{m}\cdot V(\lambda ),

{\ displaystyle K (\ lambda) = K_ {m} \ cdot V (\ lambda),}

K(\lambda )=K_{m}\cdot V(\lambda ),

Where $V(\lambda )$ ${\ displaystyle V (\ lambda)}$ $V(\lambda )$ - the relative spectral light efficiency of monochromatic radiation for daytime vision, the physical meaning of which is that it represents the relative sensitivity of the average human eye to the effects of monochromatic light on it, and $K_{m}$ ${\ displaystyle K_ {m}}$ $K_{m}$ - the maximum value of the spectral luminous efficiency of monochromatic radiation. Maximum $V(\lambda )$ ${\ displaystyle V (\ lambda)}$ $V(\lambda )$ located at a wavelength of 555 nm and is equal to unity.

In accordance with the foregoing, for light output, the following is performed:

\eta =K_{m}\cdot V(\lambda )\cdot \eta _{e}.

{\ displaystyle \ eta = K_ {m} \ cdot V (\ lambda) \ cdot \ eta _ {e}.}

In SI value $K_{m}$ ${\ displaystyle K_ {m}}$ determined by the choice of the main light unit SI candela and is 683,002 lm / W ^[3] . It follows that the maximum theoretically possible value of the light output is achieved at a wavelength of 555 nm with values $V(\lambda )$ ${\ displaystyle V (\ lambda)}$ and $\eta _{e}$ ${\ displaystyle \ eta _ {e}}$ equal to one and is 683.002 lm / W.

In most cases, with an accuracy sufficient for any practical application, a rounded value is used. $K_{m}$ ${\ displaystyle K_ {m}}$ 683 lm / W Further in the equations we will use it.

Sources of radiation in general.

If the radiation occupies a part of the spectrum of finite size, then the expression for $K$ ${\ displaystyle K}$ has the appearance

K=683\cdot {\frac {\int \limits _{380~nm}^{780~nm}\Phi _{e,\lambda }(\lambda )V(\lambda )d\lambda }{\Phi _{e}}}

{\ displaystyle K = 683 \ cdot {\ frac {\ int \ limits _ {380 ~ nm} ^ {780 ~ nm} \ Phi _ {e, \ lambda} (\ lambda) V (\ lambda) d \ lambda} {\ Phi _ {e}}}}

or equivalent to it:

K=683\cdot {\frac {\int \limits _{380~nm}^{780~nm}\Phi _{e,\lambda }(\lambda )V(\lambda )d\lambda }{\int \limits _{0}^{\infty }\Phi _{e,\lambda }(\lambda )d\lambda }}.

{\ displaystyle K = 683 \ cdot {\ frac {\ int \ limits _ {380 ~ nm} ^ {780 ~ nm} \ Phi _ {e, \ lambda} (\ lambda) V (\ lambda) d \ lambda} {\ int \ limits _ {0} ^ {\ infty} \ Phi _ {e, \ lambda} (\ lambda) d \ lambda}}.}

Here $\Phi _{e,\lambda }(\lambda )$ ${\ displaystyle \ Phi _ {e, \ lambda} (\ lambda)}$ - spectral density values $\Phi _{e},$ ${\ displaystyle \ Phi _ {e},}$ defined as a ratio of magnitude $d\Phi _{e}(\lambda ),$ ${\ displaystyle d \ Phi _ {e} (\ lambda),}$ falling on a small spectral interval between $\lambda$ ${\ displaystyle \ lambda}$ and $\lambda +d\lambda ,$ ${\ displaystyle \ lambda + d \ lambda,}$ to the width of this interval:

\Phi _{e,\lambda }(\lambda )={\frac {d\Phi _{e}(\lambda )}{d\lambda }}.

{\ displaystyle \ Phi _ {e, \ lambda} (\ lambda) = {\ frac {d \ Phi _ {e} (\ lambda)} {d \ lambda}}.}

Accordingly, for light output, the following relation becomes valid:

\eta =683\cdot {\frac {\int \limits _{380~nm}^{780~nm}\Phi _{e,\lambda }(\lambda )V(\lambda )d\lambda }{\int \limits _{0}^{\infty }\Phi _{e,\lambda }(\lambda )d\lambda }}\cdot \eta _{e}.

{\ displaystyle \ eta = 683 \ cdot {\ frac {\ int \ limits _ {380 ~ nm} ^ {780 ~ nm} \ Phi _ {e, \ lambda} (\ lambda) V (\ lambda) d \ lambda } {\ int \ limits _ {0} ^ {\ infty} \ Phi _ {e, \ lambda} (\ lambda) d \ lambda}} \ cdot \ eta _ {e}.}

Examples

Source type	Light efficiency (lm / w)	Relative light efficiency ^[4]
Incandescent lamp 100 W	13.8 ^[5]	2.0%
Incandescent lamp 200 W	15.2 ^[6]	2.2%
100W halogen lamp	16.7 ^[7]	2.4%
200W halogen lamp	17.6 ^[6]	2.6%
500W halogen lamp	19.8 ^[6]	2.9%
Kremlin stars	22 ^[8]	3.2%
Projection lamps	35 ^[9]	5.1%
LEDs	10-300 ^[10] ^[11] ^[12] ^[13] ^[14]	1.5—40%
Xenon arc lamp	30-50 ^[15] ^[16]	4.4—7.3%
Fluorescent Lamp	40-104 ^[17]	6–15%
Sulfur lamp	100	14.6%
High Pressure Sodium Lamp	85–150 ^[6] ^[18]	12-22%
Low Pressure Sodium Lamp	100—200 ^[6] ^[18] ^[19]	15-29%
Perspective samples of white LEDs with record parameters	249 ^[20] , 254 ^[21] , 276 ^[22]	36%, 37%
Theoretical maximum for a source of monochromatic green light with a frequency of 540 THz (wavelength 555.016 nm)	683 (exactly) ^[23]	99.9997%
The theoretical maximum for a source of monochromatic green light with a wavelength of 555 nm	683,002	100 %

Although the Sun does not consume energy from the outside, but emits light only through internal sources of energy, it is also sometimes attributed to the value of the light output. Having defined it in this case, as the ratio of the light flux emitted by the Sun to the power released in it , a value of 93 lm / W is obtained ^[24] .

Notes

↑ Light return. - Article in the Physical Encyclopedia
↑ Reference book on lighting / Ed. Aizenberg Yu. B. - M .: Energoatomizdat, 1983. - 472 p.
↑ Details are given in the article Candela .
↑ The ratio of the magnitude of the light output to the value of the theoretical maximum, that is, to 683.002 lm / W.
↑ Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)
↑ ¹ ² ³ ⁴ ⁵ Philips Product Catalog Archive dated July 15, 2011 on Wayback Machine (German)
↑ Osram halogen (German) (PDF) (not available link) . www.osram.de . The appeal date is January 28, 2008. Archived November 7, 2007.
↑ TSB: Kremlin stars // The Great Soviet Encyclopedia : [in 30 t.] / Ch. ed. A. M. Prokhorov . - 3rd ed. - M .: Soviet Encyclopedia, 1969-1978.
↑ Klipstein, Donald L. The Great Internet Light Bulb Book, Part I (Undefined) (inaccessible link) (1996) The appeal date is April 16, 2006. Archived June 1, 2012.
↑ Klipstein, Donald L. (Undefined) . Don Klipstein's Web Site . The date of circulation is January 15, 2008. Archived on February 17, 2012.
↑ Cree launches the new XLamp 7090 XR-E Series Power LED, the first 160-lumen LED! (Unsolved) (inaccessible link) . The appeal date is March 1, 2009. Archived February 17, 2012.
↑ Luxeon K2 with TFFC; Technical Datasheet DS60 (Unreferenced) (PDF). Philips Lumileds . The appeal date is April 23, 2008. Archived January 17, 2009.
Ree Cree Breaks 200 Lumen Per Watt Efficacy Barrier (Unreferenced) (inaccessible link) . [Cree]. The appeal date is February 8, 2010. Archived on February 17, 2012.
Mens Cree First to Break 300 Lumens-Per-Watt Barrier (Unc.) . The date of circulation is January 26, 2015. Archived January 26, 2015.
↑ Technical Information on Lamps (Unreferenced) (pdf). Optical Building Blocks . The date of circulation is October 14, 2007. Archived October 27, 2007. Note that the figure of 150 lm / W is given for this lamp. The page contains other useful information.
↑ OSRAM Lamp and Ballast Catalog. - 2007.
↑ TSB: light return // Great Soviet Encyclopedia : [in 30 tons.] / Ch. ed. A. M. Prokhorov . - 3rd ed. - M .: Soviet Encyclopedia, 1969-1978.
↑ ¹ ² LED or Neon? A scientific comparison (Unreferenced) (not available link) . The appeal date is March 1, 2009. Archived April 9, 2008.
↑ Why is lightning colored? (gas excitations) (Neopr.) . The appeal date is March 1, 2009. Archived February 17, 2012.
↑ Narukawa Y. et al. White light emitting diodes with super-high luminous efficacy // J. Phys. D: Appl. Physics. - 2010. - Vol. 43, No. 35 . - DOI : 10.1088 / 0022-3727 / 43/35/354002 .
Ree Cree Sets New R & D Performance Record with 254 Lumen-Per-Watt Power LED - Cree, Inc. Press Release, April 12, 2012
↑ Cree News: Cree Sets New R & D Performance Record with 276 Lumen-Per-Watt Power LED
↑ By definition candela in the International System of Units (SI)
↑ Light return of the Sun - According to the materials of the publication by prof. P. Marx from the magazine "Licht"

[1] Light return. - Article in the Physical Encyclopedia

[Айзенберг-2] Reference book on lighting / Ed. Aizenberg Yu. B. - M .: Energoatomizdat, 1983. - 472 p.

[3] Details are given in the article Candela .

[4] The ratio of the magnitude of the light output to the value of the theoretical maximum, that is, to 683.002 lm / W.

[5] Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)

[philc-6] ¹ ² ³ ⁴ ⁵ Philips Product Catalog Archive dated July 15, 2011 on Wayback Machine (German)

[7] Osram halogen (German) (PDF) (not available link) . www.osram.de . The appeal date is January 28, 2008. Archived November 7, 2007.

[8] TSB: Kremlin stars // The Great Soviet Encyclopedia : [in 30 t.] / Ch. ed. A. M. Prokhorov . - 3rd ed. - M .: Soviet Encyclopedia, 1969-1978.

[bulbguide-9] Klipstein, Donald L. The Great Internet Light Bulb Book, Part I (Undefined) (inaccessible link) (1996) The appeal date is April 16, 2006. Archived June 1, 2012.

[LED-10] Klipstein, Donald L. (Undefined) . Don Klipstein's Web Site . The date of circulation is January 15, 2008. Archived on February 17, 2012.

[White_LED-11] Cree launches the new XLamp 7090 XR-E Series Power LED, the first 160-lumen LED! (Unsolved) (inaccessible link) . The appeal date is March 1, 2009. Archived February 17, 2012.

[12] Luxeon K2 with TFFC; Technical Datasheet DS60 (Unreferenced) (PDF). Philips Lumileds . The appeal date is April 23, 2008. Archived January 17, 2009.

[13] Ree Cree Breaks 200 Lumen Per Watt Efficacy Barrier (Unreferenced) (inaccessible link) . [Cree]. The appeal date is February 8, 2010. Archived on February 17, 2012.

[303_lumens_per_watt_Cree_LED-14] Mens Cree First to Break 300 Lumens-Per-Watt Barrier (Unc.) . The date of circulation is January 26, 2015. Archived January 26, 2015.

[xenon-15] Technical Information on Lamps (Unreferenced) (pdf). Optical Building Blocks . The date of circulation is October 14, 2007. Archived October 27, 2007. Note that the figure of 150 lm / W is given for this lamp. The page contains other useful information.

[16] OSRAM Lamp and Ballast Catalog. - 2007.

[17] TSB: light return // Great Soviet Encyclopedia : [in 30 tons.] / Ch. ed. A. M. Prokhorov . - 3rd ed. - M .: Soviet Encyclopedia, 1969-1978.

[sodium-18] ¹ ² LED or Neon? A scientific comparison (Unreferenced) (not available link) . The appeal date is March 1, 2009. Archived April 9, 2008.

[lightning-19] Why is lightning colored? (gas excitations) (Neopr.) . The appeal date is March 1, 2009. Archived February 17, 2012.

[20] Narukawa Y. et al. White light emitting diodes with super-high luminous efficacy // J. Phys. D: Appl. Physics. - 2010. - Vol. 43, No. 35 . - DOI : 10.1088 / 0022-3727 / 43/35/354002 .

[21] Ree Cree Sets New R & D Performance Record with 254 Lumen-Per-Watt Power LED - Cree, Inc. Press Release, April 12, 2012

[22] Cree News: Cree Sets New R & D Performance Record with 276 Lumen-Per-Watt Power LED

[23] By definition candela in the International System of Units (SI)

[24] Light return of the Sun - According to the materials of the publication by prof. P. Marx from the magazine "Licht"

Light efficiency

Sources of monochromatic radiation

Sources of radiation in general.

Examples

See also

Notes

More articles:

Light efficiency
$\eta$ ${\ displaystyle \ eta}$ $\ eta$
Dimension	J. M ^-1. L ^-2. T ³
Units
SI	lm W ^-1
Notes
scalar value