Illuminance

Illuminance
Illuminance
Common symbols	Ev
SI unit	lux
Other units	phot, foot-candle
In SI base units	cd·sr·m−2
Dimension

In photometry, illuminance is the total luminous flux incident on a surface, per unit area.^[1] 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.^[2] Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.^[3]^[4]

Illuminance diagram with units and terminology. — Illuminance diagram with units and terminology

In SI units illuminance is measured in lux (lx), or equivalently in lumens per square metre (lm·m⁻²).^[2] Luminous exitance is measured in lm·m⁻² only, not lux.^[4] In the CGS system, the unit of illuminance is the phot, which is equal to 10000 lux. The foot-candle is a non-metric unit of illuminance that is used in photography.^[5]

Illuminance was formerly often called brightness, but this leads to confusion with other uses of the word, such as to mean luminance. "Brightness" should never be used for quantitative description, but only for nonquantitative references to physiological sensations and perceptions of light.

The human eye is capable of seeing somewhat more than a 2 trillion-fold range. The presence of white objects is somewhat discernible under starlight, at 5×10⁻⁵ lux (50 μlx), while at the bright end, it is possible to read large text at 10⁸ lux (100 Mlx), or about 1000 times that of direct sunlight, although this can be very uncomfortable and cause long-lasting afterimages.^{[citation needed]}

Common illuminance levels

A lux meter for measuring illuminances in work environments

Lighting condition	Foot-candles	Lux
Sunlight	10,000 ^[6]	100,000
Shade on a sunny day	1,000	10,000
Overcast day	100	1,000
Very dark day	10	100
Twilight	1	10
Deep twilight	0.1	1
Full moon	0.01	0.1
Quarter moon	0.001	0.01
Starlight	0.0001	0.001
Overcast night	0.00001	0.0001

Astronomy

In astronomy, the illuminance stars cast on the Earth's atmosphere is used as a measure of their brightness. The usual units are apparent magnitudes in the visible band.^[7] V-magnitudes can be converted to lux using the formula^[8] $E_{\mathrm {v} }=10^{(-14.18-m_{\mathrm {v} })/2.5},$ where E_v is the illuminance in lux, and m_v is the apparent magnitude. The reverse conversion is $m_{\mathrm {v} }=-14.18-2.5\log(E_{\mathrm {v} }).$

Relation to luminance

Comparison of photometric and radiometric quantities

The luminance of a reflecting surface is related to the illuminance it receives: $\int _{\Omega _{\Sigma }}L_{\mathrm {v} }\mathrm {d} \Omega _{\Sigma }\cos \theta _{\Sigma }=M_{\mathrm {v} }=E_{\mathrm {v} }R$ where the integral covers all the directions of emission $Ω Σ$ , and

M_v is the surface's luminous exitance
E_v is the received illuminance, and
R is the reflectance.

In the case of a perfectly diffuse reflector (also called a Lambertian reflector), the luminance is isotropic, per Lambert's cosine law. Then the relationship is simply $L_{\mathrm {v} }={\frac {E_{\mathrm {v} }R}{\pi }}$

References

^ "Illuminance, 17-21-060". CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition. CIE - International Commission on Illumination. 2020. Retrieved 20 April 2023.
^ ^a ^b International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-060, illuminance
^ Luminous exitance Drdrbill.com
^ ^a ^b International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-081, luminous exitance
^ One phot = 929.030400001 foot-candles, according to http://www.unitconversion.org/unit_converter/illumination.html
^ "Illuminance - Recommended Light Level". The Engineering ToolBox. Archived from the original on April 3, 2022. Retrieved July 7, 2022.
^ Schlyter, Paul. "Radiometry and photometry in astronomy FAQ, section 7".
^ "Formulae for converting to and from astronomy-relevant units" (PDF). Archived from the original (PDF) on December 2, 2013. Retrieved Nov 23, 2013.

External links

Illuminance Converter Archived 2010-02-10 at the Wayback Machine
Knowledgedoor, LLC (2005) Library of Units and Constants: Illuminance Quantity
Kodak's guide to Estimating Luminance and Illuminance using a camera's exposure meter. Also available in PDF form.

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

^ 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
^ ^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.

[1] "Illuminance, 17-21-060". CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition. CIE - International Commission on Illumination. 2020. Retrieved 20 April 2023.

[IEC_845-21-060-2] International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-060, illuminance

[3] Luminous exitance Drdrbill.com

[IEC_845-21-081-4] International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-081, luminous exitance

[5] One phot = 929.030400001 foot-candles, according to http://www.unitconversion.org/unit_converter/illumination.html

[6] "Illuminance - Recommended Light Level". The Engineering ToolBox. Archived from the original on April 3, 2022. Retrieved July 7, 2022.

[7] Schlyter, Paul. "Radiometry and photometry in astronomy FAQ, section 7".

[8] "Formulae for converting to and from astronomy-relevant units" (PDF). Archived from the original (PDF) on December 2, 2013. Retrieved Nov 23, 2013.

[note-dimension-symbol-9] 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-10] 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-11] Alternative symbols sometimes seen: $W$ for luminous energy, $P$ or $F$ for luminous flux, and $ρ$ for luminous efficacy of a source.

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