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Illuminance

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Illuminance

Common symbols

Ev
SI unitlux

Other units

phot, foot-candle
In SI base unitscd·sr·m−2
Dimension
Illuminance diagram with units and terminology

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]

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

[edit]

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

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] where Ev is the illuminance in lux, and mv is the apparent magnitude. The reverse conversion is

Relation to luminous intensity

[edit]

When the light source is sufficiently far away to be treated as a point source, the illuminance on a surface is related to the luminous intensity of light it receives by combining[9][10] the cosine law with the inverse-square law: where

Relation to luminance

[edit]

Comparison of photometric and radiometric quantities

The luminance of a reflecting surface is related to the illuminance it receives: where the integral covers all the directions of emission ΩΣ, and

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

  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.
  2. ^ a b International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-060, illuminance
  3. ^ Luminous exitance Drdrbill.com
  4. ^ a b 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.
  9. ^ IES (2022). ANSI/IES LS-1-22, Lighting Science: Nomenclature And Definitions For Illuminating Engineering. New York: Illuminating Engineering Society. §9.1.2, cosine law. Retrieved 15 Dec 2025.
  10. ^ CIE (2020). e-ILV, online version of CIE S 017:2020, International Lighting Vocabulary (2 ed.). Vienna: International Commission on Illumination. §17-25-104, photometric distance law. Retrieved 15 Dec 2025.
  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.