Illuminance
Common symbols
Ev
SI unitlux
Other units
phot, foot-candle
In SI base unitscd·sr·m−2
DimensionL−2J
Illuminance diagram with units and terminology.

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

In SI units illuminance is measured in lux (lx), or equivalently in lumens per square metre (lm·m−2).[1] Luminous exitance is measured in lm·m−2 only, not lux.[3] 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.[4]

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, while at the bright end, it is possible to read large text at 108 lux, 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 [5] 107,527
Full daylight 1,000 10,752
Overcast day 100 1,075
Very dark day 10 107
Twilight 1 10.8
Deep twilight 0.1 1.08
Full moon 0.01 0.108
Quarter moon 0.001 0.0108
Starlight 0.0001 0.0011
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.[6] V-magnitudes can be converted to lux using the formula[7]

${\displaystyle E_{\mathrm {v} }=10^{(-14.18-m_{\mathrm {v} })/2.5))$,

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

${\displaystyle m_{\mathrm {v} }=-14.18-2.5\log(E_{\mathrm {v} })}$.

## Relation to luminance

Comparison of photometric and radiometric quantities

The luminance of a reflecting surface is related to the illuminance it receives:

${\displaystyle \int _{\Omega _{\Sigma ))L_{\mathrm {v} }\mathrm {d} \Omega _{\Sigma }\cos \theta _{\Sigma }=M_{\mathrm {v} }=E_{\mathrm {v} }R}$
where the integral covers all the directions of emission 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

${\displaystyle L_{\mathrm {v} }={\frac {E_{\mathrm {v} }R}{\pi ))}$

## References

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

Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol[nb 2]
Luminous energy Qv[nb 3] lumen second lm⋅s T J The lumen second is sometimes called the talbot.
Luminous flux, luminous power Φv[nb 3] lumen (= candela steradian) lm (= cd⋅sr) J Luminous energy per unit time
Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr) J Luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 (= lm/(sr⋅m2)) L−2J Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance Ev lux (= lumen per square metre) lx (= lm/m2) L−2J Luminous flux incident on a surface
Luminous exitance, luminous emittance Mv lumen per square metre lm/m2 L−2J Luminous flux emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2T J Time-integrated illuminance
Luminous energy density ωv lumen second per cubic metre lm⋅s/m3 L−3T J
Luminous efficacy (of radiation) K lumen per watt lm/W M−1L−2T3J Ratio of luminous flux to radiant flux
Luminous efficacy (of a source) η[nb 3] lumen per watt lm/W M−1L−2T3J Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient V 1 Luminous efficacy normalized by the maximum possible efficacy