Illuminance

Not to be confused with Luminance.

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
Common symbols	Ev
SI unit	lux
Other units	phot, foot-candle
In SI base units	cd·sr·m−2
Dimension	${\displaystyle {\mathsf {L}}^{-2}{\mathsf {J}}}$

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	01,000	010,000
Overcast day	00100	001,000
Very dark day	00010	000100
Twilight	00001	000010
Deep twilight	00000.1	000001
Full moon	00000.01	000000.1
Quarter moon	00000.001	000000.01
Starlight	00000.0001	000000.001
Overcast night	00000.00001	000000.0001

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] $${\displaystyle E_{\mathrm {v} }=10^{(-14.18-m_{\mathrm {v} })/2.5},}$$ where E_v is the illuminance in lux, and m_v is the apparent magnitude. The reverse conversion is $${\displaystyle m_{\mathrm {v} }=-14.18-2.5\log(E_{\mathrm {v} }).}$$

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

See also

• Irradiance
• Exposure value
• Luminance