Illuminance

Illuminance diagram with units and terminology.

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. Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.

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

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 (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.

Common illuminance levels

File:Lux meter.jpg

A lux meter for measuring illuminances in work environments

Lighting condition	Foot-candles	Lux
Sunlight	10,000	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. V-magnitudes can be converted to lux using the formula $$E_{\mathrm{v}}=10^{(-14.18-m_{\mathrm{v}})/2.5},$$ 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 luminous intensity

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 the cosine law with the inverse-square law: $$E_{\mathrm{v}}=\frac{I_{\mathrm{v}}\cos (\theta )}{D^2}$$ where

• Template:Var_v is the luminous intensity of the source
• Template:Var is the angle of incidence, and
• Template:Var is the distance between the source and the surface.

Relation to luminance

File:Photometry radiometry units.svg

Comparison of photometric and radiometric quantities

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

• Template:Var_v is the surface's luminous exitance
• Template:Var_v is the received illuminance, and
• Template:Var 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 $$L_{\mathrm{v}}=\frac{E_{\mathrm{v}}R}{\pi }$$

See also

• Irradiance
• Exposure value
• Luminance

External links

• Illuminance Converter Template:Webarchive
• 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

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Luminous energy	Qv	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv	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−2⋅J	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−2⋅J	Luminous flux incident on a surface
Luminous exitance, luminous emittance	Mv	lumen per square metre	lm/m2	L−2⋅J	Luminous flux emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J	Time-integrated illuminance
Luminous energy density	ωv	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)	Template:Mvar	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient	Template:Mvar			1	Luminous efficacy normalized by the maximum possible efficacy
See also: Template:Hlist