Illuminance

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 Template:Val (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.Template:Citation needed

Common illuminance levels

A lux meter for measuring illuminances in work environments

Lighting condition	Foot-candles	Lux
Sunlight	10,000	100,000
Shade on a sunny day	Template:01,000	Template:010,000
Overcast day	Template:0100	Template:01,000
Very dark day	Template:010	Template:0100
Twilight	Template:01	Template:010
Deep twilight	Template:00.1	Template:01
Full moon	Template:00.01	Template:00.1
Quarter moon	Template:00.001	Template:00.01
Starlight	Template:00.0001	Template:00.001
Overcast night	Template:00.00001	Template:00.0001

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 luminance

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 Template:Math, 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.