Illuminance

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A lux meter for measuring illuminances in work environments.
Calculating illuminance at a point:[1] \begin{align}
E_v & = \frac{d\phi}{dA}\\
& =\frac{d\phi}{d\Omega} \times \frac{d\Omega}{dA}\\
& =\frac{d\phi}{d\Omega} \times \frac{d\Omega}{dS} \times \frac{dS}{dA}\\
& =I_v (\frac{\frac{dS}{r^2}}{ds})(\frac{dA \cos (\theta)}{dA})\\
& =\frac{I_v}{r^2}\cos(\theta)\\
& =\frac{I_v}{h^2}\cos^3(\theta)
\end{align}

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.[2]

In SI derived units these are measured in lux (lx) or lumens per square metre (cd·sr·m−2). 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.[3]

Illuminance was formerly often called brightness, but this leads to confusion with other uses of the word. "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]

Astronomy[edit]

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.[4] V-magnitudes can be converted to lux using the formula[5]

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

M_\mathrm{v} = -14.18-2.5 \log(E_\mathrm{v}).

See also[edit]

References[edit]

  1. ^ Jack L. Lindsey (1997). Applied Illumination Engineering. The Fairmont Press, Inc. pp. 215–219. ISBN 978-0-88173-212-2. 
  2. ^ Luminous exitance Drdrbill.com
  3. ^ One phot = 929.030400001 foot-candles, according to http://www.unitconversion.org/unit_converter/illumination.html
  4. ^ Schlyter, Paul. "Radiometry and photmetry in astronomy FAQ, section 7". 
  5. ^ "Formulae for converting to and from astronomy-relevant units". Retrieved Nov 23, 2013. 

External links[edit]

SI photometry units
Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Luminous energy Qv [nb 2] lumen second lm⋅s TJ [nb 3] units are sometimes called talbots
Luminous flux Φv [nb 2] lumen (= cd⋅sr) lm J [nb 3] also called luminous power
Luminous intensity Iv candela (= lm/sr) cd J [nb 3] an SI base unit, luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 L−2J units are sometimes called nits
Illuminance Ev lux (= lm/m2) lx L−2J used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx L−2J used for light emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2TJ
Luminous energy density ωv lumen second per metre3 lm⋅sm−3 L−3TJ
Luminous efficacy η [nb 2] lumen per watt lm/W M−1L−2T3J ratio of luminous flux to radiant flux
Luminous efficiency V 1 also called luminous coefficient
See also: SI · Photometry · Radiometry
  1. ^ Standards organizations recommend that photometric quantities be denoted with a suffix "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
  2. ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
  3. ^ a b c "J" here is the symbol for the dimension of luminous intensity, not the symbol for the unit joules.