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The lumen is defined as amount of light given into one steradian by a point source of one candela strength; while the candela, a base SI unit, is defined as the luminous intensity of a source of monochromatic radiation, of frequency 540 terahertz, and a radiant intensity of 1/683 watts per steradian.
The luminous flux is a weighted sum of the power at all wavelengths in the visible band. Light outside the visible band does not contribute. The ratio of the total luminous flux to the radiant flux is called the luminous efficacy. This model of the human visual brightness perception, is standardized by the CIE and ISO. [5]
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).
Luminous energy is related to radiant energy by the expression = / ¯ (). Here λ {\displaystyle \lambda } is the wavelength of light, and y ¯ ( λ ) {\displaystyle {\overline {y}}(\lambda )} is the luminous efficiency function , which represents the eye's sensitivity to different wavelengths of light.
Luminous efficacy of radiation measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing the luminous flux by the radiant flux. [4] Light wavelengths outside the visible spectrum reduce luminous efficacy, because they contribute to the radiant flux, while the luminous flux of such light is zero ...
In the field of photometry (optics), the luminous transmittance of a filter is a measure of the amount of luminous flux or intensity transmitted by an optical filter. It is generally defined in terms of a standard illuminant (e.g. Illuminant A, Iluminant C, or Illuminant E).
Luminous energy density ω v: lumen second per cubic metre lm⋅s/m 3: L −3 ⋅T⋅J: Luminous efficacy (of radiation) K: lumen per watt: lm/W: M −1 ⋅L −2 ⋅T 3 ⋅J: Ratio of luminous flux to radiant flux: Luminous efficacy (of a source) η [nb 3] lumen per watt: lm/W: M −1 ⋅L −2 ⋅T 3 ⋅J: Ratio of luminous flux to power ...
Example: A surface with a luminance of say 100 cd/m 2 (= 100 nits, typical PC monitor) will, if it is a perfect Lambert emitter, have a luminous emittance of 100π lm/m 2. If its area is 0.1 m 2 (~19" monitor) then the total light emitted, or luminous flux, would thus be 31.4 lm.