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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).
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.
Ratio of luminous flux to radiant flux: Luminous efficacy (of a source) η [nb 8] lumen per watt: lm/W: M −1 ⋅L −2 ⋅T 3 ⋅J: Ratio of luminous flux to power consumption Luminous efficiency, luminous coefficient V: 1: Luminous efficacy normalized by the maximum possible efficacy See also:
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.
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.
The luminance of a specified point of a light source, in a specified direction, is defined by the mixed partial derivative = where L v is the luminance ( cd / m 2 ); d 2 Φ v is the luminous flux ( lm ) leaving the area dΣ in any direction contained inside the solid angle dΩ Σ ;
The vector approach defines flux density as a vector at a point of space and time prescribed by the investigator. To distinguish this approach, one might speak of the 'full spherical flux density'. In this case, nature tells the investigator what is the magnitude, direction, and sense of the flux density at the prescribed point.