Φv=dQvdt
where Qv is the luminous energy emitted, transferred or received, and t is time
Note 1 to entry: Luminous flux is a quantity derived from the radiant flux, Φe, by evaluating the radiation according to its action upon the CIE standard photometric observer. Luminous flux can be derived from the spectral radiant flux distribution by
Φv=Km∞∫0Φe,λ(λ) V(λ) dλ
where Km is maximum luminous efficacy, Φe,λ(λ) is spectral radiant flux, V(λ) is spectral luminous efficiency and λ is wavelength.
Note 2 to entry: The distribution of the luminous intensities as a function of the direction of emission, e.g. given by the polar angles (ϑ, φ), is used to determine the luminous flux, Φv, within a certain solid angle, Ω, of a source:
Φv=∬.
Note 3 to entry: The corresponding radiometric quantity is "radiant flux". The corresponding quantity for photons is "photon flux".
Note 4 to entry: The luminous flux is expressed in lumen (lm).
Note 5 to entry: This entry was numbered 845-01-25 in IEC 60050-845:1987.
Φ v = d Q v dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai abfA6agnaaBaaaleaacaqG2baabeaakiabg2da9maalaaabaGaaeiz aiaadgfadaWgaaWcbaGaaeODaaqabaaakeaacaqGKbGaamiDaaaaaa a@3FA4@
Φ v = K m ∫ 0 ∞ Φ e,λ (λ) V(λ) dλ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai abfA6agnaaBaaaleaacaqG2baabeaakiabg2da9iaadUeadaWgaaWc baGaaeyBaaqabaGcdaWdXbqaaiabfA6agnaaBaaaleaacaqGLbGaae ilaiabeU7aSbqabaGccaGGOaGaeq4UdWMaaiykaiaaykW7caaMc8Ua amOvaiaacIcacqaH7oaBcaGGPaGaaGPaVlaacsgacqaH7oaBaSqaai aaicdaaeaacqGHEisPa0Gaey4kIipaaaa@547F@
Φ v = ∬ Ω I v ( ϑ,φ )sinϑ dφ dϑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai abfA6agnaaBaaaleaacaqG2baabeaakiabg2da9maapifabaGaamys amaaBaaaleaacaqG2baabeaakmaabmaabaGaeqy0dOKaaiilaiabeA 8aQbGaayjkaiaawMcaaiaabohacaqGPbGaaeOBaiabeg9akjaabcca caqGKbGaeqOXdOMaaeiiaiaabsgacqaHrpGsaSqaaiabfM6axbqab0 Gaey4kIiVaey4kIipaaaa@52FC@ .