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The luminosity function is a standard function established by the Commission Internationale de l'Éclairage to account for the variable sensitivity of the human eye to radiation at different wavelengths. It converts radiant energy into luminous (i.e. visible) energy. It also forms the central color matching function in the CIE 1931 color space. For the standard conditions chosen in establishing this standard luminosity function (photopic vision), the luminous flux, L, in lumens is given by where (also known as ) is the standard luminosity function, and is the spectral intensity of the radiation, in watts per unit wavelength. The standard luminosity function is normalized to a peak value of unity at 555 nm (see luminous coefficient). The value of the constant in front of the integral is usually rounded off to 683 lumens/watt. The small excess fractional value comes from the slight mismatch between the definition of the lumen and the peak of the luminosity function. The lumen is defined to be unity for a radiant energy of 1/683 watt at a frequency of 540x1012 Hz, which corresponds to a standard air wavelength of 555.016 nm rather than 555 nm, which is the peak of the luminosity curve. The value of is 0.999997 at 555.016 nm, so that a value of 683/0.999997=683.002 is the multiplicative constant (Wyszecki & Stiles, 2000). (red) and scotopic http://www.cvrl.org/database/text/lum/scvl.htm (green) luminosity functions. The photopic includes the CIE 1931 standard http://www.cvrl.org/database/text/cmfs/ciexyz31.htm (solid), the Judd-Vos 1978 modified data http://www.cvrl.org/database/text/lum/vljv.htm (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data http://www.cvrl.org/database/text/lum/ssvl2.htm (dotted)
Improvements to the standard The CIE 1931 color-matching functions, which include the CIE 1924 photopic luminosity function as the y function, have long been acknowledged to underestimate the contribution of the blue end of the spectrum to perceived luminance. There have been numerous attempts to improve the standard function, to make it more representative of human vision*. Judd in 1951, improved by Vos in 1978, resulted in a function known as CIE . More recently, Sharpe, Stockman, Jagla & Jägle (2005) developed a function consistent with the Stockman & Sharpe cone fundamentals.* These curves are plotted in the figure above. Scotopic luminosity For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the violet, peaking around 507 nm for young eyes; the sensitivity is in some sense equivalent to 1746 lumens/watt at this peak. The standard scotopic luminosity function or was adopted by the CIE in 1951, based on measurements by Wald (1945) and by Crawford (1949).* | ||||||||
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