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16 Human eye sensitivity and photometric quantities Table 16.4. Photometric and corresponding radiometric units. Photometric unit Luminous flux Luminous intensity Illuminance Luminance Dimension lm lm / sr = cd lm / m2 = lux lm / (sr m2) = cd / m2 Radiometric unit Radiant flux (optical power) Radiant intensity Irradiance (power density) Radiance Dimension W W / sr W / m2 W / (sr m2) Exercise: Photometric units. A 60 W incandescent light bulb has a luminous flux of 1000 lm. Assume that light is emitted isotropically from the bulb. (a) What is the luminous efficiency (i.e. the number of lumens emitted per watt of electrical input power) of the light bulb? (b) What number of standardized candles emit the same luminous intensity? (c) What is the illuminance, Elum, in units of lux, on a desk located 1.5 m below the bulb? (d) Is the illuminance level obtained under (c) sufficiently high for reading? (e) What is the luminous intensity, Ilum, in units of candela, of the light bulb? (f) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux, and the luminous intensity, measured in candela. (g) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux, and the luminous flux, measured in lumen. (h) The definition of the cd involves the optical power of (1/683) W. What, do you suppose, is the origin of this particular power level? Solution: (a) 16.7 lm/W. (b) 80 candles. (c) Elum = 35.4 lm/m2 = 35.4 lux. (d) Yes. (e) 79.6 lm/sr = 79.6 cd. (f) Elum r2 = Ilum. (g) Elum 4πr2 = Φlum. (h) Originally, the unit of luminous intensity had been defined as the intensity emitted by a real candle. Subsequently the unit was defined as the intensity of a light source with specified wavelength and optical power. When the power of that light source is (1/683) W, it has the same intensity as the candle. Thus this particular power level has a historical origin and results from the effort to maintain continuity. 16.3 Eye sensitivity function The conversion between radiometric and photometric units is provided by the luminous efficiency function or eye sensitivity function, V(λ). In 1924, the CIE introduced the photopic eye sensitivity function V(λ) for point-like light sources where the viewer angle is 2° (CIE, 1931). This function is referred to as the CIE 1931 V(λ) function. It is the current photometric standard in the United States. A modified V(λ) function was introduced by Judd and Vos in 1978 (Vos, 1978; Wyszecki and Stiles, 1982, 2000) and this modified function is here referred to as the CIE 1978 V(λ) function. The modification was motivated by the underestimation of the human eye sensitivity in the blue and violet spectral region by the CIE 1931 V(λ) function. The modified function V(λ) has higher values in the spectral region below 460 nm. The CIE has endorsed the CIE 1978 V(λ) 280PDF Image | Human eye sensitivity and photometric quantities
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