Surface normals FIGURE 31.5 Surface being illuminated by an extended source Illumination of surface element dA is calculated by tness and illumination The flux density of a light beam emitted from a point source decreases with the square of distance from it. Light sources are typically extended sources(being larger than point sources). The illumination of a surface from light emitted from an extended source can be calculated using Fig. 31.5. The flux incident on a surface element dA from a source element dS is given by b dA cos e dS The constant B is called the luminance or photometric brightness of the source. Its units are candles per square neter(1 stilb T lamberts)and dE is the luminous flux in lumens. The total illumination e of the surface element is calculated by integrating over the source. The illuminance or flux density on the surface is thus 、E (lumens/cm) (31.15) Two methods are commonly used for quantifying light energy, namely, the radiometric unit of watts and the photometric unit of candelas. The candela is an energy unit which is derived from light emission from a blackbody source. The two can be related using the relative visibility curve V(n), which describes the eye's sensitivity to the visible light spectrum, it being maximum near a wavelength of 550 nm. The constant which relates lumens to watts at this wavelength is 685 Im/W. The luminous flux emitted by a source can therefore be written as F=685 v()P()d7(lumens) (31.16) where V is the spectral response of the eye and P is the source radiant intensity in watts. The source radiance is normally stated as luminance in candle per square centimeter(1 lumen per steradian per square centimeter)or radiance in watts per square centimeter per steradian per nanometer. The lumen is defined as the luminous flux emitted into a solid angle of a steradian by a point source of intensity 1/60th that of a 1-cm blackbody source held at 2042 K temperature(molten platinum c2000 by CRC Press LLC
© 2000 by CRC Press LLC Brightness and Illumination The flux density of a light beam emitted from a point source decreases with the square of distance from it. Light sources are typically extended sources (being larger than point sources). The illumination of a surface from light emitted from an extended source can be calculated using Fig. 31.5. The flux incident on a surface element dA from a source element dS is given by (31.14) The constant B is called the luminance or photometric brightness of the source. Its units are candles per square meter (1 stilb = p lamberts) and dE is the luminous flux in lumens. The total illumination E of the surface element is calculated by integrating over the source. The illuminance or flux density on the surface is thus (31.15) Two methods are commonly used for quantifying light energy, namely, the radiometric unit of watts and the photometric unit of candelas. The candela is an energy unit which is derived from light emission from a blackbody source. The two can be related using the relative visibility curve V(l), which describes the eye’s sensitivity to the visible light spectrum, it being maximum near a wavelength of 550 nm. The constant which relates lumens to watts at this wavelength is 685 lm/W. The luminous flux emitted by a source can therefore be written as (31.16) where V is the spectral response of the eye and P is the source radiant intensity in watts. The source radiance is normally stated as luminance in candle per square centimeter (1 lumen per steradian per square centimeter) or radiance in watts per square centimeter per steradian per nanometer. The lumen is defined as the luminous flux emitted into a solid angle of a steradian by a point source of intensity 1/60th that of a 1-cm2 blackbody source held at 2042 K temperature (molten platinum). FIGURE 31.5 Surface being illuminated by an extended source. Illumination of surface element dA is calculated by summing the effects of elements dS. dE B dA dS r = cos q y cos 2 I E dA = (lumens/cm ) 2 F = V P d Ú 685 (l) (l) l (lumens)
100000 3000 deg K 10000 4000 deg K FIGURE 31.6 Plot of blackbody radiation for a series of temperatures. Radiation is in watts into a hemisphere direction from a l-cm2 of surface in a 1-um wavelength band. Thermal Sources Objects emit and absorb and as their temperature is increased the amount of radiation emitted increases. In addition the istribution changes, with proportionally more radiation emitted at shorter wavelengths. A blackbody s a surface which absorbs all radiation incident upon it, and Kirchhoff constant wB (31.17) stating that the ratio of emitted to absorbed radiation is a constant a at a given temperature. The energy or wavelength distribution for a blackbody is given by Plancks law W C (watts/cm area per um wavelength) 入 c1=3.7413×10 (31.18) C2=1.4380×10 Tis in degrees Kelvin, A is in micrometers, and w is the power emitted into a hemisphere direction. Blackbody radiation is incoherent, with atoms or molecules emitting radiation independently. Figure 31. 6 is a plot of the blackbody radiation spectrum for a series of temperatures ery few materials are true blackbodies; carbon lampblack is one. For this reason a surface emissivity is used which describes the ratio of actual radiation emitted to that from a perfect blackbody. Table 31.2 is a listing of emissivities for some common materials Tungsten Filament Lamp In the standard incandescent lamp a tungsten filament is heated to greater than 2000oC, and it is protected from oxidation and vaporization by an inert gas. In a quartz halogen lamp the envelope is quartz, which allows e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Thermal Sources Objects emit and absorb radiation, and as their temperature is increased the amount of radiation emitted increases. In addition, the spectral distribution changes, with proportionally more radiation emitted at shorter wavelengths. A blackbody is defined as a surface which absorbs all radiation incident upon it, and Kirchhoff’s law of radiation is given by (31.17) stating that the ratio of emitted to absorbed radiation is a constant a at a given temperature. The energy or wavelength distribution for a blackbody is given by Planck’s law (31.18) T is in degrees Kelvin, l is in micrometers, and W is the power emitted into a hemisphere direction. Blackbody radiation is incoherent, with atoms or molecules emitting radiation independently. Figure 31.6 is a plot of the blackbody radiation spectrum for a series of temperatures. Very few materials are true blackbodies; carbon lampblack is one. For this reason a surface emissivity is used which describes the ratio of actual radiation emitted to that from a perfect blackbody. Table 31.2 is a listing of emissivities for some common materials. Tungsten Filament Lamp In the standard incandescent lamp a tungsten filament is heated to greater than 2000°C, and it is protected from oxidation and vaporization by an inert gas. In a quartz halogen lamp the envelope is quartz, which allows FIGURE 31.6 Plot of blackbody radiation for a series of temperatures. Radiation is in watts into a hemisphere direction from a 1-cm2 of surface in a 1-mm wavelength band. W a = constant = WB W c c T c c = Ê Ë Á ˆ ¯ ˜ - È Î Í Í ˘ ˚ ˙ ˙ = ¥ = ¥ - 1 5 2 1 4 4 1 3 7413 10 1 4380 10 l l exp m . . (watts/cm area per m wavelength) 2 1 2