Candela
a) Origin
The candela (symbol : cd) is the SI base unit of luminous intensity; that is, luminous power per unit solid angle emitted by a point light source in a particular direction. The word candela means candle in Latin. A common candle emits light with roughly 1 cd luminous intensity.
b) History
Before 1948, there were various standards in various countries for luminous intensity measurement, typically based on the brightness of flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design, one of them being candlepower, used in England. 1 candlepower was the light produced by a pure spermaceti candle weighing 1/6th of a pound and burning at a rate of 120 grains per hour. Another was Hefnerkerze, a unit based on the output of a Hefner lamp. This was used in Germany, Austria and Scandinavia.After this Jules Violle had proposed a standard based on the light emitted by 1 cm2 of platinum at its melting point (or freezing point), calling this the Violle. The light intensity was due to the Planck radiator (a black body) effect, and was thus independent of the construction of the device. This made it easy for anyone to measure the standard, as high-purity platinum was widely available and easily prepared. The International Commission on Illumination and the CIPM proposed a “new candle” based on this basic concept. However, in the year 1946 the value of the new unit was chosen to make it similar to the earlier unit candlepower by dividing the Violle by 60. The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per cm2.
It was then ratified in 1948 by the 9th CGPM which adopted a new name for this unit, the candela. In 1967 the 13th CGPM removed the term "new candle" and gave an amended version of the candela definition, specifying the atmospheric pressure applied to the freezing platinum:
The candela is the luminous intensity, in the perpendicular direction, of a surface of 1 / 600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre.In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, the 16th CGPM adopted the modern definition of the candela. The arbitrary (1/683) term was chosen so that the new definition would exactly match the old definition. Although the candela is now defined in terms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.
c) Definition
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1683 watt per steradian.d) Explanation
The human eye is most sensitive to a frequency in the visible spectrum near green (wavelength of 555 nanometres), when adapted for bright conditions. More radiant intensity is needed to achieve the same luminous intensity for other frequencies. The luminous intensity for light of a particular wavelength λ is given by
where Iv(λ) is the luminous intensity in candelas,
lm is short for lumen,
W for watt,
Ie(λ) is the radiant intensity in W/sr and
ȳ(λ) is the standard luminosity function (photopic).
If more than one wavelength is present (as is usually the case), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.
Lumens and Lux
a) Introduction
Lumen (symbol: lm) is the SI derived unit of luminous flux. It measures the total quantity of visible light emitted by a source. Power or radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a luminosity function of the human eye's sensitivity to various wavelengths.(Full moon=1 lux, Direct sunlight=100000lux)
Relationship between lumens and lux is:-
1 lux = 1 lm/m2
The lumen is defined in relation to the candela as
1 lm = 1 cd ⋅ sr.
A whole sphere has a solid angle of 4π steradians, so an isotropic light source has a total luminous flux of
1 cd × 4π sr = 4π cd⋅sr ≈ 12.57 lumens.
b) Lighting
Lamps used for lighting are commonly labelled with their light output in lumens; this is required by law in many places.A 23 W spiral compact fluorescent lamp (CFL) emits about 1,400–1,600 lm. Many CFL lamps, LED lamps and other alternative light sources are labelled as being equivalent to an incandescent bulb with a specific (generally higher) wattage. Below is a table that shows typical luminous flux for common incandescent bulbs and their equivalents.
Electrical
power equivalents for differing lamps
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Minimum
light
output (lumens)
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Electrical
power consumption (watts)
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120
V Incandescent
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CFL
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LED
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200
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25W
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3-5W
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3W
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450
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40W
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9–11W
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5–8W
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800
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60W
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13–15W
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8–12W
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1,100
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75W
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18–20W
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10–16W
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1,600
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100W
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24–28W
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14–17W
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2,400
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150W
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30–52W
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24-30W
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3,100
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200W
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49–75W
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32W
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4,000
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300W
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75–100W
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40.5W
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|
c) Explanation
If a light source emits 1 candela of luminous intensity uniformly across a solid angle of 1 steradian, the total luminous flux emitted into that angle is 1 lumen (1 cd·1 sr = 1 lm). Alternatively, an isotropic 1 candela light-source emits a total luminous flux of exactly 4π lumens. If the source were partly covered by an ideal absorbing hemisphere, that system would radiate half the luminous flux—only 2π lumens. The luminous intensity would still be 1 candela in those directions that are not obscured.The lumen can be taken as a measure of the total amount of visible light in some defined angle, or emitted from some source. The number of candelas or lumens from a source also depends on its spectrum, via the nominal response of the human eye as represented in the luminosity function.
The difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread. A flux of 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. The same 1000 lumens, spread out over 10m2, produces a dimmer illuminance of only 100 lux. Mathematically, 1 lux = 1 lm/m2.
A source radiating a power of 1 watt of light in the color for which the eye is most efficient (a wavelength of 555 nm, in the green region of the visible spectrum) has luminous flux of 683 lumens. So a lumen represents at least 1/683 watts of visible light power, depending on the spectral distribution.
The projected surface area mentioned above follows a cosine law, i.e. the projected area is given by
Aprojected = Asurface cos Θ
where Θ is the angle between the direction considered and the surface normal. This is known as Lambert's cosine law. The light-emitting surface area and the projected area are shown in the figure below.
For LEDs, it is desirable to maximize luminous intensity and luminous flux while keeping the LED chip area minimal. Thus the luminance is a measure of how efficiently the valuable semiconductor wafer area is used to attain, at a given injection current, a certain luminous intensity.
