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Function
Essentially, there is one calculation for measuring light output at the source, and a second for measuring the product of the light's output. Illuminance, measured in lumens, measures the amount of light falling on the objects being illuminated. One lumen is equivalent to one foot candle, or the total brightness one foot from the light source. A person standing one foot from a lit candle in an otherwise dark room, perceives one foot candle of light. Radiance measures the energy emitted at the light source.
Significance
Light sources, such as light bulbs, release thousands of light rays in every direction. The quantity of light rays, or candlepower, are stated in candelas, or lumens per steradian, or cone-shaped segments expanding from the light source. Stage and movie lighting apply the inverse square law to calculate the amount of lumens delivered at specific distances. The lamp's candlepower is divided by the distance squared. Because the rays diverge when distance from the light source increases, the amount of illuminance drops by half; so, a two foot area receives 1/4 the light, a 3-foot area receives 1/9 the light.
Considerations
Lumens don't gauge the amount of brightness. A lumen is like a light ray. In essence, the amount of lumens produced is equal to the amount of brightness perceived. This is only taking into consideration the visible light perceived by the eyes and optical center of the brain. It's a subjective measurement.
Identification
Luminous intensity (I), a function of direction, is measured in candela (cd). One lumen (lm) per steradian is equal to the radius squared from the center of the light bulb; so the complete angle from the center of a sphere (i.e. a light bulb) = 4 π I lm. A new 60W tungsten incandescent lamp supplies 870 lm. Foot candles gauge the number of light rays illuminating a 1 foot square area, a LUX gauges the number of rays falling on a 1 m2 area and a phot gauges illumination on a 1 centimeter2 area. They are all measures of illumination at different scales.
Size
At the maximum sensitivity of the human eye, 680 lumens (lm) equals 1W (watt). For determining foot candles, if say, the light sources uses 100 lm to illuminate a 2 ft2 area, the average amount of light put out would be 100 lm/2 ft, or 50 foot-candles. This formula calculates the foot-candles for any distance at right angles to the light source. Luminance is calculated as candela (cd)/ m2. One lumen (lm) equals one candela (cd), 1 lumen second = 0.001464 joules or 10,000 LUX seconds. One lumen steradian also equals 1 candela.