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Principles of Radiometry and Photometry 271

the integral (or summation) of P( ) V( ) d over the appropriate wave-
length interval. From the definition of the lumen, it can be deter-
mined that one watt of radiant energy at the wavelength of maximum
visual sensitivity (0.555 m) is equal to 680 lumens. Therefore, the
luminous flux emitted by a source with a spectral power of P( ) W m 1
is given by*

F 680
V ( ) P ( ) d lumens (12.18)

The unit of luminous intensity is called the candle (or “candela”) and
is so named because the original standard of intensity was an actual
candle. A point source of one candlepower is one which emits one lumen
into a solid angle of one steradian. A source of one candle intensity
which radiates uniformly in all directions emits 4 lumens. From the
2
definition of the lumen, it is apparent that a 1-cm blackbody at 2042 K
has an intensity of 60 candles.
Illumination, or illuminance, is the luminous flux per unit area inci-
dent on a surface. The most widely used unit of illumination is the
foot-candle. One footcandle is one lumen incident per square foot. The
misleading name footcandle resulted from the fact that it is the illu-
mination produced on a surface one foot away from a source of one-candle
intensity. The photometric term illuminance corresponds to irradiance
in radiometry.
The term brightness, or luminance, corresponds to the term radiance.
Brightness is the luminous flux emitted from a surface per unit solid
angle per unit of area (projected on a plane normal to the line of sight).
There are several commonly used units of brightness. The candle per
square centimeter is equal to one lumen emitted per steradian per
square centimeter. The lambert is equal to 1/ candles per square cen-
timeter. The foot-lambert is equal to 1/ candles per square foot. The
foot-lambert is a convenient unit for illuminating engineering work,
since it is the brightness which results from one footcandle of illumi-
nation falling on a “perfect” diffusing surface. (Since one lumen is inci-
2
dent on the 1-ft area under an illumination of one footcandle, the total
flux radiated into a hemisphere of 2 ster. from a perfectly diffuse
(lambertian) surface is just one lumen. As pointed out in Sec. 12.4
2
and Example 12.1, the resulting brightness is 1/ lumen ster 1 ft ,

*Since the constant 680 in Eq. 12.18 is derived by numerical integration of a table of
measured values, this number is not an exact constant; a value of 683 is also used.