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Principles of Radiometry and Photometry 275

angle subtended by a unit area angle subtended by a unit area
of the surface from the source. of the surface from the source.
2
H N sin E B sin
2
H is the irradiance produced by a E is the illumination produced by
diffuse circular source of radiance a diffuse circular source of brightness
N at a point from which the (luminance) B at a point from which
source diameter subtends 2 . the source diameter subtends 2 .

H N E B
H is the irradiance produced by a E is the illumination produced by
diffuse source of radiance N at a a diffuse source of brightness B
point from which the area of the at a point from which the area of the
source subtends the solid angle . source subtends the solid angle .

2
H T N sin E T B sin T B/4(f/#) (m 1) 2
2
2
s′

m
(H TN ) (E TB ) f 1
H is the irradiance at an image E is the illumination at an image
formed by an optical system of formed by an optical system of trans-
transmission T the exit pupil mission T the exit pupil diameter
diameter (area) of which subtends (area) of which subtends an angle 2
an angle 2 (solid angle ) from (solid angle ) from the image point
the image point when object when the object brightness is B.
radiance is N.
Radiance: N P/( A) Brightness (luminance):
B F/( A)
N is the radiance of a diffuse source B is the brightness of a diffuse
of area A which emits radiant power source of area A which emits
P into a hemisphere of 2 steradians. luminous flux F into a hemisphere
of 2 steradians.

Example 12.3
It may be instructive to repeat Example 12.1 in photometric terms and
to indicate at each step in the calculation the conversions to the vari-
ous photometric units. We will use Fig. 12.4 again; the only change in
the starting data will be that the source A will be assumed to have a
2
brightness of 10 lumens ster 1 cm .
From Fig. 12.10, we note that the source brightness may also be
2
expressed as 10 candles cm , as 10 stilb, as 10 lamberts, or as 9290
foot-lamberts.