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528 20. Light
20.3 Photometry
For every spectral radiometric quantity there is a related photometric quantity
that measures how much of that quantity is “useful” to a human observer. Given
a spectral radiometric quantity f
r
(λ), the related photometric quantity f
p
is
f
p
= 683
lm
W
800 nm
λ=380 nm
¯y(λ)f
r
(λ) dλ,
where ¯y is the luminous efficiency function of the human visual system. This
function is zero outside the limits of integration above, so the limits could be
0 and ∞ and f
p
would not change. The luminous efficiency function will be
discussed in more detail in Chapter 21, but we discuss its general properties here.
The leading constant is to make the definition consistent with historical absolute
photometric quantities.
The luminous efficiency function is not equally sensitive to all wavelengths
(Figure 20.8). For wavelengths below 380 nm (the ultraviolet range), the light is
not visible to humans and thus has a ¯y value of zero. From 380 nm it gradually
increases until λ = 555 nm where it peaks. This is a pure green light. Then, it
gradually decreases until it reaches the boundary of the infrared region at 800 nm.
Figure 20.8. The lu-
minous efficiency function
versus wavelength (nm).
The photometric quantity that is most commonly used in graphics is lumi-
nance, the photometric analog of radiance:
Y = 683
lm
W
800 nm
λ=380 nm
¯y(λ)L(λ) dλ.
The symbol Y for luminance comes from colorimetry. Most other fields use the
symbol L; we will not follow that convention because it is too confusing to use L
for both luminance and spectral radiance. Luminance gives one a general idea of
how “bright” something is independent of the adaptation of the viewer. Note that
the black paper under noonday sun is subjectively darker than the lower luminance
white paper under moonlight; reading too much into luminance is dangerous, but
it is a very useful quantity for getting a quantitative feel for relative perceivable
light output. The unit lm stands for lu mens. Note that most light bulbs are rated
in terms of the power they consume in watts, and the useful light they produce in
lumens. More efficient bulbs produce more of their light where ¯y is large and thus
produce more lumens per watt. A “perfect” light would convert all power into
555 nm light and would produce 683 lumens per watt. The units of luminance are
thus (lm/W)(W/(m
2
sr)) = lm/(m
2
sr). The quantity one lumen per steradian is
defined to be one candela (cd), so luminance is usually described in units cd/m
2
.