Graphics Reference
In-Depth Information
(see Figure 28.1) produces light at many wavelengths; the combination of these
makes us perceive “white.” By contrast, a laser pointer uses a light-emitting diode
(LED) to create light of a single wavelength, usually around 650 nm, which we
perceive as “red.”
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0.10
0.08
0.06
The
spectral power distribution
or
SPD
is a function describing the power
in a light beam at each wavelength. It can take on virtually any shape (as long as
it's everywhere non-negative). Filters are available that allow only certain wave-
lengths, or wavelength regions, to pass through the filters; clever combinations
of these allow one to create almost any possible spectral power distribution.
We can add two such functions to get a third, or multiply such a function by a
positive constant to get a new one. Thus, the set of all spectral power distri-
bution functions forms a
convex cone
in the vector space of all functions on the
interval
[
400 nm, 700 nm
]
. The possibility of creating almost any function means
that this cone is infinite-dimensional; in particular, the spectral power distributions
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350 400 450 500 550 600 650 700
Wavelength - nm
750
Figure 28.1: The spectral power
distribution of a fluorescent lamp.
The power emitted at each wave-
length varies fairly smoothly
across the spectrum, with a
few high peaks. Figure provided
courtesy of Osram Sylvania, Inc.
)=
1f
s
≤ λ ≤
s
+
1
P
s
(
λ
(28.1)
0
otherwise,
where
s
ranges over integers between 400 and 699, are all linearly independent,
so the space is at least 299-dimensional. By making the “spikes” in the function
narrower and the spacing closer, it's easy to see that the number of linearly inde-
pendent functions is arbitrarily large.
By contrast, as we'll see in later sections, the set of color
percepts,
or color
sensations, is three-dimensional; to the degree that the mapping from spectral
power distributions to percepts is linear, it must be many-to-one. Indeed, for any
given percept, there must be an infinite-dimensional family of SPDs that give rise
to that percept.
Certain SPDs are both important and easy to understand: These are the
monospectral
distributions, in which nearly all the power is at or very near to
a single wavelength (see Figure 28.2).
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1.0
0.8
Infrared
ray
range
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0.4
0.2
0
300
400
500
600
700
800
900
Wavelength (nm)
Spectral distributions of LEDs
Blue (470 nm)
Green (525 nm)
Red (660 nm)
FarRed (735 nm)
Figure 28.2: The spectral power
distributions of several LEDs.
The light is concentrated at or
near a single wavelength for each
kind of LED; an ideal monospec-
tral source would have all energy
at a single wavelength.
One reason that these are interesting is that all other SPDs can be written
as (infinite) linear combinations of them, so they play the role of a basis for the
set of SPDs.
A pure monospectral light cannot (in our model of light) carry any energy,
because the energy is described in part by an integral over wavelength. So when
we speak of “monospectral” lights, you should think of a light whose spectrum is
entirely in the interval from 650 nm to 650.01 nm, for example.
Describing an SPD requires either tabulating its (infinitely many) values, or
somehow presenting summary information. In practice, real SPDs are tabulated
at finitely many values using a spectroradiometer, but even these tabulated values
may need to be summarized. In
colorimetry,
the terms
dominant wavelength,
excitation purity,
and
luminance
are used to present such summaries; these vary
in utility depending on the shape of the SPD. For the highly contrived SPD of Fig-
ure 28.3, the
dominant wavelength
is 500 nm. The
excitation purity
is defined in
terms of the relative amounts of the dominant wavelength and the broad-spectrum
light: If
e
1
is zero and
e
2
is large, then the excitation purity is 100%; if
e
1
=
e
2
,
the excitation purity is zero. So excitation purity measures the degree to which
the light is monospectral. (For more complex spectra, the precise definition of the
“dominant wavelength” is subtler; it's not always the one with the highest value,
which might be ill-defined if multiple peaks had the same height. These subtleties
need not concern us.)
e
2
e
1
400
500
600
700
Figure 28.3: A contrived spectral
power distribution with 500 nm
as its dominant wavelength.
