Graphics Reference
In-Depth Information
All radiometric quantities can be expressed as integrals of
L
: For the spectral radi-
ant intensity, which we mentioned briefly above, with units of watts per stera-
dian, you integrate out area and wavelength. For the nonspectral version, you also
integrate out wavelength.
Radiosity
is a name sometimes used in graphics for a
nonspectral radiant exitance; its units are watts per square meter (one integrates
out wavelength and directions).
Terms like these (and like “irradiance” and “radiant exitance”) are useful when
we try to describe the flow of light energy in a scene with an approximation in
which we aggregate light in various ways. For example, if our scene consists
entirely of diffuse reflectors (e.g., items painted with a coat of latex paint), then it
makes sense to do computations that ignore the direction in which light is radiated,
and simply compute the total light energy radiated from a surface. In the same
way, we often aggregate light into three wavelength groups, which we call “red,”
“green,” and “blue,” so that instead of computing the light transport individually
for every possible wavelength
, we simply compute it for three aggregates. This
results in approximations of the correct results, but in many cases the approxima-
tions can be very good. Indeed, it's often worth writing the light energy leaving a
surface as a sum of terms, each of which can be studied by a suitable algorithm; in
some of these algorithms summary representations of the light may be appropri-
ate, whereas in others the highly detailed representation provided by the radiance
field
L
is more appropriate.
There are also other quantities that describe aggregate properties of light in
terms that are relevant to human perception; these lie in the domain of
photometry
and are discussed in Section 28.4.1.
Finally, there is a term that can cause considerable difficulty:
intensity.
Inten-
sity occurs frequently in early graphics papers, but its meaning is rarely given
precisely. It's probably best to read these papers with a modern eye and regard
“intensity” as a proxy for “radiance,” although there may be a cosine factor or
two missing in any particular discussion. When we use the word “intensity,” it's
strictly informal, as in the sentence “When we increase the intensity of the lamp,
the scene brightens.”
λ
An alternative approach to defining radiometric terms is to take the radiant flux
Φ
as a starting point, and to derive all other quantities from it through a kind of “dif-
ferentiation.” For instance, we can look at a point
P
of some surface, and a region
R
on the surface with
P
∈
R
, and consider the light arriving at
R
from all possible
directions, and the resultant power arriving at
R
, which we call
ΔΦ
. By dividing
this power
ΔΦ
bytheareaof
R
,
Δ
A
, we get a power-per-area measurement,
ΔΦ
Δ
A
.
(26.69)
If we imagine repeating this process for various regions
R
, each with a smaller and
smaller area, but still containing the point
P
, we get a sequence of power-per-area
measurements. The argument is then that these measurements have a limit, as the
