Graphics Reference
In-Depth Information
→
d
Φ
→
θ
ω
x
d
ω
dA
Figure 1.3
Definition of radiance. The radiance is the flux in a differential cone from a differential
area
dA
.
defined in terms of differentials as
d
Φ
L
(
x
,
ω
)=
θ
.
(1.5)
d
ω
dA
cos
This definition removes the dependence on the specific surface orientation without
losing the area dependence, so that radiance is well defined at any point in space.
Radiance has a fundamental property that is particularly relevant to computer
graphics: as it travels through a transparent medium,
radiance is constant along
a line
. This is not obvious from the definition and may seem unintuitive. It
is a result of the fact that the solid angle subtended by a small area, which is
inversely proportional to the square of the distance to the area, cancels the effect
of inverse square decrease of flux density with distance. A real-world example of
this phenomenon is that an area on a wall (or a book page, or a computer monitor)
appears to have the same brightness as an observer moves toward it or away from
it. The fact that radiance is constant along a line is the basis of geometric optics,
in which light is treated as propagating along rays, and also serves as the physical
foundation of ray tracing (Section 1.3.3).
Radiance is in some sense the most fundamental physical quantity of light
used in photorealistic rendering. The definition of Equation (1.5) is not very in-
tuitive. It is probably more helpful to think of radiance as the general strength
of light at a point in a particular direction, or equivalently, as the radiant power
carried along a ray.
1.1.4 Spectral Quantities and Color
As defined above, radiance and the other radiometric quantities include energy
across the electromagnetic spectrum. They can be made to depend on wavelength
by limiting the quantity to the power in a small wavelength band. For example,
