Graphics Reference
In-Depth Information
d
v
z
v
r
2
A
3
σ
'
t
x
i
x
o
1
t
z
r
=
σ
d
r
Figure 4.6
The dipole model of multiple scattering. The dipole consists of a virtual point light source
below the surface and a virtual “negative” point source above the surface that has the neg-
ative intensity of the lower source. The sources are symmetric about the dashed line. The
resulting radiance distribution approximates diffuse multiple scattering from light incident
at
x
i
(independent of the incident direction).
the
Q
term in the light transport equation given by Equation (4.2). According to
Eason's paper, this source term
Q
in the LTE can be reasonably approximated
by placing a virtual point light source directly under the point where the outside
light enters the medium, and a second
negative
virtual point source directly above
it. This negative source is assumed to emit
negative light
, in the sense that the
emitted radiance is negative. (This is a hypothetical concept of course—negative
light sources do not really exist.) Intuitively, the negative light cancels light that
erroneously leaves the medium from the positive source below the surface. The
arrangement is known as a
dipole model
.
Figure 4.6 illustrates the dipole arrangement:
x
i
is the point at which light
enters the medium, the sources are arranged so that the line joining them hits
x
i
and is perpendicular to the surface. The model has been studied in the medical
physics community, primarily in the context of noninvasive tissue examination.
The particular dipole model employed in the 2001 subsurface scattering paper by
Jensen et al. follows the work of cancer researchers Farrell and Patterson. The
positive source is placed at a distance of one mean free path below the surface;
i.e.,
z
v
=
/
σ
t
. The position of the negative source is determined by the boundary
condition described in the previous subsection: the net inward flux at the surface
is zero. More precisely, the integral of the incoming flux over the hemisphere
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