Graphics Reference
In-Depth Information
R
T
1
1
Monte Carlo
Layer 1
Layer 2
Layer 1 & 2
++++
Monte Carlo
Layer 1
Layer 2
Layer 1 & 2
++++
0.1
0.1
0.01
0.01
0.001
0.001
+
1e - 04
1e - 04
+
1e - 05
1e - 05
1e - 06
1e - 06
1e - 07
1e - 07
0
5
10
15
20
0
5
10
15
20
r (mm)
r (mm)
(b) Transmittance
Figure 4.21
Verification of a two-layer model. The graphs show the (a) reflectance and (b) transmit-
tance profiles for the combined layers compared with those of each separate layer, and the
corresponding Monte Carlo simulations. (From [Donner and Jensen 05] c
(a) Reflectance
2005 ACM,
Inc. Included here by permission.)
ranging terms produces the formula
2
3
T
12
=
T
1
T
2
(
1
+
R
2
R
1
+(
R
2
R
1
)
+(
R
2
R
1
)
+
···
T
1
T
2
−R
2
R
1
.
=
(4.19)
1
The inverse Fourier transform of the right side of (4.19) provides the transmittance
function of the combination of the two layers.
The total diffuse reflectance of adjacent layers 1 and 2, which must account
for light scattered between the two layers, can be computed similarly. The Fourier
transform of the effective reflectance
R
12
is
+
R
1
R
2
T
1
1
R
=
R
−R
2
R
1
.
(4.20)
12
1
Repeatedly applying the formulas of (4.19) and (4.20) produces the effective dif-
fuse reflectance and transmittance profiles for multiple layers.
Figure 4.21 contains plots of the reflectance and transmittance profiles as a
function of distance for a specific material. The material consists of an upper layer
exhibiting little scattering over a thinner highly scattering lower layer. Each graph
contains plots of the convolved multipole model for two adjacent layers, those of
the individual layers, and the corresponding profiles derived from a Monte Carlo
simulation. The graphs show a close match between the convolved model and
the Monte Carlo simulation for both the reflectance and the transmittance. In
particular, the convolved multipole model appears to work well for small values
of
r
, i.e., where the the entry point of the incident light is close to the exit point.
