This paper presents a single scattering 3D graphics simulator of rainbows that
includes the thickness of the rain shaft and the background scenery. The
simulator is devised so that we can find a good configuration of the sun, the
viewers, and the volume of water drops in a complicated geometric setting. The
background-scene geometry and light-reflecting properties are modelled using 3D
graphics tools. The simulator allows both the light reflected from the
background surface and the light scattered by water drops to contribute to the
final image by taking the depth to the background surface into account. The
simulator generates an image of the rainbow by using the radiative transfer
equation (RTE). We use ray optics to compute the average scattering cross
section and the average phase function of particles that are the main parameters
of the RTE. Depending on the density distribution of the water drops, the
rainbow is perceived to be translucent, and the background scene is visible
through the rainbow. We simulate other effects of the variation of the
water-dropdensity and the location of the viewer, e.g., the visibility of the
secondary rainbow, the brightness of the sky around the rainbow, the close-up
view of the rainbow, and the full-circle rainbow. We explain these effects
partly by computing the luminance contrasts of the primary and secondary bows
against their local backgrounds.
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Threshold Rainbow: The Reference Drop Density of
a
RD
BD
Drop color
8.44
3.00
1.81
0.242
0.249
Total color
54.02
55.29
Volume percentage of water . The first row of the table
describes the drop colors without considering the surface colors
reflected by the background scene/sky. The second row describes the
total rainbow colors that take the surface color into account. The
surface color is obtained by subtracting the drop color from the
total color. The drop colors in the rainbow region (8.44) are much
brighter than the drop colors in the background region (3.00). But
this is not what the reviewer actually perceives.
is the Weber ratio for the
luminance contrast of the rainbow against the local background. The
negative value () means that the luminance of the
rainbow is less than that of the local background. RD and BD refer
to the average optical depths of the rainbow region and the
background region.
Volume percentage of . The average inter-particle
. The average optical depth of the
rainbow region (RD) approaches almost 1, four times more than that
of the threshold rainbow (0.242). The reason is that the viewer is
nearer the volume of water drops so that the drop density of the
water drops that contribute to the rainbow is greater than in the
threshold rainbow. The luminance contrast of the total colors of the
rainbow is 0.044—two times as much as that of the threshold
rainbow. The rainbow is visible though not vivid.
Volume percentage of . The average inter-particle
. The average optical depth of the
rainbow is 1.5 times as much as that of the ordinary bow in the top
right of Fig. 4. The
luminance contrast of the total colors of the rainbow (0.087) is
increased two times as much as that of the ordinary bow (0.044).
Volume percentage of . The average inter-particle
. The average optical depth of the
primary rainbow is two times as much as that of the ordinary bow in
the top right of Fig. 4.
The luminance contrast of the total colors of the primary rainbow
(0.21) is increased 4.8 times as much as that of the ordinary
rainbow (0.044). In the case of the secondary bow, the luminance
contrast of the drop colors of the bow against the background is
quite large (26.88). But the optical depth of the rainbow region
(RD) and that of the background (BD) are very different so that the
surface color of the rainbow region is attenuated greater than that
of the background. Hence the luminance contrast of the total colors
of the secondary bow is small ().
Volume percentage of . The average inter-particle
. The average optical depth of the
primary rainbow is about two times as much as that of the vivid bow
in the bottom right of Fig. 4. The luminance contrast of the total colors of the
primary rainbow (0.96) is increased 4.5 times as much as that of the
vivid bow (0.21). The luminance contrast of the total colors of the
secondary bow (0.48) is increased 600 times as much as that of the
secondary bow (0.008) in the vivid bow in the middle right of
Fig. 4. It reflects
the vividness of the secondary bow in the bottom left of
Fig. 4. The
luminance contrast of the drop colors in the rainbow region is
similar to that of the vivid rainbow and caused by the luminance
difference of the surface colors in the background region. Because
of the high drop density, the local background of the secondary bow
greatly attenuates the surface light.
Tables (5)
Table 1.
Threshold Rainbow: The Reference Drop Density of
a
RD
BD
Drop color
8.44
3.00
1.81
0.242
0.249
Total color
54.02
55.29
Volume percentage of water . The first row of the table
describes the drop colors without considering the surface colors
reflected by the background scene/sky. The second row describes the
total rainbow colors that take the surface color into account. The
surface color is obtained by subtracting the drop color from the
total color. The drop colors in the rainbow region (8.44) are much
brighter than the drop colors in the background region (3.00). But
this is not what the reviewer actually perceives.
is the Weber ratio for the
luminance contrast of the rainbow against the local background. The
negative value () means that the luminance of the
rainbow is less than that of the local background. RD and BD refer
to the average optical depths of the rainbow region and the
background region.
Volume percentage of . The average inter-particle
. The average optical depth of the
rainbow region (RD) approaches almost 1, four times more than that
of the threshold rainbow (0.242). The reason is that the viewer is
nearer the volume of water drops so that the drop density of the
water drops that contribute to the rainbow is greater than in the
threshold rainbow. The luminance contrast of the total colors of the
rainbow is 0.044—two times as much as that of the threshold
rainbow. The rainbow is visible though not vivid.
Volume percentage of . The average inter-particle
. The average optical depth of the
rainbow is 1.5 times as much as that of the ordinary bow in the top
right of Fig. 4. The
luminance contrast of the total colors of the rainbow (0.087) is
increased two times as much as that of the ordinary bow (0.044).
Volume percentage of . The average inter-particle
. The average optical depth of the
primary rainbow is two times as much as that of the ordinary bow in
the top right of Fig. 4.
The luminance contrast of the total colors of the primary rainbow
(0.21) is increased 4.8 times as much as that of the ordinary
rainbow (0.044). In the case of the secondary bow, the luminance
contrast of the drop colors of the bow against the background is
quite large (26.88). But the optical depth of the rainbow region
(RD) and that of the background (BD) are very different so that the
surface color of the rainbow region is attenuated greater than that
of the background. Hence the luminance contrast of the total colors
of the secondary bow is small ().
Volume percentage of . The average inter-particle
. The average optical depth of the
primary rainbow is about two times as much as that of the vivid bow
in the bottom right of Fig. 4. The luminance contrast of the total colors of the
primary rainbow (0.96) is increased 4.5 times as much as that of the
vivid bow (0.21). The luminance contrast of the total colors of the
secondary bow (0.48) is increased 600 times as much as that of the
secondary bow (0.008) in the vivid bow in the middle right of
Fig. 4. It reflects
the vividness of the secondary bow in the bottom left of
Fig. 4. The
luminance contrast of the drop colors in the rainbow region is
similar to that of the vivid rainbow and caused by the luminance
difference of the surface colors in the background region. Because
of the high drop density, the local background of the secondary bow
greatly attenuates the surface light.
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