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Mapping without the sun
Zhang, Jixian

from the model co-
len subsequently to
information matrix
/e the desired paral-
L image depends on
sensor, thus higher
closer to the sensor
ange. The resulting
e height above the
to compute the cor-
corresponding face
iking material prop-
r properties into ac-
ited. SARViz offers
imputation. The sta-
f Ulaby & Dobson
ughness and dielec-
Zribi (2006) and an
lost commonly used
methods, due to its
Phong, 1975), three
1 ambient) are com-
iement is calculated
rength as well as the
3). In the SAR case,
eflections strength r
'alue can be derived
reflections based on
in the mono-static
m are identical, the
;tatistical analysis of
:alistic values for the
are needed to calcu-
>re, multi-reflections
the rasterization ap-
ind every vertex and
tusions are not mod-
1978) both shadows
ow map is generated
m the position of the
ise equivalent to the
values, the distance
itten to the so-called
m the position of the
ground-range images
irmation from slant-
le scene is rendered
looking from nadir direction, keeping a parallel projection. The
distance of each pixel rendered in the nadir view is compared to
the transformed distance between the sensor position and the
object. If the distance of a pixel to the sensor exceeds the value
stored in the shadow map, the pixel is not visible and will not be
sensor view shadow map visualization
Figure 4. SAR shadow map generation
Shadow mapping is an image-based technique. It can be easily
implemented and generates fast shadow casting effects. Using
this method, the virtual camera is not allowed to be inside a
shadow area. Large distance differences between the virtual
camera and the light source are also problematic. For mono
static SAR simulation, the sensor is identical to the light source
and the virtual camera. Therefore, no such problems exist. Still,
precision and aliasing problems may occur while using shadow
3.3 Soft shadows
The edges of a shadow area created by shadow mapping are too
sharp, because each pixel is either completely inside or outside
of a shadow area. In computer graphics various methods for
visualizing soft shadows are used. Optical images have very soft
shadows, especially if they include ambient lighting. In radar
images, there is no ambient lighting. The methods visualizing
ambient light are therefore not feasible for SAR simulation.
Due to the shape of the radar lobe, areas in the edge of the sha
dow still reflect energy back to the sensor. This can be visual
ized by generating three shadow maps. One shadow map in the
image centre using parallel projection, two shadow maps at the
edges of the image. The positions of these additional shadow
maps are determined by the shape of the radar lobe, which de
pends on the length of the real aperture. Using three shadow
maps, the shadow state of a pixel is not binary anymore.
In our approach we differentiate between pixels outside any
shadow area, pixels inside one shadow area and pixels inside
two or more shadow areas. Pixels inside two or more shadow
areas are not reflecting any energy back to the sensor, but the
pixels inside just one of the shadow areas are still reflecting a
limited amount of energy back to the sensor. As it can be seen
in Figure 5, this approach is considering the shape of the radar
lobe and is visualizing soft radar shadows.
Figure 5. Visualization of a model of the ,,Burj-el-Arab“ in Du-
bai using soft shadows
3.4 Spotlight mode
The spatial resolution of SAR systems can be increased using
the spotlight mode. In the spotlight mode the squint angle of the
radar antenna is adjusted during the data acquisition to increase
the exposure time. The dynamic adjustment of the antenna in
creases the synthetic aperture length and therefore improves the
spatial resolution in azimuth.
Beside the improvement of the resolution, the spotlight mode
influences the lighting, the shadow casting and the layover ef
fect. To visualize the influence of the spotlight mode on the lay
over, the geometry is adjusted dynamically in the vertex shader.
The shadow is calculated using three shadow maps. In contrast
to the visualization of soft shadows, explained in section 3.3,
the shadow of each pixel is determined by using only one sha
dow map. Depending on the azimuth position, the respective
shadow map is selected. Therefore, the shadow map used for the
shadow calculation is dynamically changing.
Figure 7. Visualization of three simple buildings using the spot-
light mode
3.5 Speckling and multi-look image generation
Speckling is produced by mutual interference of coherent waves
that are subject to phase differences. For simplicity it can be
visualized by additive noise. The reflection value of a multi
look image is a combination of m single SAR images. The re
sulting speckle value in a multi-look image S m can be calcu
lated using:
A more realistic approach is the separate simulation of each
look. Each sub-aperture image has a different squint angle. Al
though the differences between the squint angles are small,
edges, layovers and shadows appear blurred in the combined
multi-look image (see Figure 8). Because each single sub-aper
ture image has to be simulated separately, the overall processing
time increases accordingly.