19 
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 
rendered. 
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 
maps. 
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: 
¿=1 
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.