the radar. The ground-range presentation has the advantage of being less distorted.
The process to achieve this geometric correction is called slant-range to groundrange conversion. The relationship between slant-range and ground-range on a flat,
horizontal surface is that of a simple but non-linear trigonometric function;
R g ¼ R s = sin θ i
ð14:3Þ
Where θ i is the incidence angle, R s the slant-range, and R g is the ground-range. The
slant-range, which is always smaller than the ground-range, is highly dependent on
the viewing geometry. Changes in incidence angle result in differential scale
changes across the image swath. The relationship between the change in slantrange to ground-range is
DR g ¼ DR s = sin θ i
ð14:4Þ
and differs at near-range and far-range. The scale of the slant-range presentation of
an image is therefore not constant across the image swath. It results in maximum
distortions when approaching the nadir, where the incidence angle equals zero,
producing minimal scale change in slant-range and comparatively large discrepancy in ground-range. Because of the continuous change in range scale, there is
only one range point where the slant-range scale is equal to a given map or groundrange scale; in the near-range the map scale would be smaller, and at far-range the
map scale would be larger.
Assuming flat, horizontal terrain, this distortion may be removed by re-sampling
the SAR data in the range dimension to ground-range using
Rg ¼ R s
2
À h
2
ð14:5Þ
where h represents the platform altitude. For high platform altitudes, i.e. spaceborne
SARs, the curvature of the Earth surface must also be considered and factored into
the equation.
14.4.2 External Geometric Distortions
External geometric distortions in SAR imagery are primarily induced by changes in
terrain or target elevation and by changes in platform altitude, velocity and the
effect of earth rotation. It has been demonstrated that any changes in elevation from
a reference surface results in distortions known as foreshortening and, in extreme
cases, layover. Although the internal system related distortions can be predicted by
correcting the slant-range image plane to a ground-range image plane, the removal
of external distortions due to elevation differences requires additional information.
Two sources for this information are conceivable: topographic information
(Pirasteh and Ali 2005) in form of digital elevation models (DEMs) (Mussakowski
14 Digital Processing of SAR Data and Image Analysis Techniques
287
The process to achieve this geometric correction is called slant-range to groundrange conversion. The relationship between slant-range and ground-range on a flat,
horizontal surface is that of a simple but non-linear trigonometric function;
R g ¼ R s = sin θ i
ð14:3Þ
Where θ i is the incidence angle, R s the slant-range, and R g is the ground-range. The
slant-range, which is always smaller than the ground-range, is highly dependent on
the viewing geometry. Changes in incidence angle result in differential scale
changes across the image swath. The relationship between the change in slantrange to ground-range is
DR g ¼ DR s = sin θ i
ð14:4Þ
and differs at near-range and far-range. The scale of the slant-range presentation of
an image is therefore not constant across the image swath. It results in maximum
distortions when approaching the nadir, where the incidence angle equals zero,
producing minimal scale change in slant-range and comparatively large discrepancy in ground-range. Because of the continuous change in range scale, there is
only one range point where the slant-range scale is equal to a given map or groundrange scale; in the near-range the map scale would be smaller, and at far-range the
map scale would be larger.
Assuming flat, horizontal terrain, this distortion may be removed by re-sampling
the SAR data in the range dimension to ground-range using
Rg ¼ R s
2
À h
2
ð14:5Þ
where h represents the platform altitude. For high platform altitudes, i.e. spaceborne
SARs, the curvature of the Earth surface must also be considered and factored into
the equation.
14.4.2 External Geometric Distortions
External geometric distortions in SAR imagery are primarily induced by changes in
terrain or target elevation and by changes in platform altitude, velocity and the
effect of earth rotation. It has been demonstrated that any changes in elevation from
a reference surface results in distortions known as foreshortening and, in extreme
cases, layover. Although the internal system related distortions can be predicted by
correcting the slant-range image plane to a ground-range image plane, the removal
of external distortions due to elevation differences requires additional information.
Two sources for this information are conceivable: topographic information
(Pirasteh and Ali 2005) in form of digital elevation models (DEMs) (Mussakowski
14 Digital Processing of SAR Data and Image Analysis Techniques
287