IEEE Geoscience and Remote Sensing Magazine - March 2013 - 11

domain by the complex conjugate of the spectrum of
the transmitted chirp; the result is a range compressed
image, which reveals only information about the relative
distance between the radar and any point on the ground.
Azimuth compression follows the same basic reasoning,
i.e., the signal is convolved with its reference function,
which is the complex conjugate of the response expected
from a point target on the ground. Considering an elemental scatterer at range r (t) given in (3), the azimuth
signal can be modeled by [9]
s a (t) = A v 0 exp ^i{ scatt h exp a -i

4r
r (t) k, (5)
m

where A accounts for the dependency of the received signal
on system parameters such as transmit power and losses,
and the antenna pattern weighting as a function of the azimuth and elevation angles; the radar cross section is given
by v 0 and { scatt is the scattering phase; 4rr (t) /m describes
the azimuth phase variation due to the changing distance;
and i is the imaginary unit, i.e., i = - 1 .
Interestingly, the frequency variation of the azimuth
signal turns out to be similar to that in the range domain,
i.e., a linear frequency modulated signal (azimuth chirp).
This becomes clear when substituting the approximation
(3) into the last exponent in (5) and computing the instantaneous azimuth frequency as the time differentiation of
the phase
1 2 4r
2v 2
t, (6)
fD = - 2r 2t
r (t) = m
mr0

Range Compressed Data

Image Data

Range

Raw Data

which varies linearly with
time at an azimuth-frequency
The formation of a
rate inversely proportional
synthetic
aperture
to the slant range. The azito
high
azimuth
leads
muth frequency is also
resolution, while range
called Doppler frequency in
analogy to the well-known
resolution is given by
Doppler effect. Fig. 3 shows
the transmitted chirp
the basic steps of SAR signal
bandwidth.
processing, where the range
reference function is dependent only on the transmitted
chirp waveform whereas the azimuth reference function
depends on the geometry and is adapted to the range.
The SAR image is most commonly displayed in terms of
intensity values such that each image pixel gives an indication of the reflectivity of the corresponding point on the
ground. This involves two additional steps applied on the
output of the processor: calibration and geocoding. Here
the calibration ensures that the intensity value actually represents the sigma zero (v 0) value of the reflectivity, i.e., the
radar cross section normalized to area. Proper calibration is
a non-trivial task involving both internal instrument calibration as well as external SAR calibration using targets of
known reflectivity [24]. The geocoding on the other hand
ensures that the location of any pixel in the SAR image is
directly associated to the position on the ground. Typically SAR images are geometrically distorted. The reason
for this is that the radar only measures the projection of

Azimuth

Range Reference Function

Azimuth Reference Function

Range

Amplitude

Far Range

Near Range
Amplitude

Azimuth

FIGURE 3. Summary of SAR processing steps where the range compressed data result from a convolution of the raw data with the range
reference function. In a second step the azimuth compression is performed through a convolution with the azimuth reference function,
which changes from near to far range. Here the "*" represents the convolution operation.
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2013