IEEE Geoscience and Remote Sensing Magazine - March 2013 - 12

a three-dimensional scene on the radar coordinates slantrange and azimuth. This causes effects such as shadow for
areas hidden from the radar illumination as well as foreshortening and layover manifested by a stretch and compression of sloped terrain.
A quantitative measure of the signal processing quality
is possible by investigating the impulse response function
(IRF). This is basically the two-dimensional complex image
that would be obtained from a scene consisting of a single
point-like scatterer. The IRF is
most often computed based
on simulated data, or derived
Speckle is inherent to
analytically, but it can also
imaging of distributed
be measured when strong
scatterers are present in the
scatterers because
imaged scene. Specifically
SAR is a coherent
the range/azimuth resolution
imaging sensor.
(taken as the respective halfpower width of the IRF) and
side-lobe levels are of interest.
Analyzing the IRF reveals that the phase, especially in azimuth as given by (5), is crucial for the correct focusing. This
has a strong impact on the instrument hardware, which is
required to have a high phase stability, i.e., to be coherent
during the data acquisition. This is nowadays not an issue
due to the availability of ultra-stable oscillators.
Most SAR raw data properties can be described taking
into account simple geometrical properties. Of these Range
Cell Migration (RCM) is a property originating from the fact
that the distance between the radar and any fixed point

on the ground is changing within the synthetic aperture
time. This distance change is obtained from (3) by subtracting the constant r0 and is given by

(vt) 2
RCM (t) = r 20 + (vt) 2 - r0 . 2r0 . (7)

The RCM can be observed through the curvature
of the range compressed responses in Fig. 3. If not
corrected, RCM causes an azimuth defocusing when
RCM max = RCM (t = Till /2) 2 d r /2 because in this case
the point target energy is distributed over several range
cells. The fact that the range migration is range-variant,
i.e., the curvature depends on r0, makes SAR focusing
a two-dimensional space-variant problem, and hence
the data need to be correlated with a non-stationary
two-dimensional reference function, making the accurate correction of RCM the most challenging aspect of
SAR focusing. In the beginnings of digital processing
and especially in the 90s, the efficient correction of the
RCM was an intense research topic, resulting in several
approaches, of which the most commonly known are
those based on ~ - k (or "wavenumber domain") processors [25], [26], range-Doppler algorithms [27]-[29],
as well as chirp scaling approaches [30], [31]. Detailed
analyses and comparisons of these processors, as well
as further focusing approaches, can be found in several
books [2], [8], [9], [32].
A particular effect to be observed in SAR images is the
so-called speckle, which is caused by the presence of many
elemental scatterers with a random distribution within a
resolution cell. The coherent sum of their amplitudes and
phases results in strong fluctuations of the backscattering
from resolution cell to resolution cell. Consequently, the
intensity and the phase in the final image are no longer
deterministic, but follow instead an exponential and uniform distribution, respectively [5]. The total complex reflectivity for each resolution cell is given by

U = / v i exp (i{ scatt
) $ exp a - i
i
i

Image Pixel 1

Image Pixel 2

FIGURE 4. Speckle occurs in SAR images due to the coherent

sum of many elemental scatterers within a resolution cell. The
two parallelograms show the distribution of the scatterers in each
resolution cell and the resulting amplitude and phase values. Due
to the random distribution of the scatterers, the resulting intensity
and phase change from pixel to pixel, showing an exponential
and uniform distribution, respectively [5]. Speckle appears in
areas with distributed scatterers where the radar wavelength is
comparable to the surface roughness.
12

4r k
r , (8)
m 0, i

where i is the number of elemental scatterers within the
resolution cell. Speckle is indeed a physical measurement
of the resolution cell structure at sub-resolution level.
Although it is commonly referred to as noise, speckle cannot
be reduced by increasing the transmit signal power, since
it has a multiplicative character, i.e., its variance increases
with its intensity. To mitigate speckle a technique known
as multi-look is utilized, which is basically a non-coherent
averaging of the intensity image [2], [5]. Although multilook causes a degradation in the image resolution, it greatly
improves the interpretability of the SAR image as it can be
seen in Figures 5(b)-5(d). Also the effect of speckle tends to
weaken for very high-resolution systems, since the number
of elemental scatterers within a resolution cell decreases.
One of the key issues of SAR is the signal sampling. In
range, the sampling rate of the analog-to-digital converter
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2013