2.6.1.2.3 RangeDoppler
2.6.1.2.3.1 Introduction
2.6.1.2.3.1.1 Overview
The rangeDoppler
algorithm is the most commonly
used algorithm for processing
continuously collected SAR data into
an image (see
Ref. [2.5 ]
and
Ref. [2.6 ]
). It is
computationally efficient and,
for typical spaceborne
imaging geometries, the
rangeDoppler algorithm is an
accurate approximation to the
exact SAR transfer function.
Thus, the algorithm is
phasepreserving and Single Look
Complex (SLC) images
formed with the
rangeDoppler algorithm can be
used for applications such as interferometry.
The rangeDoppler algorithm
is designed for continuously
collected data, in contrast to
SPECAN 2.6.1.2.4. which
is best suited to bursty
data, and can process the
full azimuth bandwidth.
The rangeDoppler algorithm is
used for the highresolution
Image Modes (IMS, IMP, IMG) and
the highresolution, single look
complex Alternating
Polarisation Mode (APS). ( See
Table in the
section entitled
"Organisation of
Products" in chapter 2 ).
For the APS mode, the data
between bursts is filled with
zeros to maintain a
continoustime input to the
algorithm, and a modified
rangeDoppler algorithm is used
to produce an SLC image from
AP data 2.6.1.2.3.2. .
For the detected (magnitude)
image products (IMP, IMG), a
technique called multilooking
is incorporated into the
algorithm. In this method,
separate images are formed from
different azimuth spectral
bands (looks), and
the magnitude look images are
averaged to reduce speckle.
SAR processing is a
twodimensional problem. In the
raw SAR data,
the signal energy from a
point target is spread in range and
azimuth, and the purpose of SAR
focussing is to collect this
dispersed energy into a single
pixel in the
output image. In range, the
signal is spread by duration the
linear FM transmitted
pulse. In azimuth, the
signal is spread by the duration
it is illuminated by the antenna
beam, or the synthetic
aperture. As a point target
passes through the azimuth
antenna beam, the range to the
target changes. On the scale
of the wavelength, this range
variation causes a phase
variation in the received
signal as a function of azimuth.
This phase variation over the
synthetic aperture corresponds
to the Doppler bandwidth of the
azimuth signal, and allows the
signal to be compressed in the
azimuth direction. The range
variation to point target can
result in a variation in the
range delay to the target that
is larger than the range sample
spacing, resulting in what is
called range migration. This
range migration of the signal
energy over several range bins
must be corrected before azimuth
compression can occur. The
rangeDoppler algorithm
performs this correction very
efficiently in the rangetime,
azimuthfrequency domain.
In order to process the correct
part of the azimuth frequency
spectrum, the rangeDoppler
algorithm requires as input the
Doppler centroid. It is
assumed here that Doppler
centroid estimation has already
been performed, as described in
the Doppler
Centroid Estimation 2.6.1.2.2.
section. The rangeDoppler
algorithm also requires
knowledge of the transmitted
pulse for range compression, and
of the imaging
geometry such as the range
and satellite velocity for
construction of the azimuth
matched filter.
The main steps in the version of
the rangeDoppler algorithm used
in ASAR are shown in the block
diagram below, and are described
in the following sections.

Figure 2.22 Steps of rangeDoppler algorithm used in ASAR processing 
2.6.1.2.3.1.2 Range Compression In collecting the SAR
data, a longduration linear FM
pulse is transmitted. This allows
the pulse energy to be transmitted
with a lower peak power. The
linear FM pulse has the property
that, when filtered with a matched
filter, the result is a narrow pulse
in which all the pulse energy
has been collected to the peak
value. Thus, when a matched filter
is applied to the received echo, it
is as if a narrow pulse were
transmitted, with its corresponding
range resolution and signaltonoise
ratio. This matched
filtering of the received echo
is called range compression.
Range compression is performed
on each range line of SAR data,
and can be done efficiently by
the use of the Fast Fourier
Transform (FFT). The
frequency domain range matched
filter needs to be generated
only once, and it is applied to
each range line. The range
matched filter may be
computed or generated from a
replica of the transmitted
pulse. In addition, the range
matched filter frequency
response typically includes
an amplitude weighting to
control sidelobes in
the range impulse response.
The steps in range compression
for each range line are:

Range FFT:
For most products, the range
line is divided into two
overlapping segments, and an
FFT is taken of each
segment. The amount of
overlap corresponds to the
length of the transmitted pulse.

Range matched (MF)
multiply: Each
FFT'd segment is
multiplied by the frequency
response of the matched filter.

Range Inverse
FFT: An inverse FFT
is applied to each segment
to get the range compressed
data. Part of each segment
is thrown away since the
compressed range data is
shorter than the
uncompressed range data by
the length of the
transmitted pulse. The
range matched filter is
designed so that the
throwaway is at the end of
the data after the inverse
FFT. The results from each
segment are then
joined together to get the
compressed data for the
whole range line.

Range dependent gain
correction: The
range compressed data is
multiplied by a vector that
corrects the effects due
to elevation beam pattern
and range spreading loss.

2.6.1.2.3.1.3 Azimuth FFT An FFT is performed in
the azimuth direction on each range
gate to transform the data into the
range Doppler domain. The FFTs are
performed on blocks of data
overlapped by the azimuth matched
filter length. The range
compressed data is stored in
range line order. A group FFT
algorithm is used which allows
azimuth FFTs to be performed
while still accessing the
data in range line order. Thus
the corner turn (transpose to
azimuth line order) operation
can be delayed until after RCMC.
2.6.1.2.3.1.4 Range Cell Migration
Correction (RCMC) After range
compression, the signal energy from
a point target follows a trajectory
in the twodimensional SAR data,
that depends on the changing
range delay to the target as it
passes through the antenna beam.
This trajectory may cross several
range bins. In order to capture
all the signal energy for azimuth
compression, the signal energy from
a point target must be aligned in a
signal range bin. RCMC is
the step of correcting for the
changing range delay to a point
target as the target passes
through the antenna beam (range
migration). For a given target,
this range depends on the
closest approach range from the
satellite to the target
(zeroDoppler range), and on
the angle from the satellite to
the target, relative to the
broadside (zeroDoppler)
direction. As targets at the
same closest approach range
pass through the antenna beam,
they all traverse the same
interval of angles, and so have
the same variation in range from
the radar. That is, the
signal trajectories from targets
at the same closest approach
range have the same shape, but
are displaced in azimuth because
of the different target
positions. This is shown in the
graph on the left in figure2.23 below.
Because of the relationship
between the satellitetotarget
angle and Doppler frequency, the
range migration of all
targets at the same closest
approach range can be expressed
as a function of Doppler
frequency. That is, all signal
energy from targets at the
same closest approach range is
collected into the same
trajectory in the rangeDoppler
domain. This allows RCMC to be
performed very efficiently in
the rangeDoppler domain.

Figure 2.23 Illustration of trajectories in time domain and rangeDoppler domain. 
The shift in range that is needed
to align the signal trajectory
in a single range bin is
determined for each azimuth
frequency bin. This shift is
then implemented by an
interpolation in the range
direction. The straightened
trajectories are shown by the
dotted lines in the figure.
Other steps in SAR processing
that require interpolation in
range are slant range to ground
range conversion (SR/GR), which
converts the distance from
the radar (slant range) to
distance along the ground, and
the range resampling to a
desired output pixel spacing.
For maximum efficiency, all
of these range interpolations
are combined into one operation.
2.6.1.2.3.1.5 Azimuth Compression Azimuth compression is
a matched filtering of the azimuth
signal, performed efficiently using
FFT's. Note that the azimuth
FFT has already been performed
at this point. The azimuth
FFT's were performed on blocks
of data that overlap in azimuth by
the matched filter length. The
reason for the overlap is the
throwaway after azimuth
compression. The frequency
response of the azimuth
compression filter is
precomputed using the orbital
geometry. The azimuth filter
also depends on range. Thus
the data is divided into range
invariance regions, and the same
basic matched filter is used
over a range interval called the
FM rate invariance region. The
size of this invariance region
must not be large enough to
cause severe broadening in the
compressed image. Also
included is an amplitude
weighting to control sidelobes
in the azimuth impulse response.
Note that the position of the
amplitude weighting in the
azimuth frequency array depends
on the Doppler centroid, which
also depends on range.
The way the azimuth compression
is implemented depends on the
type of image product. For
single look complex products
(IMS and APS), a single
portion of the azimuth bandwidth
is multiplied by the azimuth
matched filter frequency
response, and an inverse FFT is
taken of the entire
frequency array. The output is
complex valued and left at the
natural pixel spacing.
For magnitude image products (IMP
and IMG), a technique called
multilooking is used to reduce
speckle noise. In this case, the
azimuth frequency spectrum
is divided into several portions
called looks. The part of the
azimuth frequency array for each
look is extracted,
multiplied by the azimuth
matched filter frequency
response, and the inverse FFT is
performed. The magnitude
(detected) look images are
then averaged to reduce speckle.
This is described in more detail
as follows.
The extraction of the looks from
the frequency array is
illustrated in the figure below.
The looks are positioned
symmetrically around the
Doppler centroid frequency. As
the Doppler centroid frequency
varies with range, the look
frequency positions are
different for different
range cells. In practice, they
are kept constant within the
look frequency position
invariance region.

Figure 2.24 Look Position Parameters 
The extracted frequency array for
each look is multiplied by the
matched filter frequency
response and the inverse FFT is
performed to form the
complex look image. The matched
filter frequency response is
adjusted by a small linear phase
ramp for each look. This is
equivalent to shifting the
compressed look in time, and is
required to ensure that the
images from different looks are
aligned properly for look
summation. The amount of azimuth
shift is rangedependent. In
addition, azimuth interpolation
may also performed after look
compression to achieve a desire
azimuth pixel spacing, and it is
done on each look separately.
After look compression, each of
the look images is detected.
That is, the power of each
complex sample is calculated.
The detected azimuth looks
are then summed, and the square
root of the result is calculated
to convert to magnitude.
Finally, for the IMG product, the
multilooked image is geocoded. This
is a two dimensional
resampling operation to convert
the image to a desired map projection.
2.6.1.2.3.1.6 Summary The processing steps
for each of the types of products
processed by the rangeDoppler
algorithm are summarised below:

Precision
products: All steps
(up to and including
multilooking) except
geocoding are performed.

Single look complex
products: Only the
steps up to and including
the azimuth IFFT, for only
one look, are performed.

Geocoded
products: All steps
are performed with the
addition of geocoding (The
normal square root step is
bypassed but is later
performed as part of geocoding).

APS
products: A
slightly modified
version of the
rangeDoppler
algorithm 2.6.1.2.3.2. is used for
the APS product .

2.6.1.2.3.1.7 References
Ian G. Cumming and
John R. Bennett. Digital processing
of SEASAT SAR data. In Record of
the IEEE 1979 International
Conference on Acoustics, Speech
and Signal Processing ,
Washington, B.C., April 24, 1979.
J. C. Curlander,
R. N. McDonough, Synthetic
Aperture Radar: Systems and
Signal Processing, John
Wiley and Sons, 1991.
2.6.1.2.3.2 Processing Algorithms For AP SLC
2.6.1.2.3.2.1 Introduction
PFASAR will
produce Single Look
Complex (SLC) products from Alternating
Polarisation (AP) mode SAR data. The
primary application for this ASAR
APS product is for Interferometric
SAR (InSAR), which is a
technique that manipulates the
relative phase between a
pair of SLC images to extract topographic
information. This section
provides an overview of the
processing approach for
generating an ASAR APS product
that is suitable for InSAR
applications. The algorithm
is the rangeDoppler 2.6.1.2.3.
algorithm, modified to process
bursty data.
2.6.1.2.3.2.2 Background The primary
application for this ASAR APS
product is for Interferometric
SAR (InSAR), for which
complex (SLC) image products are
required. In SAR Interferometry, the
phase difference between two images
of the same area is used to
compute the topography of the area.
The two images are taken from
slightly different viewing
positions, and for a single
satellite, the images are acquired
during different passes (repeatpass
interferometry). In the application
of APS products for
Interferometric SAR, a complex image
from Alternating
Polarisation (AP) mode may be
combined with another complex image
from another pass, in order to
retrieve the phase difference
between the images which is related
to terrain height. The other
image be another AP mode image or an
Image Mode
(IM) image. The algorithm
used to form the APS product
must be capable of preserving
the phase information required
for SAR Interferometry. Thus, a
form of the rangeDoppler
algorithm is required since in
general SPECAN is not
phasepreserving. The image
quality requirements for the
ASAR APS product are derived
from the typical requirements
for an Image Mode SLC product,
which includes phase
preservation and adequate focussing.
Adequate focussing is typically
determined by measurements of
the impulse response shape.
However, because of the bursty
nature of AP data, there are
some important considerations in
the processing and use of
APS data.
Interferometry requires that the
two images be well correlated,
in order for the phase
difference to be an accurate
measurement of terrain
height. Because of this, the
Doppler spectral components must
be common to both images.
Doppler components that are not
common to both images are a
source of decorrelation between
the images, which introduces
phase noise and degrades the
accuracy of the terrain height
measurement. If two Image Mode
images are combined, the full
Doppler spectrum is available in
both images, and if the antenna
pointing is controlled
properly then there is
sufficient overlap of the
Doppler spectra of the two
images. In burst mode data, such
as AP data or ScanSAR data,
the bursts contain only part of
the signal from a point target,
and thus contain only part of
the Doppler spectrum. If an APS
image is combined with an IM
image, the IM image contains the
full Doppler spectrum so again
there is sufficient overlap with
the Doppler spectrum of APS image.
If the two images are acquired in
burst mode, such as two APS
images, the amount of Doppler
overlap depends on the relative
positions of the bursts in
the two data sets. If the bursts
occurred at the same locations
in the two data sets, then the
Doppler components overlap. If
the bursts do not overlap at
all, then there are no common
Doppler components, the images
are decorrelated, and
interferometry cannot be
performed. Since the two
products are processed without
knowledge of the other, it is
desired to preserve as much
Doppler information as
possible. This is referred to as
systematic
processing. If systematically
generated SLC products are to be
used for interferometry, without
reverting back to the level 0
data, then azimuth bandpass
filtering must be performed
on the SLC images to extract the
common portions of the Doppler spectrum.
Finally, it should be noted that
the APS product
will not be suitable for phase
measurements between the
interleaved polarisation because
the Doppler spectrums of the two
focussed images will be disjoint
(nonoverlapping), which implies
that the phases will be
completely uncorrelated. The
magnitude of the APS product
could be used for
polarimetry in a similar manner
to the APP product.
For this reason the two output
SLC images are coregistered.
This section reviews burst mode
interferometry, and presents the
considerations in rangeDoppler
processing of APS data.
2.6.1.2.3.2.3 Burst Mode Interferometry
An illustration of data acquired
in discrete bursts as shown in
figure.2.25 The
figure shows the timing of the
bursts, and the exposure times
of 16 targets, labelled by
to
. The lines for each target
represent the exposure time
(synthetic aperture time),
which is the duration of time
during which the target is
within the beam footprint. In
the case of the AP mode, the
azimuth aperture covers a
little more than 5 bursts'
duration. Any one target is
captured from two to three
bursts in the same
polarisation., thus allowing
2look processing in forming a
multilook
image (such as APP).
Let us just examine the spectrum
of the targets in the burst
marked by X.
The duration of the Doppler
spectrum for each target is
shown in figure2.26
(ignoring the azimuth beam
pattern effects). It is clear
that the Doppler components
contained in this burst, for a
given ground target, depend upon
the location of the target
relative to the burst timeline.
The Doppler centroid frequency
in this context is the center
frequency of the spectrum
for a given target.

Figure 2.25 Target Exposure Extents Relative to the Burst Timeline 

Figure 2.26 Location of Spectra Energy for Targets in Burst X 
To preserve the time
relationship between the data in
different bursts, the level 0 data
acquired in burst mode can be stored
in the same representation as
continuous mode data. That is, range
lines during a burst contain the
received data for that azimuth time,
and range lines between bursts
(ie. when the other polarisation is
being received) are padded with
zeroes. A problem directly
related to the varying Doppler
centroid lies in the
synchronisation between the two
passes. figure2.27 shows
the burst coverage of two
typical passes where the
bursts are slightly misaligned.
If the burst timing of the level
0 data is known, the lines of
level 0 data corresponding
to nonoverlapping areas can be
zeroed prior to SAR processing.
In this way, only burst data
with common Doppler components
are retained, so the zeroing
out of data is also equivalent
to applying a time varying band
pass filter to the data in each pass.

Figure 2.27 Synchronisation of Bursts in Two Slightly Misaligned Passes if Reprocessing from Level 0 Data (the beams are the same) 
Figure2.28 illustrates
the spectrum of one burst of
data in the two passes, again using
the 16 point targets as an example
if no level 0 data zeroing is
performed. Due to the burst
misalignment, the two sets of
spectra are also misaligned. The
effect of the bandpass filters is to
select out the overlapped portion of
the spectrum.

Figure 2.28 Spectra of Targets in a Burst for Two Slightly Misaligned Passes 
Figure2.29 shows
the azimuth spectrum for
all bursts for
a single pass when zeros are
inserted in the alternate
polarisation. Note that the data
from a single target is
bursty in nature in both the
azimuth time domain and the
Doppler frequency domain due to
the coupling between time and
frequency inherent in linear
FM signals. Here it has been
assumed that the burst cycle
time is an integral multiple of
the Pulse Repetition Interval
(PRI) which is important for the
zero padding to work. This
assumption is true for the AP
mode but is generally not true
for ScanSAR modes.

Figure 2.29 Spectra of Targets After Zero Fill Showing IFFT Positions 
Since the zeropadded
data is stored in the same
representation as continuous
moded data, it can be processed
with the rangeDoppler
algorithm. Including all the
available bursts for a given
output point simultaneously
ensures that all the Doppler
spectrum is maintained for a
given target and it can be done
independently for both passes.
This is discussed in the section below.
During InSAR processing azimuth
varying bandpass filters can be
used to select out common
continuous spectral regions from
each image of each pass.
This operation has approximately
the same result as zero padding
the level 0 data prior to SAR
processing. This technique has
been used successfully to obtain
high quality InSAR results (Guarnieri et al 2.6.1.2.3.2.6. ).
One sideeffect of processing the
entire Doppler spectrum is that
the resulting APS product will
have an impulse response that is
modulated due to the
noncontinuous spectrum used for
compression. This impulse
response shape will not meet the
current PFASAR requirements
for this product but can fully
meet the requirements of the
InSAR application. In addition,
there will be azimuth banding,
due to different number of
bursts being used to generate
the output points. This approach
is described further in the
algorithm described below
and is the recommended version
for the PFASAR, due to its
ability to satisfy the InSAR
application requirements, for
use with another APS or an
IMS, without complicating the
ASAR product structure and interpretation.
2.6.1.2.3.2.4 Modifications To Range
Doppler Algorithm The Range Doppler
algorithm 2.6.1.2.3. (RD) is well suited to
process continuous data, but can
be modified to process data acquired
in discrete bursts. This following
discusses the modifications required
to generate an AP SLC product
suitable for InSAR applications.
Let us assume a case in which
the beamwidth covers exactly
five bursts' duration
(closely resembling that in the
AP Mode). Now let us focus
our discussion on only one
polarisation. Each polarisation
will be processed separately.
The first step is to zero pad
the gaps when data of the
other polarisation is acquired.
Assume 16 equally spaced targets
as shown in figure2.25 , and
denote them by to, and assume that
they all have the same slant
range of closest approach so
that they are confined in one
range gate after Range Cell
Migration Correction
(RCMC). Because of the
missing data, the spectra of the
targets after azimuth Fast Fourier
Transform (FFT) and RCMC
are bursty, as shown in figure2.29 .
The energy received from a target
depends on its position in the
antenna azimuth beam during the
burst, which corresponds to the
position of its Doppler
components in the
azimuthfrequency domain. To
avoid scalloping, the target
energy can be corrected by
applying the inverse of the
azimuth beam pattern to the
Doppler spectrum. This is
similar to Descalloping 2.6.1.2.4.2.
in SPECAN.
The general steps of the modified
RD algorithm are the following:
 Range compression.
 Zero pad the missing data to
simulate continuous data.
 Perform an azimuth FFT to
transform the data into the
RangeDoppler domain.
 Perform RCMC.
 Apply inverse of azimuth
beam pattern to spectrum.
 Perform azimuth matched
filtering without any
windowing applied.
 Perform the azimuth IFFT.
 Repeat algorithm for
alternate polarisation and
include phase ramp term in
azimuth matched filter to
achieve coregistration.
These steps are quite
similar to the basic RD algorithm.
In this approach, a single
azimuth IFFT is applied to the
Doppler spectrum after
application of the matched
filter. This approach
satisfies the requirements for
InSAR processing, but the
impulse responses of the APS
products suffers from modulation
as shown in figure2.30 below.
The modulation arises from the
fact that the spectrum of
each target is segmented in the
IFFT .
Ref. [2.8 ]

Figure 2.30 Impulse Response from Multiple Burst Processing for Target 1 (dotted curve is envelope of one continuous burst) 
If rangeDoppler
algorithm is used without
further modification, the APS
product will not meet the
radiometric requirements. This
is due to the fact that
targets have different number of
bursts or partial bursts and
therefore will have different
energies. The energies are
modulated along azimuth based
upon the target location
relative to the burst timeline.
This will appear as azimuth
banding in the resulting
image. This poses a problem if
the APS product is to be used
for radiometric purposes by
forming the magnitude image from
the complex samples. It is
desirable to attempt to remove
this banding if possible.
The azimuth radiometric banding
that results in the single IFFT
method can be removed by
modifying the processed azimuth
bandwidth. If the processed
bandwidth is exactly four times
the burst bandwidth then there
will always be the energy from
two bursts captured. Therefore,
when the inverse beam pattern is
applied and there is no
weighting applied to the matched
filter (i.e. just rectangular
window) the total energy
processed for each target will
be the same. The truncation of
the spectrum by the rectangular
window will either capture two
complete bursts or will capture
one complete burst and two
partial bursts. In the latter
case the two partial bursts add
up to a full burst in terms
of energy. Since the burst
bandwidth is range dependent,
the processed bandwidth must be
adjusted across range.
There are implications to
changing the processed Doppler
bandwidth to remove the azimuth
radiometric banding:
 Less of the total available
Doppler bandwidth is
retained for InSAR.
 The azimuth resolution is
range dependent (but recall
that the impulse response is
modulated anyway).
In order to support
InSAR filtering it is necessary
to supply the following
parameters in the product
annotation: burst return time,
time of the start of a burst
for a specified polarisation.,
Doppler centroid coefficients,
azimuth FM rate coefficients,
and zero Doppler time of
first output line. Using these
parameters and knowing that the
processed bandwidth is centred
at the Doppler centroid with an
extent of a specified
bandwidth, the location of the
available burst spectra can be
computed for any pixel in the
output image.
2.6.1.2.3.2.5 Conclusions This section has
outlined the processing of the AP
Mode SLC product, with
considerations for performing InSAR.
The approach is a rangeDoppler
algorithm, with an adjustment to the
processed bandwidth in the single
azimuth IFFT after azimuth
compression. The resulting image
will pass all phase and geometric
image quality requirements. However,
there will be an impulse response
shape modulation. In this
approach a small amount of
Doppler information is lost,
with only moderate implications
for InSAR, in order remove the
radiometric banding in the
amplitude image.
During InSAR processing the APS
images are azimuthvarying
bandpass filtered to achieve
common Doppler spectra.
2.6.1.2.3.2.6 References
A. M. Guarnieri, C.
Prati and F. Rocca,
"Interferometry with
ScanSAR", Proceedings of
IGARSS `95.
R. Balmer and M.
Eineder," ScanSAR
Processing Using Standard High
Precision SAR Algorithms",
IEEE Transactions on Geoscience
and Remote Sensing, Vol. 34, No.
1, January 1996.
2.6.1.2.4 SPECAN
2.6.1.2.4.1 Introduction
2.6.1.2.4.1.1 Overview The SPECAN algorithm
processes periodic bursts of SAR data in the azimuth
direction. In ScanSAR (Wide Swath
(WS) and Global
Monitoring (GM)) and Alternating
Polarisation (AP) modes, the
burstiness of the data arises from
the way the data is collected. In mediumresolution
Image Modes, periodic bursts are
extracted from the continuous data
in order to form images very
quickly. In either case, if the time
between bursts is less than the synthetic
aperture time (time for a target
to cross the azimuth antenna beam),
then data from all targets on the
ground are contained within the
bursts and an image can be formed.
Because only part of the data from a
target is received during a burst
however, the full azimuth bandwidth
available in the azimuth antenna
beam is not used. This results in a
lower resolution and/or a smaller
number of looks in the
magnitude image product.
Compared to the rangeDoppler 2.6.1.2.3.
algorithm, the SPECAN algorithm
is not as accurate in
matching the exact SAR transfer
function, and so is not
appropriate for phasepreserving
applications. Essentially, the
SPECAN algorithm trades
resolution, or number of looks,
for computational efficiency.
Typically, several bursts occur
within a synthetic aperture
time. Thus, successive burst
images contain overlapping views
of the same ground area.
These burst images, or looks,
are averaged to reduce speckle.
A consequence of SPECAN or burst
imaging is an effect called scalloping.
During the relatively short
burst, targets within the
synthetic aperture are viewed
through different parts of the
azimuth antenna beam. The
azimuth beam pattern then
results in an azimuthvarying
weighting of the target
intensity in the image. Given
the antenna pattern and the
antenna beam centre location (Doppler
centroid 2.6.1.2.2. ), this effect can
be corrected. (See Descalloping 2.6.1.2.4.2. ).
The main steps in the version of
the SPECAN algorithm used in
ASAR are shown in the block
diagram below, and described in
the following sections.

Figure 2.31 Main steps in the version of the SPECAN algorithm used in ASAR 
2.6.1.2.4.1.2 Range Compression Range compression is a
filtering operation performed on
each range line of raw SAR data. It
compresses the long transmitted
pulse into a narrow pulse with
the desired range resolution and
higher signal to noise ratio, and
can be done efficiently by the use
of the Fast Fourier
Transform (FFT). It is
common to all image formation
algorithms, and is described in
detail in the section on rangeDoppler 2.6.1.2.3. .
2.6.1.2.4.1.3 Linear Range Cell
Migration Correction (RCMC) After range
compression, the signal energy from
a point target follows a trajectory
in the twodimensional SAR data,
that depends on the changing
range delay to the target as it
passes through the antenna beam
(range migration). This trajectory
may cross several range bins. In
order to capture all the signal
energy for azimuth compression, the
signal energy from a point target
must be aligned in a signal range
bin. In SPECAN processing,
the range
migration trajectory is
approximated by a straight
line of a certain slope in the
twodimensional data array.
Thus, RCMC is
done by simply skewing the data
 that is, applying a range
shift that varies linearly with
azimuth
time  in order to align the
trajectory from a target in a
single range bin. The range
shift is done by an
interpolation of the range line.
Note that this linear RCMC is
done in the rangetime,
azimuthtime domain, rather than
the rangeDoppler domain. While
the trajectories of all
targets are aligned in single
range bins, an effect of linear
RCMC in the time domain is that
the target range positions are
shifted as a function of azimuthtime,
resulting in a skewed image. In
practice, rather than
increasing the size of the data
array to hold the skewed data,
the skewed data is wrapped
around in range in the data
array, forming a
"barber pole" effect
that is undone in the output
image. This is illustrated in figure2.32 below.

Figure 2.32 Trajectories before and after linear RCMC. 
2.6.1.2.4.1.4 Azimuth Processing SPECAN azimuth
processing is based on the concept
of deramping linear FM signals
Ref. [2.9 ]
. The azimuth signal
from a point target is approximately
a linear FM signal. That is, the
instantaneous frequency of the
signal varies linearly with time. A
burst, then, contains a portion of
this linear FM signal from a
target. Thus, the instantaneous
frequency of the signal varies
linearly within the burst, about a
mean frequency that depends on
the target's position relative
to the burst time. Deramping the
burst signal refers to the
multiplication by a reference
linear FM signal whose instantaneous
frequency varies linearly at the
same rate but with opposite slope.
This has the effect of removing
the linear frequency variation of
the signal, leaving a constant
frequency signal with a frequency
that is related to the target
position. Finally, an FFT of the
deramped signal produces a
compressed signal peak at the
target position. A
convenient representation of the
signal, for purposes of
deramping, is the frequencytime
diagram. This is a plot of the
instantaneous frequency of
the signal versus time. For a
linear FM signal, it is a
sloping straight line, where the
slope is the frequency rate. For
a sinusoid of constant
frequency, the frequencytime
diagram is a horizontal line. figure2.33 below
shows the frequencytime diagram
of azimuth SAR signals,
assumed to be linear FM. Each
line represents the signal from
a target at a different azimuth
position. The portions of the
signal that are contained in
the burst are shown. After
deramping of the burst, as shown
in the bottom part of the
figure, the signals have been
converted to sinusoids, with
frequencies related to the
target positions.

Figure 2.33 Illustration of SPECAN with frequencytime diagrams. 
The basic steps of
SPECAN, then, are the reference
function multiply of the burst
in the azimuth
direction (deramp), followed
by an azimuth FFT. The FFT
length must be as least twice as
long as the azimuth block
size to achieve the oversampling
that is necessary prior to
detection. The output of the FFT
is the compressed image formed
from the burst, and from
this image the good points are
selected. Good points correspond
to targets that were illuminated
by the antenna beam during
the entire burst. Finally, a radiometric
correction of the burst
image is performed with a
vector multiply in the azimuth
direction. This corrects for a
variation in target intensity
due to the azimuth antenna
beam pattern, as described in
the section on descalloping. 2.6.1.2.4.2.
The location of a target position
depends on the slope of the
frequencytime diagram, or the
frequency
rate of the linear FM
signal. In the SAR azimuth
signal, the azimuth
frequency rate depends on
range. This geometric distortion
needs to be corrected by an
azimuth interpolation of the
burst image, as described later
under resampling.
2.6.1.2.4.1.5 Look Summation and Resampling After the basic SPECAN
azimuth processing to form the burst
images, several operations are done
to form the image product. These
steps are summarised as follows.
First, the burst image is
shifted in range to correct for
the skew that was applied during
linear RCMC. This step is called
deskew. Only the integer
portion is corrected in this
step. The fractional portion is
handled during the SR/GR
resampling step.
Next, an optional range
multilooking is applied. This
consists of applying a set of
range bandpass filters to the
image to extract rangelook
images corresponding to
different range frequency bands.
The squared magnitude of the
complex burst image for each
range look is then computed.
This is called detection. The
squared magnitude, rather
than the magnitude, is taken to
avoid aliasing during the
following interpolation steps.
The squared magnitude looks are
then summed in range. Also,
different burst images of the
same area of the ground form
different azimuth looks, and
these are summed. The summation
of looks is done to reduce speckle.
The looksummed image is then
resampled in range. This is a
shift and interpolation to
correct for the fractional
sample part of the deskew.
At the same time the data is
resampled in range in order to
convert to ground range and to
achieve the required output
sample spacing.
Then, azimuth resampling to the
desired output pixel spacing.
This compensates for the
rangedepend pixel spacing at
the output of deramp and
FFT. This may also include
averaging to extract additional
azimuth looks.
Finally, the square root of the
image is taken to obtain the
magnitude image.
2.6.1.2.4.1.6 Product Processing The output at this
point is a valid mediumresolution
(IMM), ScanSAR (WSM, GM1), or
alternating polarisation (APP, APM) product. (
See Table in the
section entitled "Organisation
of Products" in chapter 2
). Generation of other products
require the following steps.

Block
Averaging: The
image is averaged and
subsampled to form a browse
product (IMB, APB, WSB,
GMB). ( See Table 2.47 in
the section entitled
"Browse
Products" ).

Geocoding:
For the geocoded
product (APG), the image is
resampled in two dimensions
convert the image to a
desired map projection.

2.6.1.2.4.1.7 Summary The processing steps
for the products processed by the
SPECAN algorithm are summarised
below:

Alternating
Polarisation Precision
product, and all
mediumresolution
products: All steps
except geocoding and block
averaging are performed.

Geocoded
products: All steps
except azimuth resampling
(resampling is done during
geocoding) and block
averaging are performed.

Browse
Product: All steps
except geocoding are performed.

2.6.1.2.4.1.8 References
. J. C. Curlander, R.
N. McDonough, Synthetic Aperture
Radar: Systems and Signal
Processing, John Wiley and Sons,
1991.
