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Synthetic Aperture Radar Interferometry
INTERFEROMETRIC ERROR SOURCES

Interferometric Decorrelation
In addition to the decorrelation contributions, several other sources
of error exist in interferometry. These include







Layover and shadow in radar imagery from slant range geometry
Multiple scattering within and among resolution cells
Range and Azimuth sidelobes due to bandwidth/resolution
constraints
Range and azimuth ambiguities due to design constraints
Multipath and channel cross-talk noise as low-level interference
Calibration errors
Propagation delay errors from atmosphere and ionosphere
J
Synthetic Aperture Radar Interferometry
LAYOVER AND SHADOW IN RADAR IMAGING
Mapping of Earth’s
surface into slant range
distorts highly sloped
areas
RADAR IMAGE
TERRAIN
Layover
Shadow
Ground Range
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Synthetic Aperture Radar Interferometry
LAYOVER EFFECTS IN INTERFEROMETRY

As slopes increase and approach the look direction, the resolution
element size normal to the look direction increases toward infinity.
This has the following consequences:
– Radar backscatter return becomes very bright, giving high
interferometric correlation (high SNR)
– Effective critical baseline decreases toward zero, with
interferometric fringe rate approaching one cycle of phase per
pixel
No surface slope
Surface slope
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Synthetic Aperture Radar Interferometry
LAYOVER EFFECTS IN INTERFEROMETRY

The distortion of terrain into slant range coordinates has
consequences for the inference of terrain height from
interferometric phase
– Widely spaced points on the sloping ground, well outside a
particular ground resolution element, can contribute to the
complex backscatter in a range resolution element,
particularly when the slope exceeds the look angle, leading to
incorrect heights.
– The close proximity in slant range of widely space ground
elements at very different heights leads to phase shears that
confound phase unwrapping algorithms.
Two scatterers with range
Two scatterers with range
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Synthetic Aperture Radar Interferometry
MULTIPLE SCATTERING EFFECTS

Layover illustration is also an example of multiple scattering
effects that occur among resolution cells. In this case, the bridge
return will dominate the water return. There will be multiple
images of the bridge in the radar image at different ranges. Each
range element in an interferogram will have its own interpretation
of the height, depending on the scattering phase function of the
bridge and water
Similar effects occur within the volume
of a resolution element in forming the
coherent backscatter. The aggregate
height is not necessarily the uniformly
weighted average of the scatter heights
Two scatterers with range
Two scatterers with range
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Synthetic Aperture Radar Interferometry
SHADOW EFFECTS IN INTERFEROMETRY

As slopes approach being parallel to the look direction, the
resolution element size normal to the look direction decreases
toward zero. This has the following consequences:
– Radar backscatter return becomes very dim, giving low
interferometric correlation (low SNR), adding difficulty to
phase unwrapping
– Effective critical baseline increases toward infinity, with
interferometric fringe rate slowing down, easing phase
unwrapping
r
r
Loc
al S
lo
No surface slope
pe
Surface slope
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Synthetic Aperture Radar Interferometry
LAYOVER AND SHADOW MITIGATION


For wide-swath interferometric systems that span a large range of
incidence angles, the effects of layover and shadow can be
mitigated through parallel track imaging:
– Layover more likely in near swath where look angle is shallow
– Shadow more likely in far swath where look angle is steep
– By flying parallel tracks with partial swath overlap, near swath
layover regions are likely to be intact in far swath of parallel
track, and shadow regions in far swath are likely to be intact in
near swath of a different parallel track
For narrow swath systems, orthogonal imaging geometries are
probably best
– Opposite side imaging (anti-parallel tracks) not optimal
because near swath layover of one track corresponds to far
swath shadow of anti-parallel track
J
Synthetic Aperture Radar Interferometry
EXAMPLE OF LAYOVER/SHADOW MITIGATION

Figure of Northridge Mosaic here.
J
Synthetic Aperture Radar Interferometry
RANGE SIDELOBES IN RADAR IMAGING

Range sidelobes arise in extended time-bandwidth implementations of linear FM pulsed systems. For a pulse of duration  p with
chirp rate K , observing a target located at temporal position t T ,
the impulse response is:
t  t  jK(t  t ) 2  jK(t  t ) 2
T
0
W(t 0 )   rect T e
e
dt
  p 


tT   p
e
jK (tT  t0 ) 2
e
j2 K(t 0 t T )t
dt
tT
  pe
 jKt 0 2  / 4
sin K(t 0  t T ) p
K(t0  t T ) p
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Synthetic Aperture Radar Interferometry
RANGE SIDELOBES IN INTERFEROMETRY



The interferometric phase associated with the main lobe of a
resolution element contributes to the surrounding resolution
elements weighted by the range impulse response
Phase noise contributed by range sidelobes usually modeled as
additive noise term at the level NSR = ISLR. NSR is multiplied by
expected signal level to compute noise power to add.
Range sidelobes actually contribute multiplicative noise: consider
the case when the peak side lobe is brighter than the ambient
backscatter
Main lobe with
interferometric phase  
side lobes with
interferometric phase  
peak side lobe
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Synthetic Aperture Radar Interferometry
AZIMUTH SIDELOBES IN RADAR IMAGING

Azimuth sidelobes arise in the naturally extended time-bandwidth
environment of synthetic aperture systems. For a system with
Fresnel zone F , azimuth antenna length L , observing a targe at
azimuth location xT , the azimuth impulse response is:
x  xT  x p / 2  j(x  x ) 2 / F 2  j(x x ) 2 / F 2
T
0
W(x0 )   rect
e
dx
e
x


p


xT  x p / 2
e
jK (x T  x0 ) 2
e
j 2(x 0  xT )x / F 2
xT  x p / 2
 x pe
 jKx 0
2 
2F 2
dx , x p 
L
2
sin
(x

x
)x
/
F


0
T
p
/4
(x0  x T )x p / F 2
In interferometry, treatment of azimuth sidelobes is similar to range
sidelobes
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Synthetic Aperture Radar Interferometry
SIDELOBE MITIGATION STRATEGIES




In regions of high contrast, where sidelobes can lie above the
ambient backscatter, or in regions that are are very dark and
cannot tolerate a significant additional noise contribution,
sidelobes must be reduced
Weighting of the matched filter function in range or azimuth
compression can effectively reduce sidelobes in a controlled
fashion
Cost of weighting is reduction in processing bandwidth, leading to
reduction in resolution.
Design of an interferometer should consider bandwidth and
weighting functions suited to the mapping problem of interest:
e.g. urban mapping requires very fine resolution and very low
sidelobes because the scenes are highly contrasted.
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Synthetic Aperture Radar Interferometry
RANGE AMBIGUITIES IN INTERFEROMETRY




Range ambiguities arise in spaceborne systems primarily,
because the radar must pulse faster than the round-trip light time
for a single pulse event.
Because multiple pulses are in the air, it is possible for the tail end
of energy from a preceding pulse or leading end of energy from a
succeeding pulse to contribute to a pulse of interest.
Though multiplicative noise, range ambiguities are modeled as
additive thermal noise at a level NSR = total power integrated in
ambiguous pulses within the swath. This noise ratio multiplied by
the expected mean signal power sets the additive noise level. This
roughly determines the interferometric phase noise contributed to
the system.
Through adjustment of the pulse width and the pulse repetition
frequency, it is possible to control range ambiguities.
J
Synthetic Aperture Radar Interferometry
ILLUSTRATION OF RANGE AMBIGUITIES

Range ambiguity figure here
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Synthetic Aperture Radar Interferometry
AZIMUTH AMBIGUITIES IN RADAR IMAGING



Azimuth ambiguities arise in radar imaging because the pulse
repetition frequency is insufficient to satisfy the Nyquist criterion
for adequate sampling of the Doppler spectrum.
Spaceborne systems are typically designed for low PRF, near the
3dB spectral width, to reduce data rate. As a result, energy in the
tails of the azimuth spectrum aliases.
Azimuth ambiguities are again multiplicative, but are modeled in
the usual additive way.
Limiting the processing
bandwidth to a fraction
of the PRF reduces
ambiguity level
PRF
f
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Synthetic Aperture Radar Interferometry
AMBIGUITY MITIGATION STRATEGY





Range and azimuth ambiguities contribute to the random phase
noise in interferometry multiplicatively.
Both range and azimuth ambiguities rising above the ambient
backscatter significantly corrupt the interferometric phase.
To reduce azimuth ambiguities, PRF should be increased to
properly sample azimuth spectrum.
To reduce range ambiguities, PRF should be decreased (in
general) to separate pulses in time as much as possible.
Trade-off must consider the required azimuth resolution, desired
look angles, swath width, and noise level.
J
Synthetic Aperture Radar Interferometry
INTERFEROMETRIC RADAR SCHEMATIC
In addition to baseline and
position, time and phase
delays in the radar require
calibration.
J
Synthetic Aperture Radar Interferometry
RELATIONSHIP BETWEEN PARAMETERS AND
INTERFEROMETER ELEMENTS
Parameter
B aseline vector , B , including
length and attitude, for
r eduction of inter fer om etric
phase to height
A bsolute r adar r ange from one
antenna to tar gets, for
geolocation
D ifferential r adar r ange
between channels, for im age
alignment in interfer ogram
for mation
D ifferential phase betw een
channels, for deter mination of
the topogr aphy
Element
Locations of the phase
center s of both antennas
Time delay thr ough the
com posite tr ansmitter /
r eceiver
Time delays thr ough the
r eceiver chains (but not the
transm itter chain)
Phase delays thr ough the
r eceiver chains (but not the
transm itter chain)
Accuracy
a few millimeter s
a few nanoseconds
few er nanoseconds
a few degr ees
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Synthetic Aperture Radar Interferometry
CALIBRATION PARAMETER EQUATIONS
The phase at the receiver outputs is given by
N 2

a
i

b
i
a (t)   BB (t   )   
a
r
i 0
N 2
b (t)   BB (t   )   
b
r
i 0

N 1
N 1
i 0
i 0

N 1
N 1
i 0
i0
k  i 1 k   a  i   ia 
N1
k  i1k   b i    ib 
N 1
N 1
Baseband frequency:
 B B   c   i
i 0
N 1
Receiver time delay:
Transmitter phase delay:
   x    ix , x  a,b
x
r
t
i 0
4

2

ra  t
(ra  rb )  t
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Synthetic Aperture Radar Interferometry
CALIBRATION PARAMETER EQUATIONS II
The phase difference between the channels is
   a   b
  BB (   )  (   ) 
a
r
b
r
a
r
b
r
2

(ra  rb )
Channel phase constant:
N2

   
x
r
i 0
x
i

N 1
N1
x






 k i 1 k
 i
x i
N 1
i 0
,
x  a,b
i0
If total time and phase delay differences can be measured, then
range difference proportional to topography (final term in equation)
can be known. Note: this term is also dependent on baseline knowledge accuracy.
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Synthetic Aperture Radar Interferometry
CALIBRATION STRATEGIES

To determine the channel time and phase delays, assume that the
interferometer is stable over time and baseline is known.
– Total time delay (range) can be determined by comparing
location of known target to inferred location
– Differential time delay can be determined by scene matching
over a flat surface
– Differential phase delay can be determined by inserting a
calibration tone near the receiving antennas
a,calto ne (t)   BB,cal (t   ra)   ra
b,calto ne (t)   BB,cal (t   br )   rb
 calto ne   BB,cal ( ar   br ) ( ra   rb )
J
Synthetic Aperture Radar Interferometry
CALIBRATION STRATEGIES II


It is also possible to calibrate the radar interferometer through
simultaneous least squares adjustment, utilizing the sensitivity
equations described earlier and reference data, such as a DEM
– Requires radar receiver time and phase stability over all time,
which is difficult to achieve
– Requires baseline stability over all time
– Least squares adjustment and calibration tone is generally
needed
One solution to potentially remove receiver delays without
calibration tone: operate the interferometer in “ping-pong” mode.
– By using a single transmitter and receiver, differential time and
phase delays are zero.
– Cost: double pulse repetition frequency for the one receiver
required to properly sample azimuth spectrum.
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Synthetic Aperture Radar Interferometry
CHANNEL ISOLATION IN RADAR
INTERFEROMETRY




In some single-pass dual-aperture systems, energy can leak
between receiver channels
– Standard mode: radiation from other antenna or platform
scatterers entering the antenna (multipath)
– Ping-pong mode: switch between receiving antennas has
some leakage, and multipath
Switch leakage and multipath from other antenna appear in
interferometric phase signature as phase modulation at the
interferometric fringe frequency.
Multipath from other platform scattering sources appears as
phase modulation at a frequency proportional to the scattererantenna separation.
Repeat-pass single-aperture systems do not suffer from channel
isolation problems.
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Synthetic Aperture Radar Interferometry
SWITCH ISOLATION
with leakage 
In ping-pong operation,
switch alternates antenna
setting for transmit/receive.
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Synthetic Aperture Radar Interferometry
SWITCH ISOLATION II
First term of
Expression
First two terms
All three terms
J
Synthetic Aperture Radar Interferometry
ANTENNA MULTIPATH IN INTERFEROMETRY
STALO
Transmitter
jb
Ab e e
Receiver
 j 4 ra

j b
  Abe e
 j 4  ( rb  B)

Pure Switch
Antenna a
Scatter to b
B
Scatter to a
j b
Ab e e
 j 4 rb

j b
  Ab e e
 j 4 (ra  B)

Antenna b
Backscatter
from target
4
 j 4 (ra rb )
j (ra rb ) 
4

2
ab : A e 
2 cos B   e 




*
2
b
Baseline B is constant. Multipath off antennas has same
effect as switch leakage.
Backscatter
from target
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Synthetic Aperture Radar Interferometry
PLATFORM MULTIPATH
Multipath cross terms depend on “baseline” from platform scatterer
J
Synthetic Aperture Radar Interferometry
EXAMPLES OF MULTIPATH
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Synthetic Aperture Radar Interferometry
ATMOSPHERIC PROPAGATION EFFECTS IN RADAR
INTERFEROMETRY




Due to turbulent mixing in the troposphere, particularly in the wet
layers, the refractive index along the radar ray path varies within
the scene.
Wet tropospheric variations of refractivity are typically an order of
magnitude smaller than the dry troposphere total path refractivity
because the wet troposphere is concentrated in a layer near the
earth’s surface.
For single-pass two-aperture systems, the difference in path delay
variations cancels to first order because the ray path sensed is
nearly identical. The total path delay does affect the absolute
range, as seen previously, but not significantly the differential
range or phase.
For repeat-pass single-aperture systems, the difference in path
delay is a substantial limiting factor.
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Synthetic Aperture Radar Interferometry
IONOSPHERIC PROPAGATION EFFECTS IN RADAR
INTERFEROMETRY





Due to turbulent mixing in the ionosphere, and diurnal variations
of earth’s response to the solar wind, the refractive index along
the radar ray path varies within the scene.
For airborne systems, the ionosphere is not a concern.
For spaceborne platforms, the scale size of ionospheric anomalies
is large in the radar scene because the ionosphere is relatively
close to the sensor.
For single-pass two-aperture systems, the difference in path delay
variations cancels to first order because the ray path sensed is
nearly identical.
For repeat-pass single-aperture systems, the difference in path
delay is a substantial limiting factor.