826 InSAR Basics-F15
826 InSAR Basics-F15
826 InSAR Basics-F15
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Outline
SAR limitations
Interferometry
SAR interferometry (InSAR)
Single-pass InSAR
Multipass InSAR
InSAR geometry
InSAR processing steps
Phase unwrapping
Phase decorrelation
Baseline decorrelation
Temporal decorrelation
Rotational decorrelation
Phase noise
Persistent scatterers
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SAR limitations
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SAR limitations
All signals are mapped onto reference plane
This leads to foreshortening and layover
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Shadow, layover, and foreshortening distortion
SEASAT Synthetic Aperture Radar
Launched: June 28, 1978
Died: October 10, 1978
orbit: 800 km
f: 1.3 GHz PTX: 1 kW
: 33.8 s B: 19 MHz
: 23 3 PRF: 1464 to 1647 Hz
ant: 10.7 m x 2.2 m
x = 18 to 23 m y = 23 m
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SAR limitations layover
Layover: ( is the local slope)
Causes an inversion of the image geometry. Peaks of hills or mountains
with a steep slope commute with their bases in the slant range resulting in
severe image distortion.
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SAR limitations shadow
Shadow: - /2 ( is the local slope)
A region without any backscattered signal. This effect can extend over
other areas regardless of the slope of those areas.
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Foreshortening and geocoding
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Interferometry
interferometryThe use of interference phenomena for
purposes of measurement.
In radar, one use of interferometric techniques is to
determine the angle of arrival of a wave by comparing the
phases of the signals received at separate antennas or at
separate points on the same antenna.
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SAR interferometry how does it work?
A2
B
Radar A1
Antenna 1
Antenna 2
Return could be
from anywhere
on this circle
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SAR interferometry how is it done?
R R 2 R 2 B2 2 B R cos
2
cos sin
2
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j R R R
E1 E e
*
2
4
j R
E1E *2 e
e j
Since is measured,
R can be determined
R
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Example
Let = 10 cm (f = 3 GHz)
measure to /100 (3.6)
equivalent to 0.1 mm or 0.3 ps Multipass baseline
Transmit and receive on antenna A1
resolution Transmit and receive on antenna A2 16
Interferometric SAR radar phase
For single-pass InSAR
where transmission is on
antenna A1 and reception
uses both A1 and A2:
4R
j
E1 e jscatterer e
2 2 R R
j
E 2 e jscatterer e
2
j 2 R 2 R R
E1E*2 e
2
j R
E1E*2 e
e j
And
R Simultaneous baseline
2 Transmit on antenna A1
Receive on both A1 and A2 17
Radar interferometry geometry
From geometry we know
zx h R cos
but is undetermined if the
scatterer is not on the
reference plane.
To determine we use
R B sin
R
a 2
where a = 1 for single-pass
and a = 2 for multipass
So that
sin
a 2B
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Radar interferometry geometry
From
sin
a 2B
we find
sin 1
a 2B
and
1
zx h R cos sin
a 2B
where
a = 1 for single-pass
a = 2 for multipass
a = 2 for single-pass, ping-pong mode
Ra nge S phe re
D opple r C one
Ba se line
Ve ctor
Aircra ft
Position
Ve locity
Ve ctor
Pha se C one
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SAR Interferometry
Multi-pass interferometry
Two pass
Two scenes, one interferogram
topography, change detection
surface velocity (along-track interferometry temporal baseline)
Three pass
Three scenes, two interferograms
topography, change detection, surface deformation
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Differential interferometry how does it work?
Three-pass repeat track
Two different baselines
(B1 , 1 ) (B2 , 2 )
B2 sin( 2 )
2 1 0
B1 sin( 1 )
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Interferometric SAR processing
Production of interferometric SAR images and data sets
involves multiple processes.
Independent SAR data sets must be collected
Complex SAR images are produced
SAR images must be registered with one another
Interferometric phase information extracted pixel-by-pixel
Coherence is analyzed
Phase is unwrapped (removes modulo-2 ambiguity)
Phase is interpolated
Phase is converted into height
Interferometric image is geocoded
To produce surface velocity or displacement maps,
successive pairs of InSAR images are processed to
separate elevation effects from displacements.
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InSAR processing steps
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Phase history and magnitude image
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Phase image
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Illustrated InSAR processes (1 of 3)
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Illustrated InSAR processes (2 of 3)
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Illustrated InSAR processes (3 of 3)
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Phase coherence
Lack of coherence caused by decorrelation
Baseline decorrelation
Sufficient change in incidence angle results in scatterer interference
(fading effect)
Temporal decorrelation
Motion of scatterers between observations produces random phase
Windblown vegetation
Continual change of water surface
Precipitation effects
Atmospheric or ionospheric variations
Manmade effects
Rotational decorrelation
Data collected from nonparallel paths
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SAR Interferometry
The radar does not measure the path length directly, rather it measures
the interferometric phase difference, , that is related to the path length
difference, R
a 2 a 2
R B sin
The measured phase will vary across the
radar swath width even for a surface without
relief (i.e., a flat surface or smooth Earth)
increases as the sine of
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SAR Interferometry
It follows that
a 2 a 2 a 2
B sin o B sin o B coso
phase due to phase due to
smooth Earth relief
a 2
B coso
z
flat
R o sin o
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SAR Interferometry
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Ambiguity height
The interferometric ambiguity height, e, which is the elevation for which
the flattened interferogram changes by one cycle, is
R o sin o
e
a B coso
The ambiguity height is like the sensitivity of the InSAR to relief.
From this relationship we know
A large baseline B improves the InSARs sensitivity to height variations.
However since the radar measures interferometric phase in a modulo 2
manner, to obtain a continuous relief profile over the whole scene the
interferometric phase must be unwrapped.
To unambiguously unwrap the phase, the interferometric phase must be
adequately sampled.
This sampling occurs at each pixel, thus if the interferometric phase changes
by 2 or more across one pixel a random phase pattern results making
unwrapping difficult if not impossible.
The problem is aggravated for positive terrain slopes (sloping toward radar)
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Phase unwrapping
z Phase
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Phase
2
2
0 0
x x
x
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Baseline decorrelation
To illustrate this consider two adjacent pixels in
the range dimension pixel 1 & pixel 2 on a
surface with slope .
The interferometric phase for these two pixels is
a 2
1 B sin
a 2
2 B sin
For small r (small slant range pixel spacing)
a 2 a 2 a 2
2 B sin B cos 1 B cos
and from geometry we know
r
R o tan
so that
a 2 r
2 1 B cos
R o tan
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Baseline decorrelation
Limiting to 2 results in a critical baseline, Bc such that if
B > Bc the interferometric phases will be hopelessly
unwrappable.
This phenomenon is know as baseline decorrelation.
R o tan
B c Bc cos
a r
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Perpendicular Baseline
Perpendicular Baseline, B
Parallel-ray assumption
Orthogonal baseline component, B, is
key parameter used in InSAR analysis
B = B cos( - )
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Baseline decorrelation
While Bc represents the theoretical maximum baseline that
will avoid decorrelation, experiments show that a more
conservative baseline should be used.
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Correlation
The degree of coherence between the two complex SAR
images, s1 and s2, is defined as the cross-correlation
coefficient, , or simply the correlation
E{s1 s*2 }
E{ s1 } E{ s 2 }
2 2
where
s2* is the complex conjugate of s2
E{ } is ensemble averaging
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Decorrelation effects
Factors contributing to decorrelation include:
Spatial baseline
Inadequate spatial phase sampling (a.k.a. baseline decorrelation)
Fading effects
Rotation
Non-parallel data-collection trajectories
Fading effects
Temporal baseline
Physical change in propagation path and/or scatterer between observations
Noise
Thermal noise
Quantization effects
Processing imperfections
Misregistration
Uncompensated range migration
Phase artifacts
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Noise effects
Random noise (thermal, external, or otherwise) contributes
to interferometric phase decorrelation.
Analysis goes as follows:
Consider two complex SAR signals, s1 and s2, each of
which is modeled as
s1 c n 1 and s2 c n 2
where c is a correlated part common to the signal from both
antennas and the thermal noise components are n1 and n2.
The correlation coefficient due to noise, N, of s1 and s2 is
E{s1 s*2 }
N
E{s1 s1*} E{s 2 s*2 }
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Noise effects
Since the noise and signal components are uncorrelated, we
get 2
c
N
c n
2 2
1 1
N
1 n
2
c
2
1 SNR 1
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Noise effects
Noise also increases the uncertainty in the phase
measurement, i.e., the standard deviation of the phase,
n 1
signal SNR
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Noise effects
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Noise with another decorrelation factor
Now re-introducing noise we get
2
c
spatial noise
c d n
2 2 2
2
c 1
spatial noise
c d
2 2
1 SNR 1
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Decorrelation and phase
The decorrelation effects from the
various causes compound, i.e.,
scene N H
where
scene denotes long-term scene coherence
N represents decorrelation due to noise
H includes system decorrelation sources
including baseline decorrelation,
misregistration, etc.
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Rotational decorrelation
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Temporal decorrelation
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Fading effects
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Misregistration effects
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Misregistration
Misregistration leads to increased phase variance, not a phase offset
(bias).
SAR imaging geometry variations contribute to misregistration.
Removing geometric distortion and
shifts is called coregistration or
registration.
A two-part process for achieving
acceptable registration involves
a coarse or rough registration
followed by a fine or precise
registration process.
The goal is to register
the two complex SAR
images to within 1/8 of
a pixel.
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Rough registration
In the rough registration process reference points
(pass points) are identified in both images.
Transformations are determined that will align
the pass points in both images.
The transformation and resampling is applied to
one of the images so that the two images are
registered at the pixel level.
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Rough registration
Spline interpolation is used to resample the image to
provide the pixel-level registration.
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Precise registration
Following rough registration, a precise
registration process is used to achieve the
desired 1/8 pixel registration.
Again reference (pass) points are selected.
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Precise registration
An image segment from the
master image is selected and in
the same location in the slave
image a slightly smaller image
segment is selected.
These image segments undergo
8:1 interpolation (to achieve a 1/8
pixel registration).
A search for the proper two-
dimensional shift is conducted
using the correlation coefficient as
the measure of goodness.
Results from this search process
are applied to the overall image.
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Precise registration
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Geometric correction
gr _ r sl _ r 2 H 0 z
2
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Geometric correction
The steep slope, as seen in the The areas affected by layover are
slant range axis, appears to have identified and undergo additional
a negative slope. processing to remove the
This phenomenon is used as a associated geometric distortion.
layover indicator.
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Geometric correction
The pixels affected by layover can
then be resorted to correct for the
geometric distortion resulting from
the layover effect.
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Geometric correction
In regions of shadow, the low
SNR results in large phase errors
and, consequently, large height
errors.
Height errors must be detected
and corrected to produce valuable
elevation maps.
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Geometric correction
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Geometric correction
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Temporal decorrelation and persistent scatterers
Material taken from Ferretti, Prati, and Rocca, Permanent scatterers in SAR interferometry, IEEE
Transactions on Geoscience and Remote Sensing, 39(1), pp. 8-20, 2001.
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Temporal decorrelation and persistent scatterers
Conventional InSAR processing relies on the correlation
coefficient as a quality indicator of the interferometric
phase.
These decorrelation factors all degrade the overall scene
correlation.
However, studies have found that scenes frequently
contain permanent or persistent scatterers (PS) that
maintain phase coherence over long time intervals.
Often times the dimensions of the PS are smaller than the
SARs spatial resolution. This feature enables the use of
spatial baseline lengths greater than the critcal baseline.
Pixels containing PSs submeter DEM accuracy and
millimetric terrain motion (in the line of sight direction) can
be detected.
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Temporal decorrelation and persistent scatterers
The availability of multiple persistent scatterers widely
distributed over the scene enables estimation of the
atmospheric phase screen (APS)
With an estimate of the APS, these effects can be removed
enabling production of reliable elevation and velocity
measurements.
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Persistent scatterer
What makes a good persistent scatterer ?
Scatterers with a large RCS and a large scattering beamwidth.
For example, naturally occuring dihedrals and trihedrals.
These can often be found in urban areas and rocky terrrain.
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Temporal decorrelation and persistent scatterers
Taken from Warren, Sowter, and Bigley, A DEM-free approach to persistent point scatterer
interferometry, FIG Symposium, 2006.
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Temporal decorrelation and persistent scatterers
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Temporal decorrelation and persistent scatterers
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Temporal decorrelation and persistent scatterers
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Temporal decorrelation and persistent scatterers
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Temporal decorrelation and persistent scatterers
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Temporal decorrelation and persistent scatterers
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