Interferometric Synthetic-Aperture
Radar (InSAR) Basics
1
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
2
SAR limitations
3
SAR limitations
All signals are mapped onto reference plane
This leads to foreshortening and layover
4
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
Figure 5-4. Example of radar image layover.
Seasat image of the Alaska Range showing
the top of a mountain imaged onto the
glacier at its foot (center). Shadows are also
present on many of the backslopes of these
steep mountains. Illumination is from the top
[from Ford et al., 1989].
5
SAR limitations – foreshortening
Foreshortening: - <  <  ( is local slope).
Dilates or compresses the resolution cell (pixel) on the ground with respect to
the planar case.
6
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.
7
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.
8
Foreshortening and geocoding
9
Interferometry
interferometry—The 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.
10
SAR interferometry – how does it work?
A2
B
Radar
A1
Antenna 1
Antenna 2
Return could be
from anywhere
on this circle
Return comes from
intersection
Single antenna SAR
Interferometric SAR
11
SAR interferometry – how is it done?
B is the interferometric baseline
Single pass or
Simultaneous baseline
Two radars acquire data from different
vantage points at the same time
Repeat pass or
Repeat track
Two radars acquire data from different
vantage points at different times
12
Single-pass interferometry
Single-pass interferometry. Two antennas offset by known baseline.
13
Interferometric SAR – geometry
The key to InSAR is to collect complex SAR data from slightly offset
perspectives, the separation between these two observation points is
termed the baseline, B.
This baseline introduces for each point in the scene a slight range
difference that results in a phase shift that can be used to determine the
scatterer’s elevation.
From trigonometry (law of cosines)
R  R 2  R 2  B2  2 B R sin    
Furthermore for R » B
R   B sin   
[Note that B amplifies R]
For scatterers in the reference plane 
is known ( = o), otherwise  is
unknown
Finding R enables determination of 
and z(x)
14
Law of cosines
c 2  a 2  b 2  2ab cos 
R  R 2  R 2  B2  2 B R cos       
2



cos        sin    
2

R  R 2  R 2  B2  2 B R sin    
 R 2  2R R  R 2  R 2  B2  2BR sin    
R 2 B2
2R R  R  B  2BR sin      R 

 B sin      R   B sin    
2R 2 R
2
2
15
Interferometric SAR– radar phase
Radar phases
E1  e j scatterer e
j
E 2  e j scatterer e
E1E  e
*
2
E1E *2  e
j
j
4R

j
4  R  R 

4
R   R  R 

4
R

 e j
Since  is measured,
R can be determined
R 

4
Example
Let  = 10 cm (f = 3 GHz)
measure  to /100 (3.6º)
equivalent to 0.1 mm or 0.3 ps
resolution
Multipass baseline
Transmit and receive on antenna A1
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:
E1  e jscatterer e
j
E 2  e jscatterer e
E1E*2  e
E1E*2  e
j
j
4R

j
2  2 R  R 

2
2 R  2 R  R 

2
R

 e j
And
R 

2
Simultaneous baseline
Transmit on antenna A1
Receive on both A1 and A2
17
Radar interferometry – geometry
From geometry we know
zx   h  R cos 
but  is undetermined if the
scatterer is not on the
reference plane.
To determine  we use
R   B sin   

a 2
where a = 1 for single-pass
and a = 2 for multipass
R 
So that

 sin    
a 2B
18
Radar interferometry – geometry
From

 sin    
a 2B
we find
  

    sin 
 a 2B
1
and

  
1 
 
zx   h  R cos    sin 
 a 2B 

where
a = 1 for single-pass
a = 2 for multipass
a = 2 for single-pass, ping-pong mode
Precise estimates of z(x) require accurate knowledge of B, , and 
as well as R and h
19
Interferometric SAR processing geometry
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
S ca tte re r is a t inte rse ction of Ra nge
S phe re , D opple r C one a nd Pha se
C one
20
SAR Interferometry
InSAR provides additional information via phase
measurements
This additional information enables a variety of new
capabilities
Topography measurement
Vertical surface displacement (uplift or subsidence)
Lateral surface displacement (velocity)
Change detection (via phase decorrelation)
21
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
22
Differential interferometry – how does it work?
Three-pass repeat track
Two different baselines
(B1 , 1 )
(B2 ,  2 )
Same incidence angle
Same absolute range
Parallel ray approximation used
to detect changes
If the surface did not change between
observations, then
 B2 sin(  2  ) 
  0
2  1 
 B1 sin( 1  ) 
23
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.
24
InSAR processing steps
25
Phase history and magnitude image
26
Phase image
27
Illustrated InSAR processes (1 of 3)
28
Illustrated InSAR processes (2 of 3)
29
Illustrated InSAR processes (3 of 3)
30
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
Phase unwrapping to obtain absolute phase requires
reference point
31
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 
If o is the incidence angle in the absence
of relief and z is the elevation of a pixel at
the same Ro, then the change in incidence
angle induced by the relief is
z
 
R o sin o   
32
SAR Interferometry
It follows that

a 2
a 2
a 2
B sin o     
B sin o   
B coso  



phase due to
smooth Earth
flat  
phase due to
relief
a 2
z
B coso   

R o sin o
Removing the phase component due to the smooth Earth yields a
“flattened interferogram”
33
SAR Interferometry
34
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
a B coso   
The ambiguity height is like the sensitivity of the InSAR to relief.
e
From this relationship we know
•
•
•
•
•
A large baseline B improves the InSAR’s 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)
35
Phase unwrapping
z
Phase
8

6
Phase

2
2
x
ACTUAL ELEVATION PROFILE
4
0
0
x
x
WRAPPED PHASE
UNWRAPPED PHASE
Formerly phase unwrapping was an active research area, now Matlab
has a built-in function (unwrap.m) that does this reliably for most cases.
36
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
  2  1  
r
a 2
B cos   

R o tan  
37
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.
B c  Bc cos    
 R o tan   
a r
B denotes the perpendicular component of baseline B
where
a = 1 for single-pass
a = 2 for multipass
a = 2 for ping-pong mode
[i.e., Tx(A1)–Rx(A1 , A2); Tx(A2)–Rx(A1, A2); repeat]
38
Perpendicular Baseline
Perpendicular Baseline, B
Parallel-ray assumption
Orthogonal baseline component, B, is
key parameter used in InSAR analysis
B = B cos( - )
39
Baseline decorrelation
While Bc represents the theoretical maximum baseline that
will avoid decorrelation, experiments show that a more
conservative baseline should be used.
40
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

where
E{s1  s*2 }
E{ s1 }  E{ s 2 }
2
2
s2* is the complex conjugate of s2
E{ } is ensemble averaging
(incoherent) 0 <  < 1 (coherent)
 is a quality indicator of the interferometric phase,
for precise information extraction, a high value is required.
41
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
42
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  n1
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
N 
E{s1  s*2 }
E{s1  s1*}  E{s 2  s*2 }
43
Noise effects
Since the noise and signal components are uncorrelated, we
2
get
N 
c
c n
2
2
Recall that the signal-to-noise ratio (SNR) is |c|2/|n|2 yields
N 
1
1 n
2
c
2

1
1  SNR 1
For an SNR of , the expected correlation due to noise is 1
For an SNR of 10 (10 dB), N = 0.91
For an SNR of 4.5 (6.5 dB), the N = 0.81
44
Noise effects
Noise also increases the uncertainty in the phase
measurement, i.e., the standard deviation of the phase, 
n
1
 

signal
SNR
45
Noise effects
Note that the
slope   as
1
A 6.5 dB SNR yields a 50
standard deviation and a
correlation of about 0.8
46
Noise with another decorrelation factor
Now consider two complex SAR signals, s1 and s2, each of
which is modeled as
s1  c  d1  n1 and
s2  c  d2  n 2
where c is a correlated part common to the signal from both
antennas, di is the uncorrelated part due to spatial baseline
decorrelation (exclusive of noise), and the thermal noise
component is ni.
The correlation of s1 and s2 for an infinite SNR is
 spatial 
c
2
c d
2
2
47
Noise with another decorrelation factor
Now re-introducing noise we get
c
 spatial noise 
2
c d n
2
2
2
and since SNR is (|c|2 + |d|2 )/|n|2
 spatial noise 
 spatial noise 
c
c d
2
c
2
2

2
c d
2
c d
2
2

2
c d n
2
2
2
1
1  SNR 1
 spatial noise   spatial   N
48
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.
The probability density function (pdf)
reveals some statistical characteristics of
the interferometric phase.
For strong correlations (  1) the phase
difference is very small and only a few
outliers exist.
Bamler, R. and D. Just, “Phase statistics and
decorrelation in SAR interferograms,” IGARSS ’93,
Toyko, pp. 980-984, 1993.
49
Spatial baseline decorrelation
50
Rotational decorrelation
Complete decorrelation results after
rotation of 2.8 at L-band and 0.7 
at C-band.
51
Temporal decorrelation
Complete decorrelation results after
rms motion of ~ /3
 ~ 0.5 yields reasonably reliable
topographic maps
52
Fading effects
Increasing the number of looks reduces the phase
standard deviation, especially for N > 8
53
Uncompensated range migration effects
54
Misregistration effects
Residual misregistration of 1/8 resolution
cell leads to a 42-standard deviation for
a 10-dB SNR and a 23-standard
deviation for an SNR of .
55
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.
56
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.
57
Rough registration
Spline interpolation is used to resample the image to
provide the pixel-level registration.
58
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.
59
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 twodimensional shift is conducted
using the correlation coefficient as
the measure of goodness.
Results from this search process
are applied to the overall image.
60
Precise registration
61
Geometric correction
gr _ r  sl _ r 2  H 0  z 
2
62
Geometric correction
The steep slope, as seen in the
slant range axis, appears to have
a negative slope.
This phenomenon is used as a
layover indicator.
The areas affected by layover are
identified and undergo additional
processing to remove the
associated geometric distortion.
63
Geometric correction
The pixels affected by layover can
then be resorted to correct for the
geometric distortion resulting from
the layover effect.
Uncorrected residual height (elevation) errors will prevent complete
removal of layover effects.
64
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.
65
Geometric correction
66
Geometric correction
67
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.
Multipass SAR interferometry involves phase comparison
of SAR images gathered at different times with slightly
different look angles.
Multipass InSAR enables production of digital elevation
maps (DEMs) with meter accuracy as well as terrain
deformations with millimetric accuracy.
Factors limiting the usefulness of multipass InSAR include:
temporal decorrelation
geometric decorrelation
atmospheric inhomogeneities
Without these difficulties, very long term temporal baseline
interferometric analyses would be possible revealing subtle
trends.
68
Temporal decorrelation and persistent scatterers
Temporal decorrelation
Scenes containing elements whose electromagnetic response
(scattering) changes over time render multipass InSAR infeasible.
Vegetated areas are prime examples.
Geometric decorrelation
Scenes containing scatterers whose scattering varies with
incidence angle limits the number of image pairs suitable for
interferometric applications.
Atmospheric inhomogeneity
Atmospheric heterogeneity superimposes on each complex SAR
image an atmospheric phase screen (APS) that compromises
interferometric precision.
69
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
SAR’s 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.
70
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.
A network of persistent scatterers in a scene has been
likened to a “natural” GPS network useful for monitoring
sliding areas, urban subsidence, seismic faults, and
volcanoes.
71
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.
72
Temporal decorrelation and persistent scatterers
Taken from Warren, Sowter, and Bigley, “A DEM-free approach to persistent point scatterer
interferometry,” FIG Symposium, 2006.
73
Temporal decorrelation and persistent scatterers
Atmospheric phase screen estimated from analysis of two complex
SAR images separated over a 425 day period.
74
Temporal decorrelation and persistent scatterers
75
Temporal decorrelation and persistent scatterers
76
Temporal decorrelation and persistent scatterers
77
Temporal decorrelation and persistent scatterers
78
Temporal decorrelation and persistent scatterers
79