Interferometric Synthetic-Aperture Radar (InSAR) Basics

1
Interferometric Synthetic-Aperture Radar (InSAR)
Basics
2
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

3
SAR limitations
4
SAR limitations

• All signals are mapped onto reference plane
• This leads to foreshortening and layover

5
Shadow, layover, and foreshortening distortion
SEASAT Synthetic Aperture RadarLaunched June
28, 1978Died October 10, 1978orbit 800 kmf
1.3 GHz PTX 1 kW? 33.8 ?s B 19 MHz? 23 ?
3? PRF 1464 to 1647 Hzant 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.
6
SAR limitations foreshortening

• Foreshortening -? lt ? lt ? (? is local slope).
• Dilates or compresses the resolution cell (pixel)
  on the ground with respect to the planar case.

7
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.

8
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.

9
Foreshortening and geocoding
10
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.

11
SAR interferometry how does it work?
Interferometric SAR
Single antenna SAR
12
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
13
Single-pass interferometry
Single-pass interferometry. Two antennas offset
by known baseline.
14
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
  scatterers elevation.
• From trigonometry (law of cosines)
• Furthermore for R B
• 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)

15
Law of cosines
16
Interferometric SAR radar phase

• Radar phases
• Since ? is measured, ?R can be determined
• 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 A1Transmit and receive on antenna A2
17
Interferometric SAR radar phase

• For single-pass InSAR where transmission is on
  antenna A1 and reception uses both A1 and A2
• And

Simultaneous baseline Transmit on antenna
A1Receive on both A1 and A2
18
Radar interferometry geometry

• From geometry we know
• but ? is undetermined if the scatterer is not on
  the reference plane.
• To determine ? we use
• where a 1 for single-pass and a 2 for
  multipass
• So that

19
Radar interferometry geometry

• From
• we find
• and
• where a 1 for single-passa 2 for
  multipassa 2 for single-pass, ping-pong mode
• Precise estimates of z(x) require accurate
  knowledge of B, ?, and ? as well as R and h

20
Interferometric SAR processing geometry
21
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)

22
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

23
Differential interferometry how does it work?

• Three-pass repeat track
• Two different baselines
• Same incidence angle
• Same absolute range
• Parallel ray approximation used to detect
  changes
• If the surface did not change between
  observations, then

24
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.

25
InSAR processing steps
26
Phase history and magnitude image
27
Phase image
28
Illustrated InSAR processes (1 of 3)
29
Illustrated InSAR processes (2 of 3)
30
Illustrated InSAR processes (3 of 3)
31
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

32
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
• 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

33
SAR Interferometry

• It follows that
• phase due to phase due to smooth Earth relief
• Removing the phase component due to the smooth
  Earth yields a flattened interferogram

34
SAR Interferometry
35
Ambiguity height

• The interferometric ambiguity height, e, which is
  the elevation for which the flattened
  interferogram changes by one cycle, is
• 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)

36
Phase unwrapping

• Formerly phase unwrapping was an active research
  area, now Matlab has a built-in function
  (unwrap.m) that does this reliably for most cases.

37
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
• For small ?r (small slant range pixel spacing)
• and from geometry we know
• so that

38
Baseline decorrelation

• Limiting ?? to 2? results in a critical baseline,
  Bc such that if B gt Bc the interferometric phases
  will be hopelessly unwrappable.
• This phenomenon is know as baseline
  decorrelation.
• B? denotes the perpendicular component of
  baseline B
• where a 1 for single-passa 2 for
  multipassa 2 for ping-pong mode
• i.e., Tx(A1)Rx(A1 , A2) Tx(A2)Rx(A1, A2)
  repeat

39
Perpendicular Baseline

• Perpendicular Baseline, B?

Parallel-ray assumption Orthogonal baseline
component, B?, is key parameter used in InSAR
analysis B? B cos(? - ?)
40
Baseline decorrelation

• While Bc represents the theoretical maximum
  baseline that will avoid decorrelation,
  experiments show that a more conservative
  baseline should be used.

41
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
• s2 is the complex conjugate of s2
• E is ensemble averaging
• (incoherent) 0 lt ? lt 1 (coherent)
• ? is a quality indicator of the interferometric
  phase,for precise information extraction, a high
  value is required.

42
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

43
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
• 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

44
Noise effects

• Since the noise and signal components are
  uncorrelated, we get
• Recall that the signal-to-noise ratio (SNR) is
  c2/n2 yields
• 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

45
Noise effects

• Noise also increases the uncertainty in the phase
  measurement, i.e., the standard deviation of the
  phase, ??

46
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
47
Noise with another decorrelation factor

• Now consider two complex SAR signals, s1 and s2,
  each of which is modeled as
• 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

48
Noise with another decorrelation factor

• Now re-introducing noise we get
• and since SNR is (c2 d2 )/n2

49
Decorrelation and phase

• The decorrelation effects from the various causes
  compound, i.e.,
• 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.
50
Spatial baseline decorrelation
51
Rotational decorrelation
Complete decorrelation results after rotation of
2.8? at L-band and 0.7 ? at C-band.
52
Temporal decorrelation
Complete decorrelation results after rms motion
of ?/3
? 0.5 yields reasonably reliable topographic
maps
53
Fading effects
Increasing the number of looks reduces the phase
standard deviation, especially for N gt 8
54
Uncompensated range migration effects
55
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 ?.
56
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.

57
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.

58
Rough registration

• Spline interpolation is used to resample the
  image to provide the pixel-level registration.

59
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.

60
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 81 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.

61
Precise registration
62
Geometric correction
63
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.

64
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.

65
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.

66
Geometric correction
67
Geometric correction
68
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.

69
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.

70
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.

71
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.

72
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.

73
Temporal decorrelation and persistent scatterers

• Taken from Warren, Sowter, and Bigley, A
  DEM-free approach to persistent point scatterer
  interferometry, FIG Symposium, 2006.

74
Temporal decorrelation and persistent scatterers

• Atmospheric phase screen estimated from analysis
  of two complex SAR images separated over a 425
  day period.

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
Temporal decorrelation and persistent scatterers