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 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].

6. SAR limitations – foreshortening
Foreshortening: - <  <  ( 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
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.

11. SAR interferometry – how does it work?B A1 A2
Antenna 1
Antenna 2
Return comes from
intersection
Radar
Return could be
from anywhere
on this circle
Single antenna SAR
Interferometric 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 scatterer’s 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 A1 Transmit 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 A1 Receive 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-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

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 Three 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 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)

36. Phase unwrapping z x
ACTUAL ELEVATION PROFILE
Phase
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.

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 > 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-pass a = 2 for multipass a = 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. (incoherent) 0 <  < 1 (coherent)
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 <  < 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
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 |c|2/|n|2 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. Note that the slope   as   1
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 (|c|2 + |d|2 )/|n|2

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 , 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 > 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 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.

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
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 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.

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