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Introduction to Radar Interferometry
Presenter: F.Sarti (ESA/ESRIN)
Introduction to radar interferometry
With kind contribution by the Radar Department of CNES
Potentialities of radar
All-weather observationsystem (active system)
Penetration capabilities
Sensitivity to geometrical structures with scalesof the same order than the wavelength
Dielectric properties of mediumSensitivity to water content
estimation of vegetal biomass
λENVISAT ASAR ERS SAR, Radarsat: C band 5,6 cm
JERS, ALOS PalSAR: L band 23 cm
Sea roughness
Waves, wind, sea pollution, storms
Topography, slope
Cities
Ships and military detection
RADARSAT SCANSAR IMAGE
(500 km SWATH)
Active instrument. Intensity and Phase. Coherent illumination.Speckle noise (consequence of a coherent illumination)
φΔ
eℜ
mℑ
1°npixel 2°npixel
eℜ
mℑ
scattereroneofoncontributiresponsepixel
Image SETHI, bande C, 3 m
The speckle noise, consequence of a coherent illumination
The speckle noise is a multiplicativenoise
Low radiometry : low noise
Large radiometry : large noise
Interferometry : contentPrinciple of interferometry
ProductsDigital Elevation Models (DEMs)Ground Movement mappingCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Principle
ProductsDigital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Principle 1/8
Each image pixel (of a single look complex LSC product) contains twoterms:
Amplitude : APhase :
is not estimable
(Single) Phase cannot be used as an information
Pixel = A . e Pixel = A . e jjφφdistspecificpixel ϕϕϕ +=
DistDist WayTwodist λπ
λπϕ 42
== −
specificϕ
PixelPixel11 = A= A11 . e. ejjφ1φ1
PixelPixel22 = A= A22 . e. ejjφ2φ2
If we have two images andif the ground didn’t change,
Image of is called anInterferogram
Image of “Distance differences”
(removal of unknown phase term, pixel-specific)
1_2_1_2_ distdistimim ϕϕϕϕϕ −=−=Δ⇒2_1_ specificspecific ϕϕ =
)(412 DistDist −=Δ
λπϕ
ϕΔ
1Dist
2Dist
Principle 2/8
Geometry image 2 (slave)
1 2
Geometry image1 (Master)
Terrain geometry
Slave image
Master image
The distance measurement principle relies on the same terrain pixel. Practically, the twoimages have (always) a (slightly) different geometry. In order to compute a phasedifference pixel by pixel, the images must be first precisely co-registered (made superimposable) : resampling of the slave image into the master image geometry. Coregistration must be sub-pixel precise (better than 0.3 pixels) and can be achieved bymeans of complex correlation.
Principle 3/8 Co-registration of images
1. Ground displacement
Only the componentof the displacement in the radarviewing direction can be measured by interferometry
Principle 4/8Geometric information included in the interferograms (1/5)
1
Master image(Day 1)
1
Slave image(Day 2)
2. Atmospheric propagation effects
Day 1 Day 2
Principle 5/8Geometric information included in the interferograms (2/5)
3. topography : DEM
Etna Etna -- simulationsimulation
Iso Altitude Iso Altitude CurvesCurves
Principle 6/8Geometric information included in the interferograms (3/5)
4. orbital configuration (baseline)
iδi
1R2RBorth
x̂
)(412 DistDist −=Δ
λπϕ
Dist1
Dist2
Phases variations over a flat terrain (1D approach)contribution removed by the interferometric processing
Principle 7/8Geometric information included in the interferograms (4/5)
4. orbital configuration (baseline) (Cntd) residual fringes
Phases variations over a flat terrain (3D approach)
Principle 8/8Geometric information included in the interferograms (5/5)
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
ElevationElevation GroundGround DisplacementsDisplacements
IsoIso--displacementdisplacement curvescurves (non (non simultaneoussimultaneous acquisitions)acquisitions)
IsoIso--altitude altitude curvescurves
AfterAfter eliminationelimination of orbital of orbital fringesfringes, , groundground elevationelevation isis representedrepresented by isoby iso--altitude altitude curvescurves. Phase . Phase givesgives thenthen a a measuremeasure of of elevationelevation modulo the modulo the altitude of altitude of ambiguityambiguity ((functionfunction of the of the orbital orbital baselinebaseline, , causingcausing a a stereoscopicstereoscopic effecteffect). ).
If a pixel If a pixel waswas displaceddisplaced betweenbetween the the twotwoacquisitions, acquisitions, thisthis generatesgenerates a a differencedifference in in distance and distance and thereforetherefore a phase a phase differencedifference. . The The accuracyaccuracy of the of the measurementmeasurement isis of the of the orderorder of mm. Phase of mm. Phase measurementsmeasurements are are modulo 2modulo 2ππ, , thusthus showingshowing up as up as fringesfringes ((needneedof of unwrappingunwrapping))
Etn
aE
tna
Land
ers
Land
ers
i
B
Borth
HA, Height of ambiguity = variation of altitude between two pixels induced by topography, giving one fringe on the interferogram (by stereo-scopic effect). For ERS: H.A.~10,000 /Borth (m)
H.A.
Principle
Products (applications)Digital Elevation ModelsTerrain MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
ReliefSlight stereo effect (B/H = 10-4 !)
But sufficient for small image distortions (only at phase level)
few centimetersenough to produce phase shiftsproportional to Elevation
Precise measurementbut known modulocreates fringesneed to be unwrapped
Etna Etna -- simulationsimulationλIso Altitude Iso Altitude CurvesCurves
question : what variation of altitude corresponds to one fringe? By definition, it corresponds to the altitude of ambiguity
ReliefThe altitude of ambiguity (1/3)
)sin(44
iihd
λδπ
λπϕ ==Δ
DistBi orth=δ
S 1
δ i
S 2
i
d
Borth
h
A
BDist
ϕδπ
λΔ= .
.4)sin(.
iih
With :
ReliefThe altitude of ambiguity (2/3)
Altitude of ambiguity : elevation that correspondsto a 2π phase shift
orthBiDistEa
.2)sin(..λ
=
orthBiDist
iih
.2)sin(..
2)sin(2 λ
δλπϕ ==⇒=Δ
Ea
Numerical example : Borth : 100 m, Dist=890 km, i=23°, λ=5.6 cm Ea=97 mIf Borth = 0, then Ea=infinite
ReliefThe altitude of ambiguity (3/3)
(Ea=500m) (Ea=250m)
Influence of the altitude of ambiguity on
the fringe density
ReliefAccuracy
Vertical Accuracya fraction of the “Altitude of Ambiguity”depends on the interferogram noise
depends on the phase standard-deviation
Examples
ERS, ENVISAT : Ea/4 or Ea/5 50 down to 3 mSRTM : Ea/15 18 m in C Band ; 6 m in X BandAirborne : better than Ea/100 down to 10 cm
Eaz ..2 π
σσ ϕ=
Relief :The SRTM mission
3D view
X-SARSRTM
Cotopaxi
altimetricresolution:
6 m
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Ground movements (1/6)
Non-simultaneous acquisitions
If we can eliminate fringes due to the relief (Diff. Interferometry)⇒ Direct measurement ofdisplacement (movement)
sub-centimetric accuracy: each fringecorresponds to a displacement equalsto λ/2 (irrespective of the baseline) differential within the image (relative)movements towards the satellite
LandersLanders -- 1992 1992 -- 7.5 Magnitude ERS7.5 Magnitude ERS
Iso Iso DisplacementDisplacement CurvesCurves
Ground movements (2/6)
λπδϕ //..4 displ
=
• The visible displacement is of the same order of magnitude as a fraction of λ (a few mm)• The interferometric measurement is insensitive to displ_orth (North-South slip not measurable by interferometry with polar orbiting SAR)• Remark: Non-simultaneous observations• Relief effect correction (by model or topographic interferogram substraction)
1
Master image(Day 1) 1
Slave image(Day 2)
Movement in the radarviewing direction
//displ
orthdispl _
Ground movements (3/6)Effect of a DEM error on the differential interferometric processing
12
Dist1
Dist2_corDist2
Dist1_cor
Real terrain
Corrupted DEMinformation
Err_DEM
4π/λ.[(Dist2_cor-Dist1_cor)-(Dist2-Dist1)] ≈ 2π . Err_DEM/Ea
Numerical example : Err_DEM=30m, Ea=90m, Err_DEM/Ea=0.33The DEM error creates 0.33 fringe on the differential interferogram, which is equivalent
to an displacement error of 0.9 cm.
Ground movements (4/6)
Measurement Accuracya fraction of half the wavelenghtdepends on the interferogram noise (↔ coherency)
depends on the phase standard-deviation
ExamplesERS : One fringe = λ/2 = 28 mm few mmJERS : One fringe = λ/2 = 11,5 cm few cm
2..2.
λπ
σσ ϕ=displDisplacement measurement accuracy
Ground movements (4/6)Izmit earthquake
I : MeanAmplitude
H: Phase(Interf.)
S: Coherence
Izmit17/08/99
• Monitoring ground deformation : magmatic chambervariations, seismic deformation (reverse modelling)
• Pre, post-seismic deformation (millimeters)• Fault monitoring• Integration with GPS
Ground Displacement Modelling
Ground movements (1/6) Subsidences over Paris
1Km
© ONERA97/CNES 99
Paris
1,6 cm
ERS
Processing chain DIFSAR
Co-registration
DEM
Orbital data
Phase model
Interferogram
CoherencyUnwrapped phase interferogram
Geocodeddisplacement map
n SLC images
Selection of M pairs
Co-registration of images
Interferogramsand coherence
maps generation
Preliminary estimates of the
displacement maps (optional input)
3D-displacement map
Interferograms
Coherence maps Topography
(DEM or a tandem
interferometricpair)
GPS Data (optional)
Precise orbital data
Temporal analysisTemporal analysis
Flattened phase
FlatteningFlattening
Sparse unwrappingSparse unwrapping
Interferometric processing
• Steps:– Coregister all the images– Topography elimination– Unwrap the phase– Combine the measures at the
different times
• The output consists in sparse space-time displacement measurements (no model assumptions)
• Additionally steps to improve the results:
– Accurate estimation of orbital data
– Filter, model and fit/interpolate the sparse space-time measurements
Principle
Products (applications)Digital Elevation ModelsTerrain MovementCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Coherency Map
Computed on a window (n = 5, 20, 80, …)Measures mainly the phase stability between the twoacquisitions : quality and reliability index of interferometric measurementA low level of coherence reflects the fact that changestook place between the two acquisitionsVery sensitive to temporal change and therefore to land cover (vegetation, flow & erosion, human activity, …) : thematic applications
10;.
*.22
≤≤==∑ ∑
∑ γγii
ii
EM
EMcoherence
Coherence Map (thematic mapping)
Forest damage
1) Cartographic reference 2) Forestry inventory 3) SPOT data
4) Coherence before storm 5) Coherence after storm 6) Damaged areas (pink)
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
performances:• precise measurement• large surfaces• temporal information• Accuracy of a few mm
limitations:•geometrical constraints (baseline)•coherency loss (noise on interferograms)•atmospheric artifacts
S.Paul de Fenouillet
LIMITATIONS
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Temporal Limitations
Liquid surfaces (always in movement)Vegetation (growth, wind, plough, harvest, …)ErosionUnstable surfacesHuman activityUnderground concealmentAny change on the ground
Remark: higher (multitemporal) coherency in L band on low vegetation (penetration: soil coherency). Better for deformation monitoring
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Geometric limitations 1/6
The specific phase comes from the physicalmechanism of wave backscatteringIt is linked to the speckle (reconstruction phase)Speckle derives from the vectorial summation of response of each elementary reflector in one pixel (coherent illumination)
Aφ
1 pixel
vectorial summation(amplitude and phase)
Apparent pixel sizeviewed from the
radar
LowIncidence
Slope > 0
HighIncidence
radar sampling
Geometric limitations 2/6
If the incidence angle changes,the reconstruction phase changesThe larger the pixel, the more sensitiveit is to a small variation of incidenceangle (directivity, like antenna)Sensitive to incidenceSensitive to slopeSensitive to Baseline (δi)
Geometric loss of coherence
S1
δi
S2
1 pixel
Geometric limitations 3/6
The same stands for volumic backscattering
Remark: for simultaneous interferometric, X band (smaller penetration, smaller apparent pixel) is more coherent on forests than L band : better for surfacicDEM
ERS1&2 tandem coherenceForest / Non ForestCoast lines
volumicbackscattering
Apparent pixelsize, viewedfrom the radar
surfacicbackscattering
radarsampling
Geometric limitations 4/6
Equivalent Frequency shift :)(..
.)(
.αλα
δ−
=−
=ΔitgDist
Bcitg
iFF orthp
α
pFT /1=iδi
1R2R
( ))sin(./1 α−iFp
( ))sin(/1 iiFp δα −−⋅
Borth
Observing a surface under two slightly different point of view (R1 and R2) is equivalent to a two-frequencies observation from one given location (ex : R1)
Geometric limitations 5/6
If , there is no coherence
High resolution is more resistant for interferometry
Range spectraldomain
B
Δ fd
Image 1
Image 2
BB
Δ f d
Range spectraldomain
Range spectraldomain
Δ f d
BF ≥Δ
Geometric limitations 6/6
Comparison between ERS and a SAR
ERS / " HR Radar " (2m) comparison
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Local terrain slope (in °)
% c
omm
on s
pect
rum
ERS High Resolution
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Propagation Effects 1/4
Interferometry is corrupted by atmospheric artifacts, creating a pathdifference between the two images. Two types:iStandard atmosphere variation (time-varying but topography-related) iLocal heterogeneities (time-varying)
Propagation Effects 2/4
TroposphereThe refactive index is function of the partialvapor contentNot a function of the frequencydilatation of the distancescreates heterogeneitiesstrong limitation in case of non-simultaneousacquisitions
∫=
=
−
≅Δ max
00
6
).(.cos10 hh
htropo dhhNlθ
epTN Δ+Δ+Δ−=Δ .51,4.269,0.45,1
Propagation Effects 3/4
Troposphere and ReliefEven in case of global vapor content changeDilatation of distance depends on the relief
Vapor content
Propagation Effects 4/4
IonosphereThe refactive index is function of the Total Electronic Content (TEC)Depends on the frequency bandStrong effects in L Band (or P Band)Less effects in X or C Band
TECf
liono .28,402−=Δ
Atmospheric artifacts
Ionospheric hole
Cloud chain (Etna)
Clouds - Cumulus
•Expert interpretation, on the basis of a-priori knowledge (topography, climate, displacement models and prediction, GPS ...)
•Atmospheric modelling - limited application, need of dense vertical profiles, ionosphere...
•Stacking of interferograms for averaging
•Correlation of interferograms
•Permanent scatterers
A mixed solution is possible. Compromise to be found as a function of required accuracy, auxiliary data available, number of images
LIMITATIONS : POSSIBLE SOLUTIONS
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Signal-to-Noise ratio (1/3)
as a function of the image Signal-to-Noise ratio and Window size:
INTERFEROMETIC PHASE NOISE
0
20
40
60
80
100
120
-20 -15 -10 -5 0 5 10 15 20
Signal to Noise ratio
Stan
dard
dev
iatio
n (°)
1 2 5 10 20 50 100
Noise Signal
Window size
ϕσ
Signal-to-Noise ratio (2/3)
“Interferometric Coherence” as a function of the image Signal-to-Noise ratio and Window size:
INTERFEROMETRIC COHERENCE
00,10,20,30,40,50,60,70,80,9
1
-20 -15 -10 -5 0 5 10 15 20
Signal to Noise ratio
Coh
eren
ce
1 2 5 10 20 50 100
Noise Signal
Window size
Signal-to-Noise ratio (3/3)
distributionϕσPhase histogram in fonction of Standard Deviation
0
0,2
0,4
0,6
0,8
1
-40 -30 -20 -10 0 10 20 30 40
Phase (°)
5°10°20°40°80°
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
Area : 90 km x 90 km(7.3 event)
Interferogram processed with a pair of ERS-1 images taken before
(April 24, 92) and after (June 93) Earthquake
June 28th 1992 Landers
Earthquake(California)
One fringe =28 mm displacement
0 2π
Main rift
Post-sismicevent
Gulf of CorintheGreece (North-
East Peloponese)1995
Subsidence effectthat contributes in enlarging the Gulf
(ERS imagery)
Loss of coherence(the interferometric
measurementcannot be used
locally. Various reasons :meteo, vegetation, relief, ...
A sad recent application :
Abbruzzoearthquake deformation field mapping with radar interferometry
(April 2009)
ENVISAR ASAR ascendinggeometry
Abbruzzoearthquake deformation field mapping with radar interferometry
(April 2009)
ENVISAR ASAR descendinggeometry
Abbruzzoearthquake deformation field mapping with radar interferometry
COSMO-SkyMedinterferogram
Model (P.Briole, ENS Paris)
Monitoring of industrial risks : Impact of a geothermalpower plant on the environment (MESA, USA)
ERS radar image Interferogram processed with a pair of ERS images separated by 2 years
USA
Mexico
Powerplant
Mount Etna :Volcano deflation
monitored by radar interferometry
Map projection interferogramshowing large scale deflation
2 orbits : + 133 days, +518 days
Modelling of the deflation onthe same period
(Institut de Physique du Globe, Paris)
30 ERS-1 images studied(May 1992 → Oct. 1993)
Piton de la Fournaise
Réunion Island(June 1998)
Interferogram processed with a pair of RADARSAT images(orbites 7753 et 14270)
Radarsat1 Differential Interferogram : Mars 1998 Eruption
10/04/97 - 30/07/98 348 m altitude of ambiguity
Piton de la FournaiseIle de la Réunion
(Juin 1998)
Principle
Products (applications)Digital Elevation ModelsGround MovementsCoherence map
LimitationsTemporalGeometricAtmospheric propagationSignal-to-Noise Ratio
Illustrations of Applications
An alternative technique: Permanent scatterers
An alternative: Permanent scatterers
• not all backscatterers are PS! • not uniform distribution• needs many acquisitions(40-60)
An alternative: Permanent scatterers
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