introduction to radarearth.esa.int/download/eoedu/earthnet-website-material/...introduction to radar...

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



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


3. topography : DEM

Etna Etna -- simulationsimulation

Iso Altitude Iso Altitude CurvesCurves


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


4. orbital configuration (baseline) (Cntd) residual fringes

Phases variations over a flat terrain (3D approach)


Principle

Products (applications)Digital Elevation ModelsGround MovementsCoherence map



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



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 :


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


(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




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


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.


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



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




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




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




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


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


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


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)


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



Δ f d

BF ≥Δ


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




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)


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


Troposphere and ReliefEven in case of global vapor content changeDilatation of distance depends on the relief

Vapor content


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




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


“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


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




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


(April 2009)

ENVISAR ASAR descendinggeometry


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




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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