polarimetry and interferometry applications

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1Institut für Hochfrequenztechnk und RadarsystemeQue

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1Institut für Hochfrequenztechnk und Radar

Polarimetry and Interferometry Applications

Wolfgang KeydelMicrowaves and Radar Institut

DLR OberpfaffenhofenContact Address:

Mittelfeld 4,D-82229 Hechendorf Germany

Tel.:49-8152-980 523E-mails: [email protected]

[email protected]

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Goal

Point out exemplary some Application Possibilities of theInterferometric & to some extent Polarimetric Techniques & Systems

considered & presented in the forgoing respective Lectures in order to deepen & fasten the Auditories Understanding & Comprehension

Offer a Glance into a Selection of Representative Activities in the Domains of

Scientific , Commercial, & Operational Applicationsof

Interferometry & Polarimetry

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Safety for Air Traffic TelecommunicationsDisaster management

Applications for Digital Height Models

Infrastructure planning Hydrology

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Application Areas and Specific User RequirementsDriver for research & development of all SAR Technique, Technology & Systems

Real TimeRegularlyReal TimeRegularlyData access

1 hr –1 dayYearly1 hr – 1 day1 Year….Application

Revisit Time

5km – 100km40 km–100 kmVariable10km -350 km

VariableSwath Width

0,1 m -10 m1m – 5 m0.5 m – 100m3 m – 5 mSpatial Resolution

Variable20° - 60°

Variable20° - 60°

Variable20° - 60°

VariableIncidence Interval

QuadQuadQuadPolarizationL, XL, C, XL,C,L, C, XFrequency

MilitaryUrban Mapping

Disaster Management

CartographyParameter

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QuadDual/quaddual/quadquadquadPolarization

Raw Data TomographyAdditional

Real TimeRegularlyRegularlyRegularlyReal TimeData access

1 day10 days –15 days

Seasonal0.3 - 1 Year≤ 15 daysRevisit Time

Variable25 km-350 km

Variable100 km

Variable40 km – 100 km

Variable30 kmSwath Width

30 m-1 km3m – 10m3m – 10m10 m3m-30mSpatial Resolution

20° -45°20°- 45°20° -60°20° - 45°25° – 45°Incidence Interval

L,CL, C, XL, C, XL, C, XL,CFrequency

OceanographyHydrologyGeologyForestryAgricultureParameter

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SAR Interferometry Applications & User

Creation of Land Deformation Maps with Millimetre Accuracy

Generation of Digital Elevation Models with Meter Accuracy,

Improved Target Recognition by Creation of 3D Images of Targets

Improved Land Use Classification by exploiting Coherence Measurements,

Measurement of Current Fields & Moving Target Indication

Economical & Operational Importance for Constructors (Building a Tunnel can cause Unwanted Deformation),

Governments (Dike Monitoring, Disaster Monitoring),

Military (Target Detection,Identification, Classificationm, Area Exploration

Governments & Companies creating Georectified SAR Imagery (Need for Topographic Maps), etc.

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SAR Polarimetry Applications

Polarimetry offers Maximal Information an Electromagnetic Wave can carry. Most Modern Civil & Military Applications require full Polarimetric Systems.

Polarization will Improve exemplary:Ice Detection &Classification, Man Made Target Detection & Classification, Crop Monitoring & Clasification etc..

::

Commercial Aspects are widely in the Foreground

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PolarimetryPolarization is the Orientation of the Electric Vector (E) in an Electro Magnetic Wave, frequently "Horizontal" (H) or "Vertical" (V) in conventional imaging radar systems. Polarization is Established by the Antenna.

Complete State of scattered Electromagnetic Wave described by the Scattering Matrix S, which connects

the Received Field Vector Er with the Transmitted Field Vector Et. (Börner)

Scattering Matrix Decomposition into 3 Components (Example Sperical Basis):

EHr

EVr S

EHt

EVt

SHH SHVSVH SVV

EHt

EVt

L

NMMM

O

QPPP

=L

NMMM

O

QPPP

=LNMM

OQPPL

NMMM

O

QPPP

[ ] [ ] [ ] [ ]S e e k S k S k Sj j ss sphere d diplane k helix= + +ϕ ϕn s

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Scattering Matrix

E kr e j t= − +E0e r−α

ω ϕ( ) …α = jk +γ

EHscat SHHEH

inc SHVEVinc

EVscat SVHEH

inc SVVEVinc

= +

= +

IJFG

IEscat inc

EHscat

EVscatIKJJ

SFG HH

VH

SHVSVVSH

EHinc

VincE

(S) E= GFHG K

J= KHG J =

Si ki ke

j i k,

, ,= σϕ

0

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Basis MatricesA generic Matrix is decomposable into Basis Matrices

SS SS S

HH HV

VH VV= LNM

OQP

a b cc a b

a b c+

−LNM

OQP

= LNMOQP

+−

LNM

OQP

+ LNMOQP

1 00 1

1 00 1

0 11 0

a b S a b SHH VV+ = − =;

a S S b S S c S SHH VV HH VV HV VH= + = − = =; ;

Scattering Vector k = (a,b,c) = (SHH + SVV ; SHH - SVV ; SHV)

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Pauli Distribution

Single Bounce, odd

Double Bounce, even

Volume Scattering,diffuse

RoughSurfacePlate,

Sphere, Dihedral;

TiltedDihedral;

α

Vegetation

=

=

0110

cos2αsin2αsin2αcos2α Sdiff

= ,

1001Sodd Seven

Scattering Vector kscat = (kodd, keven, kdiff) = (SHH+ SHV, SHH- SHV; 2SHV)→

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=

=

=

0110

S,cos2αsin2αsin2αcos2α

S,1001

S dfiffus21

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Example for three-dimensional ‘POL-IN-DEM’ information

E-SAR, L - Band

Differential interferogram

between HH and VV

HH-Polarization

∆- Polarization (HH-VV)

VV-Polarization

Vegetation with verticalStructures

CoherentDecomposition in orthogonal Parts

ScatteringMatrix

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Combination of Polarimetry and InterferometrySAR Polarimetry (PolSAR) SAR Interferometry (InSAR)

Allows the decomposition of different scattering processes occurring inside the resolution cell

Allows the location of the effective scattering center inside the resolution cell

Polarimetric SAR Interferometry (Pol-InSAR)Potential to separate in height different scattering processes occurring inside the

resolution cell.

Sensitivity to the vertical distribution of the scattering mechanisms

Allows the investigation of 3D structure of volume scatterers

InSAR DEMSAR ImagePol. Pauli Decomposition RGB

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The Combination of Polarimetry and InterferometryPhase sensitivity SAR InterferometrySAR Polarimetry

Established technique for terrain topography estimation

allows Location of scattering centers

inside the resolution cell

Sensitive to scatterersshape, orientation and dielectric properties

Allows decomposition of different scattering processes

occurring inside the resolution cell

Polarimetric SAR InterferometryPotential to separate in height different scattering processes

occuring inside the resolution cell.

Sensitivity to the vertical distribution of the scattering mechanisms

Allows the investigation of 3D structure of volume scatterersrecovering co-registered textural plus spatial properties simultaneously

Central Part: Coherence

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Applications for Digital Elevation Models DEM)

Example: Air traffic Safety

“Virtual Cockpit”

• Precise Information about Aircraft Position by GPS

• Precise Information about Topography below fromglobal, consistent DEM

(SRTM)

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Hydrology: Water Flow Simulation

Globe-30 DEM SRTM DEM

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Example: Polarimetric Ice, Water, & Land Classification

HH Ice Type

HV Ice Edge

HH Ice Type

HV Ice Edge

H/A/α Maximum Likelihood Classification

Results After Five Iterations

Courtesy Mc Donald Dettwiler & Associateswww.rsi.ca/rsic/ice/eoadp.asp

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Military Use of Interferometry and Polarimetry“The war is father of everything”Task of Military Reconnaissance Systems

“Assist the Military Leaders in the Early Detection of Crisis Prevention & Crisis Management Efforts, Support the Top Military Leadership to plan and prepare military operations and Support Deployed Forces in the Timely Collection of Current Intelligence Information”.(Col. F. Kriegel on ”European Satellites for Security” in Brussels, June 2002),

One of the Biggest Tasks For Tactical & Strategic Consideration to get Things Timely, Safely & Efficiently at the Battlefield.

Interferometry & Polarimetry driven intensively by Military Requirements. For Target Detection, Recognition, Identification & Classification full polarimetric information is indispensable.Decomposition Theorems excellently suited for Target Exploration under Vegetation Layers due to Foliage Penetration Capability of dm-Waves etc.

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Polarimetric & Interferometric SAR indispensablefor Collecting Terrain Information like Engineering Resources, Trafficability, Obstacles, Visibility, Camouflage, Concealment Potential, Information on Camping Ground, Water Supply etc.Systems mounted on Aircrafts, UAV’s, & Satellites allow actual updating of already existing Maps or establishing of new Feature Maps in Real Time.

Example: DEM’sMilitary Topographic Maps are most important for Terrain Evaluation.

Aircraft & Helicopter Missions in mountainous ore even hilly Terrain can be supported in Advance & during the Mission with DEM of respective Areas.

Soil Moisture Maps help to identify the best Way for off Road Movements etc. (necessary also for establishing Communication Links etc).

US NIMA has financed the SRTM Missionilluminating the Importance of DEM’s for Military Purposes.

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Flight over unknown Area

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Technical ApplicationsSRTM Systems Operation Geometry

YIC S

ZI C S

Ou tbo ard C oo rd in ate System (OCS)

Xo cs

Yo cs

Zo cs

X IC S

B

Inb oard Co ordinate System (ICS)

–YIC S

–YO RB

L ook A ngle

C ro ss-Track A lo ng-Track (Velocity Vector)

B Y

• • •• • •

• • •• • •

- 22 5 k m- 80 k m

- 50 k m

- 6 2 k m

- 5 8 k m

- 6 1 m- 233 – 247 km

Flig

ht D

irec

tion

Tim

e

1 55 0 PR F 13 441 34 415 50

Inc ide nc e A ngle

ZIC S

45°

B e am 1B 2B 3B 4C H -po lC VC VCH

Z OR B 14°

X V

- 3 0 °- 6 0 ° - 4 3 °- 5 0 °- 5 6 °

Courtesy JPL

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Technical ApplicationsSRTM Systems Operation Geometry

•••

•••

•••

•

••

- 2 2 5 k m

- 8 0 k m

- 5 0 k m

- 6 2 k m

- 5 8 k m

Fli

gh

tD

ire

ct i

on

1 5 5 0P R F

1 3 4 41 3 4 41 5 5 0

45 km

PRF 1700

Tim

e

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Tomography

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45° Steps 5° Steps

1° Step

Simulation

Illumination Source

Principle of TomographyPrinciple of TomographyIll

umin

atio

n So

urce

ImageReconstruction

Algorithm

Slice Image

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Polarimetric E-SAR Image, L-BandPolarimetric E-SAR Image, L-Band

Polarimetric E-SAR Image, L-

Band

1) spruce forest2) buildings3) cars4) corner reflector

1 2 3 4

SAR Tomography

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SAR-Tomography2-dimensional image of a cut (τοµή) through a 3-dimensional Objekt

Multiple parallel repeat-pass POL-IN-SAR imaging

y

z

x

12..N-1N

n

rL

Multiple horizontal Flights

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Tomography for Scattering Analysis

Scattering Mechanisms along Yellow Line at different Altitudes & Polarizations. Buildings Roof is Bright: Bright HH and VV Single Bounce is the Corner Reflector. Double Bounces at Parts of the Buildigs Roof & the Lower Parts of Trunks, Volume Scattering dominates in Tree Crowns & Under Story[Reigber, Moreira, First Demonstration of Airborne SAR Tomography IEEE Trans. GRSS, vol 38. No. 5, Sept: 2000]

VVHH

HV

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Use of Interferometry for Building Measurements

Using Terrain Elevation Data from Interferometry in Combination wth Gray Value Images &

Object Shadows Allows Building Mapping

Accuracy of Buildings Mapped from Sensor with 30 cm Pixelsabout ± 3 Pixels or ± 1 m.

2 Overlapping Data Sets are Definitely Needed.

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Bottom view Left &BottomResulting Minimum Bounding Rectangles fit to point clouds detected automatically from maximum combined height map for different view combinations.area 200 m x 150 m

Leberl F. W., Regine Bolter, From Multiple View Interferometric Radar to Building Models, Proc. EUSAR 2002

Left+Right+Bottom

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Footprints from shadows, reconstructed from two perpendicular views, right + top Overlaid are the computed optimum rectangles to fit the Point clouds.The area covers approximately 200 m x 150Leberl F. W., Regine Bolter, From Multiple View Interferometric Radar to Building Models, Proc. EUSAR 2002

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View Combination Area Error (RMS)

Height Error (RMS)

detectedBuildings

Bottom ± 2,1 m 21

Left + Right ± 276 m2 ± 2,6 m 12

Left + Bottom ± 422 m2 ± 1,6 m 14

Left +Right + Bottom

± 207 m2 ± 1,4 m 16

Left + Right +Top + Bottom

± 120 m2 ± 1,4 m 15

± 205 m2

Resulting rms error of area & maximum height, result of applying the automated building detection algorithms to different view combinations. “Maximum height” is used to avoid the confusion resulting from sloping roofs. Leberl F. W., Regine Bolter, From Multiple View Interferometric Radar to Building Models, Proc. EUSAR 2002

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S lant RangeProcessing

InterferometricProcessing

Fusion

Result

Simulation

Comparision

Multiple View InSAR Data

Slant RangeProcessingSlant RangeProcessing



FusionFusion

ResultResult

SimulationSimulation

ComparisionComparision

Multiple View InSAR Data

Procedure for the extraction of building models from a combination of SAR images and associated interferometric data [6] R. Bolter, F. Leberl [2000]: „Phenomenology-Based and Interferometry-Guided Building Reconstruction from Multiple SAR Images“, Proc. EUSAR 2000, München, Germany, pp. 687-690

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Traffic Monitoring

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Velocity Measurements with Interferometric SAR

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Ambigous Determination of Pixel Velocity

V FV x

rPRF

ve grae= + nFHG

IKJ3 6

20,

λAzimuth Displacement:

VV

Bnve

ae= − +λ

ππ

42Φa fAlong Track Interferometry:

B: ATI Baseline; Fgr: Slant to Ground Range Factor: n: Ambiguity Number; PRF:Pulse Repetition Frequency; r0: Slant Range Distance; x: DopplerDisplacement; Vve: vehicle velocity; Vae: aercraft velocity;

λ: wavelength; Φ: Measured ATI Phase; 3.6:Conversion Factor m/s to km/h;

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Airborne Moving Target Indication

Courtesy Joao Moreira, MFFU Summerschool 2001

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39Institut für Hochfrequenztechnk und Radar Courtesy Joao Moreira, MFFU Summerschool 2001

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Courtesy Joao Moreira, MFFU Summerschool 2001

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41Institut für Hochfrequenztechnk und RadarCourtesy Joao Moreira, MFFU Summerschool 2001

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43Institut für Hochfrequenztechnk und RadarCourtesy Joao Moreira, MFFU Summerschool 2001

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Space-borne Moving Target Indication with SRTM

Along Track Interferometry Capability

Due to Antenna Displacement

FGAN

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Coherence map featuring a 3 km long section of the Autobahn Munich– Nuremberg. The black dots are cars displaced from the red road due to their velocities

Coherence loss indicates the presence of a moving target. The larger low coherent areas are Lakes

[Breit et. al. , Traffic Momitioring using SRTM, Proc. IGARSS 2003]

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Results of the Validation Experiment Comparing 3 Measurement Methods

48.33 km/hGround VelocityVelocity resulting from GPS Measurement

52,5 km/hGround Velocity from ATI Phase42,2 km/hRadial Velocity from ATI Phase

Velocities resulting from ATI Phase (127°)47,1 km/hGround Velocity from Displacement37,9 km/hRadial Velocity from Displacement

Velocities resulting from measured azimuth displacement (130.6 pixel)InSAR data evaluation

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MTI- Interferometry, SRTM/X-SAR (Bamler, DLR)

Left: Motorway A9, Munich – Nuremberg, Germany, arrow: SRTM track. Right: SRTM/X-SAR image, motorway blue, red arrows vehicles with theirvelocities (yellow)

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Ocean Current Measurements with SRTM Along Track Interferometry

Line-of-sight current field derived from the SRTM data (left) & obtained from KUSTWALD for the tidal phase 20 minutes before SRTM overpass (right); grid resolution is 100 m ×100 m; data points with valid currents from SRTM and KUSTWAD are shown only.

Romeiser et. al. Validation of SRTM-Derived Surface Currents IEEE Proc. IGARSS 03,

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Romeiser et. al. Validation of SRTM-Derived Surface Currents IEEE Proc. IGARSS 03,

Scatter diagram showing the distribution of SRTM-derived vs. KUSTWAD-derived current components in the SRTM look direction, as well as corresponding statistical quantities, for the tidal phase 20 minutes before the SRTM overpass.

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Mining Induced Subsidence by means of

Differential SAR- & Permanent Scattering Interferometry

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Determination of Subsidence Effect caused by Ground Water Withdrawal in a Brown Coal Mining Area with D - InSAR using

Permanent Scatterers as Reference Points. Goal

Clarify Correlation between Ground Water Withdrawal, Tectonics & Subsidence on Surface by means of both

Differential SAR Interferometry & Permanent Scatterer Technique

D – InSAR: 28 ERS-1 Images registered to the same Master ImagePSI: 39 Interferograms from May 1995 to December 2000.

Perpendicular Baselines: 23 m --- 500 m (--- 1158m). 17 D-InSAR Interferograms showed Concentric, nearly Elliptic Fringes, each

corresponding to 28 mm Line of Sight Movement. For PSI 11.000 Permanent Scatterers were identified & within a reference network selected for more point wise informationFrom May 1995 to December 2000 the area affected by groundwater withdrawal sank continuously with 5 cm/year.

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Subs

iden

ce/c

m

+4 cm - 4 cm

Time / day

Subsidence from PSI

Subsidence from Differential Interferogram

Results: Both techniques lead to the same subsidence rates of about 5 cm/year. Even over a time span of 1401 days reliable results were achieved with both methods. The estimated values could be verified by ground measurements of the land surveying office NRB, Germany.

Kircher et. al. Proc.Remote Sensing observations of mining induced subsidence, IGARSS 2003,

Differential Interferogram with Amplitude Overlay

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Soil Moisture & Biomass Estimationusing

Polarimetric Scattering Theory

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User Requirements

Volumetric Moisture 10% - 20 %

Tree height estimation: 10%Mean forest height on Earth: 20 m

Height Accuracy: 2 m

Required Accuracy

Seasonal observation> 2 per Year

Average Tree Height Change: 3m -- 4 m per Year

Differential Height Accuracy:1 m

4 YearsTemporal Resolution

1/2 ha = 5000m2 70x70mSpatialResolution

SOIL MOISTURE CONTENTBIOMASS

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State of the Art for Soil Moisture Estimation

accuracy moisture content & surface roughness of bare surfaces :10 - 20%, moisture content ranging from 0 up to 40 [vol. %]

roughness scales up to ks < 1.

Uncertainties during measuring the surface parameters lead to inaccuracies.

Main ProblemPresence of Vegetation Cover Limits Algorithm Performance Drastically

Scattering Decomposition Techniques lead to Improvements but do not solvethe problem

Possible Solutions

Dual-Frequency Polarimetry (for example: L- and P-band) Combination of Mono- and Bi-Static Polarimetric MeasurementsCombination of Polarimetric and Interferometric Measurements

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Assumption: Surface ScattererEntropy H < 0.4 & α < 0.40°

C e e e e e e C C C

Ci HVi VVi

=+

++

++

= + +

+

λ λ λ

λ

1 1 1 2 2 2 3 3 3 1 2 3

2= ki ki with ki = iei = HHi , ,

[C1] represents deterministic anisotropic surface scattering [C2] & [C3] correspond to double-bounce and/or multiple scattering components respectively. In this sense: |HH1|, |VV1|, and |HV1| values represent the scattering amplitudes corresponding to the surface scattering only. The disturbing double-bounce (if present) and multiple scattering effects affecting the original |HH|, |VV|, and |HV| have been filtered out.

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The Polarimetric Eigenvector Decomposition TechniqueCovariance Matrix [C] & Scattering Vector k

C kk

HH HHHV

HVHH HV HVVV

VVHH VVHv

=+

=

L

N

MMMMM

O

Q

PPPPP

2 2

2 2 2 2

2 VV 2

* HHVV*

* *

* *

HH HV VV T= 2, ,k

C e e e e e e C C C

Ci HVi VVi

=+

++

++

= + +

+

λ λ λ

λ

1 1 1 2 2 2 3 3 3 1 2 3

2= ki ki with ki = iei = HHi , ,

Decomposition of [C] leads to three 3 x 3 Independent Rank 1 Covariance Matrices [Ci ]

λ1>λ2>λ3: real non negative eigenvalues of [C]; ei (i = 1,2,3): eigenvectors. [Ci] orthogonal & independent

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5

10

15

20

25

30

35Soil moisture Map: mv in Vol %

Hajnsek et. al., Terrain Correction for Quantitative Moisture and Roughness Retrieval… Proc.IGARSS’00,

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Soil Surface Roughness Map ks

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9


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Measured versus Estimated Soil Moisture

0-4 cm 4-8 cm corr.Elbe RMSerror 8 3 0.7/0.8Weih RMSerror 7 6 0.2/-

Estimated Volumetric Moisture

0 500 m

Field 10

Field 13

Field 14

Field 16

Volu

met

ricM

oist

ure

mv/%

0

10

20

30

40

0 10 20 30 40v

v

Elbe 0-4 cmElbe 4-8 cmWeiherbach 0-4 cmWeiherbach 4-8 cm

measured mv/vol%


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Which is the Optimum Frequency Band ???

C-band

Pro:

Established Technology

Contra:

Limited Penetration Capabilityin Dense Vegetation

Temporal Decorrelation(repeat pass implementation)

ks range to small for a variety of natural surfaces

(repea

L-band

Pro:

Established TechnologyHigher Penetration Capability

Wide Spectrum of Applications

ks range covers most natural surfaces

Contra:

Long TermTemporal Decorrelation

t pass implementation)

Open Question:

Does L-band see the groundin tropical forest???

P-band

Pro:

Approved Penetration Capabilityin Tropical Forest

Contra:

Spatial Resolution(Limited Bandwidth)

Non-Established Technology

Limited ApplicationSpectrum

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Interpretation of Coherence MapsResults from SIR-C

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Multifrequency Interferogram Magnitudes, Mt. EtnaSIR-C

Co-registered slant range SAR images. Ground range: 66.8 km x 9 km X-band:16000 pulses &1024 range bins, L- and C-band: 2048 range bins

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Coregistered Interferogrammes with flat earth, Mt. Etna, SIR-C

Coregistered Set of Interferogrammes

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Coregistered Multifrequency Interferogrammes, Mt. Etna, after Flat Earth Removal

Ground range: 66.8 km x 9 km. X-band:16000 pulses &1024 range bins, L- and C-band: 2048 range bins

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Coregistered Coherence Maps, Mt. Etna, SIR-C

X-Band

C-Band

L-Band

Ground range: 66.8 km x 9 km. X-band:16000 pulses &1024 range bins, L- and C-band: 2048 range bins

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Multifrequency Phase UnwrappingWrapped

Phases with Ef

Ef: Scaled Flat Earth Funktion

UnwrappedPhases without Ef

Scaling to X-Band for Comparision Purposes

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F

X CXc L

X

L

=

+F

HG

I

KJ +

F

HG

I

KJ

12 2

γ γλ

λ γλ

λ

Multifrequency Phase Fusion Scheme

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Effect of Filtering

unfiltered filtered

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Pixel

unfiltered

filtered

rad

Pixel Size: 21 m

3200 Pixel ~ 67 km

2π ~

Filtering

before phase unwrapping

400020001000 3000

200

200

400

400

Pixel

unfiltered

filtered

rad

400020001000 3000

200

200

400

400

Multifrequency evaluation: Unwrapped Phase Profiles

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Main Features considered in the Fusion Algorithm

19 m4,5 m2,5 mHeight standard deviation

highlowlowCoherence over areaswith dense vegetation

highmediumlowCoherence over areaswith sparse vegetation

highhighhighCoherence over areaswithout vegetation

noyesyesBias

L-BandC-BandX-BandFeatures

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∆ Φ ∆ΦzR

B=

−

λ ϑ

π ϑ ξ0

4

sin

cos( )

∆Φ = 12°; γL= γL= γL= 0,9

SNR > 10 dB

ϑ =49°; B =54 m; ξ = 41°

R = 316 km

∆Φ = 2π

∆zλ = λ 2,23 km

∆zL= 512 m

∆zc= 111,5 m

∆zx= 66,9 m

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Coherence and Phase Error Examples from SIR-C

±0,13 °-50 dB

±4,02 °-20 dB±12,8 °-10 dB

±50,7 °0 dB

Phase Error∆Φ (rms)

Ambiguity Ratio

±4°30 dB

±9°25 dB

±13°20 dB

±21°15 dB

±40°10 dB

Phase Error∆Φ (rms)

SNR

Good coherencebetween 2 passes

X-Band: < 1 day

C-Band: < 3 days

L-Band: < 30 days

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Coherence Classification, Mt. Etna, Sir-C Data

polarimetry and interferometry applications

Documents