Radar Polarimetry (1)

E. Pottier 01 / 13

E. Pottier 01 / 13

xy

( )E z t,

Radar Polarimetry

0z

Radar Polarimetry (Polar : polarisation Metry: measure)i th i f i i i d l i

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is the science of acquiring, processing and analysing the polarization state of an electromagnetic field

Radar Polarimetry deals with the full vector nature of polarized electromagnetic waves

The POLARISATION informationContained in the waves backscattered

from a given medium is highly related to:

Radar Polarimetry

E. Pottier 01 / 13

its geometrical structurereflectivity, shape and orientation

its geophysical properties such as humidity, roughness,

SAR Polarimetry Applications

E. Pottier 01 / 13Courtesy of Dr. I. Hajnsek

A Bit Of History

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Radar Polarimetry

Discovery of the Phenomena of Polarized Electromagnetic Energy

AD 1000Use of the polarizedskylight to locate a

hidden sun1669

First knownQuantitative work 1677

W t

Corpuscular model or longitudinal waves

on light observation Wave natureof light discovery

Explanation of thedouble refraction

1808Discovery of the

polarization of light( intrinsic propertyof light and not of

crystals)

1704Corpuscular

Model of light

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Crystal of calciteIceland Spar

Sunstone Huygens

MalusX-1795

Bartholinus

Discovery of the doublerefraction in calcite Newton

Non Exhaustive Chronological List of the Main Pionners who contributed to the discovery

of Polarization leading to Radar Polarimetry

Brewster

Fresnel

Faraday

Stokes

Maxwell

Helmholtz

Rayleigh

Kirchhoff

18161820

1832

1852

1873

E. Pottier 01 / 13

1873

1881

1881

1883

Transverse natureof light waves

Electromagnetictheory of light



Hertz

Drude

Sommerfeld

Poincar

Wiener

MarconiLorentz

Lie

1897

1892

1896

1889

1886

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1928

19221908

1897

PauliDeschamp



Wolf

Born

1954

1954

Deschamp

1950

1951

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Kennaugh

1952

KennaughHuynen

W M Boerner



1952

W. M. Boerner

1970

1980

The

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TheRadar Polarimetric

Triptych

KennaughHuynen

W M Boerner



1952

W. M. Boerner

1970

1980

1990 - 2000

J.J. Van Zyl A. Freeman R. Touzi

T. Ainsworth

C. Lopez

J.S. Lee

Y. Yamaguchi

E. PottierS.R. CloudeP. Dubois

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1990 2000Radar PolarimetryScientific Progress

H. Mott

Z. Czyz

E. Lueneburg

K. Papathanassiou J.C. Souyris

Y.L. DesnosA. Moreira

E. Krogager

I. HajnsekT. Le Toan

Polarimetric SAR

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Airborne Sensors

Airborne PolSAR Sensors

DOSAREADS / Dornier GmbH (D)

DO 228 (89), C160 (98), G222 (00)S, C, X-Band (Quad), Ka-Band (VV)

AIRSARNASA / JPL (USA)

DC8P, L, C-Band (Quad)

AES1InterMap Technologies (D)

GulfStream CommanderX-Band (HH), P-Band (Quad)

AuSAR - INGARAD.S.T.O (Aus)

DC3 (97) KingAir 350 (00) Beach 1900CX-Band (Quad) S, C, X Band (Quad), Ka Band (VV)P, L, C Band (Quad)X Band (HH), P Band (Quad)

EMISARDCRS (DK)G3 Aircraft

L, C-Band (Quad)

ESARDLR (D)DO 228

P, L, S-Band (Quad)C, X-Band (Sngl)

MEMPHIS / AER II-PAMIRFGAN (D)

Transal C160Ka, W-Band (Quad) / X-Band (Quad)

STORMUVSQ / CETP (F)

Merlin IVC-Band (Quad)

X Band (Quad)

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PISARNASDA / CRL (J)

GulfStreamL, X-Band (Quad)

PHARUSTNO - FEL (NL)

CESSNA Citation IIC-Band (Quad)

RAMSESONERA (F)

Transal C160P, L, S, C, X, Ku, Ka, W-Band (Quad)

SAR580Environnement Canada (CA)

Convair CV-580C, X-Band (Quad)

AIRSAR


AIRSAR

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Google Earth San Francisco Bay (1988) (L-Band)

AIRSAR

Airborne PolSAR SensorsTx Rx

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|HH|dB

AIRSAR


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|VV|dB

AIRSAR


E. Pottier 01 / 13San Francisco Bay (1988) (L-Band)

|HV|dB Google Earth

Tx Rx Tx Rx Tx Rx

AIRSAR


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|HH|dB |HV|dB |VV|dB

AIRSAR


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|HH+VV| |HV | |HH-VV| Google Earth San Francisco Bay (1988) (L-Band)

TopoSAR (AeS-1)InterMAP

GullStream Commander

IECASIECAS - MOTL (C)

Upcoming Airborne PolSAR Sensors

GullStream CommanderP, L-Band (Quad) P, X-Band (Quad)

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SETHIONERA (F)Mystere 20


yP, L, S, C, X (Quad - Pol)


P-Band Quad-PolB=70MHz

(P-Vh, X-Hh, L-Vh)

FSARDLR (G)DO 228

S-Band


S, X (Quad - Pol)


(HH-VV, HV, HH+VV)

UAVSARGulf-Stream IIIL (Quad - Pol)

Salton Sea California ( March 2008 )


( )


(HH-VV, HV, HH+VV)

Polarimetric SAR

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Spaceborne Sensors

Space-borne Sensors

SEASATNASA/JPL (USA)

L-Band, 1978

ERS-1European Space Agency (ESA)

C-Band, 1991-2000

SIR-C/X-SARNASA/JPL, L- and C-Band (quad)

DLR / ASI, X-bandApril and October 1994

J-ERS-1Japanese Space Agency (NASDA)

L-Band, 1992-1998 April and October 1994

RadarSAT-1Canadian Space Agency (CSA)

C-Band, 1995-todayERS-2

European Space Agency (ESA)C-Band, 1995-today

Shuttle Radar Topography Mission (SRTM)NASA/JPL (C-Band), DLR (X-Band)

February 2000

ENVISAT / ASAREuropean Space Agency (ESA)

C-Band (dual), 2002-today

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ALOS / PALSARJapanese Space Agency (JAXA)

L-Band (quad), 2006

TerraSAR-XGerman Aerospace Center (DLR) / Astirum

X-Band (dual), 2007

RadarSAT-IICanadian Space Agency (CSA)

C-Band (quad), 2007

COSMO-SkyMedItalian Space Agency (ASI)

X-Band, 2007

Space-borne Sensors


L-Band, 1978


C-Band, 1991-2000









February 2000



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L-Band (quad), 2006


X-Band (dual), 2007


C-Band (quad), 2007


X-Band, 2007

T

RXAX

Scattering Coefficient

XXS XXS XXS XXS

X X X XT

RX

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TRANSMITTER: XRECEIVER: X

{{{{ }}}}XXS

XX XX XX XX

BACKSCATTERINGCOEFFICIENT

NO POLARIMETRY

T

RXAXAY

Wave Polarimetry

RY

S

XXS

S

XXS

S

XXS

S

XXS

X X X XT

RX

RY

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TRANSMITTER: XRECEIVERS: X & Y

====YX

XXS S

SE

YXS YXS YXS YXS

JONES VECTORS

WAVE POLARIMETRY

Space-borne PolSAR Sensors


L-Band, 1978


C-Band, 1991-2000









February 2000



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X-Band (dual), 2007


L-Band (quad), 2006


C-Band (quad), 2007


X-Band, 2007

T

RXAXAY

Scattering Polarimetry

RY

S

XXS

S

XYS

S

XXS

S

XYS

X Y X YT

RX

RY

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[[[[ ]]]] ====YY

XY

YX

XX

SS

SS

S

YXS YYS YXS YYS

SINCLAIR MATRICES

SCATTERING POLARIMETRY

TRANSMITTER: X & YRECEIVERS: X & Y



L-Band, 1978


C-Band, 1991-2000









February 2000



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L-Band (quad), 2006


X-Band (quad), 2007


C-Band (quad), 2007


X-Band, 2007

ALOS - PALSARJanuary 2006

L-Band (Sngl / Twin / Quad)


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ALOS : Advanced Land Observing SatellitePALSAR : Phase Array L-Band SAR

TerraSAR - X


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June 2007X-Band (Sngl / Twin / Quad ?)

RADARSAT - 2 December 2007C-Band (Quad)


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What About The Future ?

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From Tomorrow

RISAT

Future Space-Borne PolSARPol-InSAR Sensors

Sentinel 1

BIOMASS

ALOS 2

RCM

SAOCOM

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TanDEML DESDynil

What About

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Software / Toolbox ?

PolSARpro v5.0

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PolSARpro v5.0

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Learning / Training

Next P.I Generations

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Polarimetric Radar Imaging: From basics to applications

Books On Polarimetric RadarSAR, Polarimetric Interferometry

Jong-Sen LEE Eric POTTIERCRC Press; 1st ed., February 2009, pp 422ISBN: 978-1420054972

Polarisation: Applications in Remote Sensing

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Polarisation: Applications in Remote SensingShane R. CLOUDEOxford University Press, October 2009, pp 352ISBN: 978-0199569731

Questions ?

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y( )

0

x ( )E z t,

z

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BASIC CONCEPTS

xy

( )E z t,

0z

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WAVE POLARIMETRY

(((( ))))t,zEREAL ELECTRIC FIELD VECTOR

(((( ))))tBMAXWELL EQUATIONS

PROPAGATION EQUATION

(((( )))) (((( ))))

(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) 0t,zB

t,zt,zDt,zJt,zHt

t,zBt,zE

T

========

====

====

(((( ))))

MAXWELL FARADAY EQUATION

MAXWELL AMPERE EQUATION

GAUSS THEOREM

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(((( )))) (((( )))) (((( ))))

(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))t,zEt,zD

t,zHt,zBt,zEt,zJ

tt,zDt,zJt,zJ

C

CT

============

++++====

xy

( )E z t,

POLARISATION ELLIPSE

0

z

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(((( ))))(((( ))))(((( ))))

============

====0E

kztcosEEkztcosEE

t,zE

z

yy0y

xx0x

REAL ELECTRIC FIELD VECTOR

y ( )E z t0 ,x

y( )E z t,


z0

x0

z

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(((( )))) (((( )))) 22

y0

y

y0x0

yx2

x0

x sinEE

cosEEEE

2EE ====++++

THE REAL ELECTRIC FIELD VECTOR MOVES IN TIME ALONG AN ELLIPSE

With: xy ====

yy0

x0( )E z t, = 0


0A

x,zn

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A : WAVE AMPLITUDE

ORIENTATION ANGLE ELLIPTICITY ANGLE

ABSOLUTE PHASE

22

40

POLARISATION HANDENESS

ROTATION SENSE: LOOKING INTO THE DIRECTION OF THE WAVE PROPAGATION

xy

0

z

++++

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ANTI-CLOCKWISE ROTATION CLOCKWISE ROTATION

LEFT HANDED POLARISATION RIGHT HANDED POLARISATION

ELLIPTICITY ANGLE : ELLIPTICITY ANGLE : 44

REAL ELECTRIC FIELD VECTOR

(((( ))))(((( ))))(((( ))))====

========

0EkztcosEEkztcosEE

t,zE yy0yxx0x

========

====y

x

joyy

joxx

eEEeEE

E

PHASOR = JONES VECTOR

JONES VECTOR

==== 0Ez

GEOMETRICAL PARAMETERS

ABSOLUTE PHASE

x ==== 2y02x0 EEA ++++====

AMPLITUDE

(((( )))) (((( ))))==== kztjeEt,zE With:

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cosEE

EE22tan 2

y02x0

y0x0

====

y

sinEE

EE22sin 2

y02x0

y0x0

++++====

ORIENTATION ANGLE ELLIPTICITY ANGLE

POLARISATION HANDENESS: Sign()

Special Unitary Matrices Group and Jones Vector

JONES VECTOR

++++

============

====)sin()cos(j)cos()sin()sin()sin(j)cos()cos(jAe

eEEeEE

Ey

x

joyy

joxx

)y,x(

====

)sin(j)cos(

)cos()sin()sin()cos(jAeE )y,x(

)()(j)()(oyy

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====01

je00je

)cos()sin(j)sin(j)cos(

)cos()sin()sin()cos(

AE )y,x(

HORIZONTAL POLARISATION STATE

E z t( , )

y

E z t( , )

y

====01

H ====10

V

VERTICAL POLARISATION STATE

JONES VECTOR

0 zx

0 zx

00

========

02

====

====

E z t( , )

y

E z t( , )

y

====11RC

LEFT CIRCULAR POLARISATION STATE RIGHT CIRCULAR POLARISATION STATE

====11LC

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0 zx

0 z

x

==

j2RC

4

22

++++====

++++

==j2

LC

4

22

====

++++

y

y0 x0

yy0

ORTHOGONAL JONES VECTOR

0A

x,zn

y

0

x,zn

x0

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ORTHOGONALITY CONDITIONS

(((( ))))====

++++====

2,

CHANGE OF POLARISATION HANDENESS

(((( ))))[[[[ ]]]] (((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))

====

jj

00e

ijsinjcos

isincos

,,U

SU(2) : SPECIAL UNITARY TRANSFORMATION MATRIX

ELLIPTICAL BASIS TRANSFORMATION

(((( )))) (((( )))) (((( )))) (((( )))) je0cossinjcossin

(((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]]==== ,,UU 1BBAAELLIPTICAL BASIS TRANSFORMATION MATRIX

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(((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]](((( )))) (((( ))))

(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))

====

cossinsincos

cossinjsinjcos

e00e

,,UU

j

jB,BA,A

0

xy

z 0

xy

z

PARTIALLY POLARISED WAVES

RANDOM SCATTERINGDETERMINISTIC SCATTERING

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PARTIALLY POLARISED WAVECOMPLETELY POLARISED WAVE

Polarisation Ellipse varies in timeAmplitude, Phase: Random processes

STATISTICAL DESCRIPTION


WAVE COVARIANCE MATRIX

[[[[ ]]]] ======== 2**yx

2x*T

EEEEEJ 2

y*xy EEE

DIAGONAL ELEMENTS : INTENSITIES ON EACH OF THE 2 ORTHOGONALCOMPONENTS OF THE WAVE

OFF-DIAGONAL ELEMENTS : CROSS-CORRELATIONS BETWEEN THE 2ORTHOGONAL COMPONENTS OF THE WAVE

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[[[[ ]]]](((( )))) 22y2x AEEJTrace ====++++==== TOTAL WAVE INTENSITY

THE WAVE COVARIANCE MATRIX IS A 2x2 HERMITIAN POSITIVE SEMI-DEFINITE MATRIX

EIGENVALUES DECOMPOSITION

[[[[ ]]]] [[[[ ]]]] [[[[ ]]]] *T*T11 U0UJ


2 ORTHOGONAL EIGENVECTORS

[[[[ ]]]] [[[[ ]]]] [[[[ ]]]] T222T111122

12 uuuuU0

UJ

++++========

[[[[ ]]]] [[[[ ]]]]212 u,uU ====

{{{{ }}}}2221

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2 REAL EIGENVALUES{{{{ }}}}{{{{ }}}}23222102

23

22

2101

gggg21

gggg21

++++++++====

++++++++++++====

Degree of Polarisation


PARTIALLY POLARISED WAVES DESCRIPTORS

Anisotropy

[[[[ ]]]](((( ))))[[[[ ]]]](((( ))))====++++

====++++++++

====JTrace

Jdet41g

gggDoP 2

21

21

0

23

22

21

Polarised Wave PowerTotal Wave Power 1DoP0

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Wave Entropy

With:(((( ))))====

====

====2i

1ii2i plogpH

21

iip

++++

====

Degree of randomness, statistical disorder

1H0


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ShannonEntropy


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Anisotropy = DoP

Questions ?

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xy

( )E z t,

0z

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SCATTERINGPOLARIMETRY

T

RXAXAY

WAVE POLARIMETRY

RY

S

XXS

S

XXS

S

XXS

S

XXS

X X X XT

RX

RY

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TRANSMITTER: XRECEIVERS: X & Y

====YX

XXS S

SE

YXS YXS YXS YXS

JONES VECTORS

WAVE POLARIMETRY

T

RXAXAY


RY

S

XXS

S

XYS

S

XXS

S

XYS

X Y X YT

RX

RY

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[[[[ ]]]] ====YY

XY

YX

XX

SS

SS

S

YXS YYS YXS YYS

SINCLAIR MATRICES


TRANSMITTER: X & YRECEIVERS: X & Y

Tx Rx Tx Rx Tx Rx


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-15dB 0dB-30dB

|HH|dB |HV|dB |VV|dB

Sinclair Color Coding


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|HH| |HV| |VV| Google Earth

(((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] ==== B,BA,AA,ATB,BA,AB,B USUSCON-SIMILARITY TRANSFORMATION


SU(2) SPECIAL UNITARY ELLIPTICALBASIS TRANSFORMATION MATRIX (((( )))) (((( ))))[[[[ ]]]] B,BA,AU

[[[[ ]]]] (((( ))))[[[[ ]]]] 1

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(((( ))))[[[[ ]]]]2U(((( ))))[[[[ ]]]]2U(((( ))))[[[[ ]]]]2U

(((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]](((( )))) (((( ))))

(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))

====

====

cossinsincos

cossinjsinjcos

e00e

,,UU

j

j

1B,BA,A

(H,V) POLARISATION BASIS


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|HH+VV| |HV | |HH-VV| Google Earth

(+45,-45) POLARISATION BASIS


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|AA+BB| |AB | |AA-BB|With: A=Linear +45, B=Linear 45

Google Earth

(LC,RC) POLARISATION BASIS


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|LL+RR| |LR | |LL-RR| Google Earth

SINCLAIR MATRIX

POLARIMETRIC DESCRIPTORS

[S] SINCLAIR Matrix

[[[[ ]]]] ====VV

HV

VH

HH

SS

SS

S

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TRANSMITTER: H & VRECEIVERS: H & V

k Target Vector

[T] 3x3 COHERENCY Matrix

VECTORIZATION OF [S]

[[[[ ]]]] [[[[ ]]]](((( )))) [[[[ ]]]][[[[ ]]]](((( ))))STraceSVkSSSS

SVVHV

HVHH

21============

TARGET VECTOR

SS VVHV 2

[[[[ ]]]]

====0110

2,10

012,

1001

2P

SET OF 2x2 COMPLEX MATRICESFROM THE PAULI MATRICES GROUP

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TARGET VECTOR

[ ]k S S S S SHH VV HH VV HV T= + 12 2

TARGET VECTOR k

[ ]k S S S S SHH VV HH VV HV T= + 12 2

COHERENCY MATRIX

COHERENCY MATRIX [T]

[ ]T k kA C jD H jG

C jD B B E jFH jG E jF B B

T= = +

+ + +

*2 0

0

0

HERMITIAN MATRIX - RANK 1

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HERMITIAN MATRIX RANK 1

A0, B0+B, B0-B : HUYNEN TARGET GENERATORS

[T] is closer related to Physical and Geometrical Properties of the ScatteringProcess, and thus allows a better and direct physical interpretation

PHYSICAL INTERPRETATION

SINGLE BOUNCE DOUBLE BOUNCE VOLUME

TARGET GENERATORS

SINGLE BOUNCESCATTERING

(ROUGH SURFACE)

DOUBLE BOUNCESCATTERING

VOLUMESCATTERING

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2YYXX011 SSA2T ++++========

2YYXX022 SSBBT ====++++====

2XY033 S2BBT ========

TARGET GENERATORS

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-15dB 0dB-30dB

|HH+VV|dB |HV|dB |HH-VV|dB

(H,V) POLARISATION BASIS

TARGET GENERATORS

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|HH+VV| |HV | |HH-VV| Google Earth

(((( )))) (((( ))))[[[[ ]]]] (((( ))))i A,AA,As A,A ESE ==== (((( )))) (((( ))))[[[[ ]]]] (((( ))))i B,BB,Bs B,B ESE ====SINCLAIR MATRIX


(((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] ==== B,BA,AA,ATB,BA,AB,B USUSCON-SIMILARITY TRANSFORMATION

(((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] 1BBAA3AABBAA3BB UTUT ====COHERENCY MATRIX

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(((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]] (((( )))) (((( ))))[[[[ ]]]]B,BA,A3A,AB,BA,A3B,B SIMILARITY TRANSFORMATION

U(3) SPECIAL UNITARY ELLIPTICALBASIS TRANSFORMATION MATRIX (((( )))) (((( ))))[[[[ ]]]] B,BA,A3U

SPECIAL UNITARY SU(2) GROUP

[[[[ ]]]] (((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))(((( )))) (((( ))))

====

j

j

2 e00e

cossinjsinjcos

cossinsincos

U

(((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]] (((( ))))[[[[ ]]]]


SPECIAL UNITARY SU(3) GROUP

(((( ))))[[[[ ]]]]2U (((( ))))[[[[ ]]]]2U (((( ))))[[[[ ]]]]2U

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[U3(2)] [U3(2)] [U3(2)]

(((( )))) (((( ))))(((( )))) (((( ))))

(((( )))) (((( ))))

(((( )))) (((( ))))

(((( )))) (((( ))))(((( )))) (((( ))))

10002cos2sinj02sinj2cos

2cos02sinj010

2sinj02cos

2cos2sin02sin2cos0

001

TARGET EQUATIONS

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POLARIMETRIC TARGET DIMENSION

POLARIMETRIC GOLDEN NUMBER

[[[[ ]]]] ====YYYX

XYXX

SSSS

S

POLARIMETRIC TARGET DIMENSION

XXYYXXXY

YYXYXX

,S,S,S

5 DEGREES OF FREEDOMCOHERENCY MATRIX [T]

9 HUYNEN REAL PARAMETERS(A0, B0, B, C, D, E, F, G, H)

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TARGET MONOSTATIC POLARIMETRIC DIMENSION

5

=

9 - 5 = 4 TARGET EQUATIONS

[[[[ ]]]] ++++++++++++++++

======== jFEBBjDCjGHjDCA2

kkT 00

T*

PURE TARGET MONOSTATIC CASE

TARGET EQUATIONS

(((( )))) (((( )))) 0HGBBA20DCBBA2 22002200 ========++++

BBjFEjGH 03x3 HERMITIAN MATRIX - RANK 1

9 PRINCIPAL MINORS = 0

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(((( )))) (((( ))))

(((( )))) (((( ))))(((( ))))

(((( )))) 0DFCEBBH0EDFCBBG0DHCGFA20GEFHBBD0GFEHBBC

0FEBB0DGCHEA20G0C

0

00

00

222200

0000

====++++====++++++++========++++====

========++++++

[[[[ ]]]] ====YYYX

XYXX

SSSS

S

TARGET EQUATIONS

XXYYXXXY

YYXYXX

,S,S,S

5 DEGREES OF FREEDOM COHERENCY MATRIX [T]9 HUYNEN REAL PARAMETERS

(A0, B0, B, C, D, E, F, G, H)

9 5 = 4 TARGET EQUATIONS

E.Pottier(2013)

TARGET MONOSTATIC POLARIMETRIC DIMENSION

5

=

9 - 5 = 4 TARGET EQUATIONS

(((( ))))(((( ))))

DHCGFA2DGCHEA2HGBBA2DCBBA2

0

0

2200

2200

++++========++++====++++====++++

POLARIMETRIC DESCRIPTORS

REMOTE SENSING

[S] SINCLAIR Matrix

k Target Vector

[T] 3 3 COHERENCY M t i

[[[[ ]]]] ====VV

HV

VH

HH

SS

SS

S

E.Pottier(2013)

TRANSMITTER: H & VRECEIVERS: H & V

[T] 3x3 COHERENCY Matrix

POLARIMETRIC REMOTE SENSING

Questions ?

E.Pottier(2013)

Documents

Radar Polarimetry (1)