8. Grundlagen der SAR Polarimetrie - Pixelplaatkeydel.pixelplaat.de/uploads/File/erlangen 07-08/Polarimetry.pdf · Quellenangabe Institut für Hochfrequenztechnk und Radar W. Keydel,

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1Institut für Hochfrequenztechnk und Radar W. Keydel, Vorlesung IHFT Erlangen

8. Grundlagen der SAR Polarimetrie

Vorlesung: Hochauflösende RadarsystemeWS 2007/08,

Friedrich-Alexander-Universität Erlangen NürnbergLehrstuhl für Hochfrequenztechnik

Wolfgang KeydelDLR Oberpfaffenhofen, Institut für Hochfrequenztechnik und Radarsysteme

e-mail: [email protected], Web: http://www.keydel.com

Literatur: Martin Hellmann, SAR Polarimetry, Tutorialhttp://www.fpk.tu-berlin.de/~anderl/epsilon/polarimetrytutorial.pdf

Keydel, W. (Editor) Radar Polarimetry and Interferometry Lecture Series RTO-EN-SET-081 Radar Interferometry and Polarimetry

http://www.rta.nato.int/panel.asp?panel=SET&O=RTOPubNumber#

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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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Polarisation Ellipse & Spatial Helixdecomposed

into orthogonal components x (horizontal H) and y (vertical V)

Courtesy Shane Cloude

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X

Y

RXAX

RY

AY

YXS

XXS

YYS

XYS

YXS

XXS

YYS

XYS

X Y X Y

RX

RY

SCATTERING POLARIMETRYSCATTERING POLARIMETRY

TRANSMITTER: X & YRECEIVERS: X & Y

TT

T

SINCLAIR MATRIX

SCATTERING POLARIMETRY

[ ]⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡=

YY

XY

YX

XX

SS

SS

S

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Polarization Ellipse

χ = Ellipticity Angle: 0 ≤ χ ≤ π/4

Ψ= Orientation Angle: - π/2 ≤ ψ ≤ π/2

ξχ

Ψx

y

majoraxis

minor axis

η

αa ξ

aη

Ev

EX0

EY0

( ) ( ) ( ) cos)2tan()2tan(andsin2sin2sin

aa

)tan(andcosEEEE2

)2tan( 020y

20x

0x0y

ϕαψϕαχ

χϕψηξ

ξ

==

±=−

=

withsincosEEEE

2EE

EE

yx0000x0y

xy2

0x

x

2

0y

y ϕϕϕϕϕ −==⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

rrr

rrr

rrr

yjjkz

0yjkz

yy eee)z(Ee)z(E)z(E yϕ==

xjjkz

0xjkz

xx eee)z(Ee)z(E)z(E xϕ==

yyxx e)z(Ee)z(E)z(E +=

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x

Polarization Ratio:

For each Polarization State ρ exists an orthogonal Polarization State ρorth

)2cos()2cos(1)2sin(j)2sin()2cos(e

EE )(j

xO

yO yx

ψχχψχρ ϕϕ

−+

== −

1*orth −=ρρ

Ψ

χ = 45°

x

y

Ψ

χ = 0°

y

Orthogonal PolarizationsCircular LinearElliptical

χ

Ψ

y

x

ξη

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Examples:[S] SINCLAIR Matrix

k Target VectorE Jones Vektorg Stokes Vector

[T] Coherency Matrix[C] Covariance Matrix

X

Y

DIFFERENT TARGET POLARIMETRIC

DESCRIPTORS

POLARIMETRIC DESCRIPTORSPOLARIMETRIC DESCRIPTORS

TRANSMITTER: X & YRECEIVERS: X & Y

Courtesy Eric Poitier

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Streumatrix (Sinclaire Matrix)

EHscat SHHEH

inc SHVEVinc

EVscat SVHEH

inc SVVEVinc

= +

= +

EscatEH

scat

EVscat

SHH SHVSVH SVV

EHinc

EVinc S(HV) Einc=

FHGGIKJJ =FHG

IKJFHGG

IKJJ =

Si ki ke

j i k,

, ,= σϕ

0

E kr e j t= − +E0e r−α

ω ϕ( )…α = jk +γ

8 unabhängige Parameter

Bei monostatischer Rückstreuung:SHV= SVH 5 Parameter

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Streumatrix {S(HV)} = SHH SHVSVH SVV

FHG

IKJ

Elemente:

|SHH|, |SHV|, |SVV|, ΦHH, ΦHV, ΦHV ΦVV

|SHH|2, |SHV|2, |SVV|2,

Invarianten: Eigenwerte λ1, λ2

resultierend aus

Spur {S(HV)} & Det {S(HV)}

Spur {S(HV)} = = |SHH|2 + 2|SHV|2 + |SVV|2 = | λ1 |2 + | λ2 |2

Det {S(HV)} = |SHHSVV – S2VV| = | λ1λ2 |

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Jones Vectorcomplete information about the Polarization Ellipse, except handleness!

r

With Polarisation Ratio ρ the Jones Vector can be written as:

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

ρ1

EEE

E xy

xxyr

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

y

x

j0y

j0x

y

xxy eE

eEEE

E ϕ

ϕr

yyxx e)z(Ee)z(E)z(E += r r

r

Two plane waves propagating in opposite directiond havethe same Jones Vector

Using the subscripts „ + “ and „-“ compensates this lack of consistency

Subscript „ + “ : propagation in +k direction, Subscript „ - “ : propagation in - k direction,

r

}{ }{ )rkt(j)rkt(j eERe)t(,E & eERe)t(,Errrr rrrr +

−−−

++ == ωω

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Change of Polarization Basis{ } { }

[ ]

[ ] {

0for

newbasistheofvectorstheareUofcolumnsThe

e,eande,e:basesonpolarizatilorthonormaTwo

1Y

y2y1x2x1

⇒=

eEeEeEeEE:Field-E y2y2y1y1x2x2x1x1 +=+=

[ ]1

11

1Ux

*x

*xx

⎥⎦

⎤⎢⎣

⎡ −

+=

ρρ

ρρϕ[ ]

eeee

11U jj

x

j*x

j

*xx

1Y1Y

1Y1Y

⎥⎦

⎤⎢⎣

⎡ −

+=

−

−

ρρ

ρρ ϕϕ

ϕϕ

}e,e y2y1rr

1ρ

ρρ11eeand

ρ1

ρρ11ee

*x

*xx

jy2

x*xx

jy1

Y2Y1 ⎥⎦

⎤⎢⎣

⎡−

+=⎥

⎦

⎤⎢⎣

⎡

+= ϕϕ rr

{ }:e,ebasis-YforrsBasisvecto y2y1rr

{ }e,ebasis-Xforratioonpolarizatiingcorrespondρ x2x1x = rr

[ ]EUE

UMatrix via 2x2EEvectorcomplexElement2oftionTransforma

2x,1x2y,1y

2y,1y2x,1x

=

⇒−rr

rrEE

EandEE

E:VectorsonesJ2y

1y2y,1y

2x

1x2x,1x ⎥

⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

rr

rrrrr

rrrr

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13Institut für Hochfrequenztechnk und Radar W. Keydel, Vorlesung IHFT Erlangen Courtesy Eric Poitier

x x

xx

y

y y

y

Jones Vector Descriptions for Characteristic Polarization States

Propagation Direction out of Page

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Different Polarization States

Courtesy Eric Pottier

x x

xx

y

yy

y

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Poincarés Polarization Sphere

Courtesy Eric Poitier

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Poincare Sphere

Ellip

ticity

Ang

le χ

Orientation Angle Ψ

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The Stokes Vector

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−+

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−+

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

ϕϕ

sinEE2cosEE2EEEE

)EEIm(2)EERe(2

EEEE

gggg

)E(g

0h0v

0h0v

20h

20v

20h

20v

h*v

h*v

2h

2v

2h

2v

3

2

1

0

rr

;g´ggg 23

22

21

20 ++=

g0 ~ total wave intensity,g1 ~ Difference between

hor. & vert. linear Parts, g2 & g3 ~ Phase difference between

hor. & vert. linear Parts

Absolute Phase lost!!

Completely polarized waves:

Incompletely polarized waves:;g´ggg 2

322

21

20 ++>

Completely polarized waves:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

)2sin(g)2cos()2sin(g)2cos()2cos(g

g

g

0

0

0

0

ψχψχψr

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Depolarization Scheme

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Stokes Vektor Decomposition

Degree of Polarization:o

23

22

21

gggg

p++

=

Decomposition into completly polarized & unpolarized Component

21

21

21

20 gggg ++>General Case:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −

000

p1

+=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

gggg

3

2

1

0

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

)2sin(p)2cos()2sin(p)2cos()2cos(p

p

g0

χχψχψ

=gr

All 4 Parameter derivable from intensity measurements

Orthogonal Polarization States located on diametrally opposite positions on Poincaré Sphere

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BasismatrizenEine generische Matrix ist in Basismatrizen zerlegbar;

Beispiel:

{S}S 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= + = − = =; ;

Streuvektor (Target Vector) k = (a,b,c) = (SHH + SVV ; SHH - SVV ; 2SHV)

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Pauli Matrices

RoughSurfacePlate,

Sphere, Dihedral;

TiltedDihedral;

α

Vegetation

⎥⎦

⎤⎢⎣

⎡=

0110Sdiff⎥

⎦

⎤⎢⎣

⎡= ,

1001Sodd ⎥

⎦

⎤⎢⎣

⎡=

cos2αsin2αsin2αcos2αSeven

Single Bounce, odd

Double Bounce, even

Volume Scattering,diffuse

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

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Dihedral with 45-degree tilt

Even-bounce, π/4-TiltDihedral

DihedralEven-bounce

Surface, sphere, Corner reflectors

Odd-bounce

Scattering mechanism

Scattering typePauli matrix

1 00 1

⎡ ⎤⎢ ⎥⎣ ⎦1 00 1

⎡ ⎤⎢ ⎥−⎣ ⎦

0 11 0

⎡ ⎤⎢ ⎥⎣ ⎦

Physical significance of elementary scatterers

D.G. Corr:Potential of Radar Polarimetry. QinetiQ, Cody Technology Park, A8/1008 Ively Road, Farnborough, Hampshire, GU14 0LX, United Kingdom

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Moore Pauli Matrices

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=αα

αα

2

2

linesin2sin

21

2sin21cos

S

Sphere Statisical Volume

⎥⎦

⎤⎢⎣

⎡=

0110Sdiff⎥

⎦

⎤⎢⎣

⎡= ,

1001Sodd

Wire

α

⎥⎦

⎤⎢⎣

⎡=

cos2αsin2αsin2αcos2αSeven

Diplane

α

[ ] ⎥⎦

⎤⎢⎣

⎡±

±= ±

1jj1

e21S 2j

helixα

Helix

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⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

0110

S,cos2αsin2αsin2αcos2α

S,1001

S dfiffus21

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Transformation from linear to circular Basis

( )

( )

( )VVHHRL

VVHHHVLL

VVHHHVRR

SS2j´S

SS21jSS

SS21jSS

+=

−−=

−+=

Circular Basis Radar Responses

NOYESNOLeft HelixNONOYESRight HelixNOYESYESDiplaneYESNONOSphereLRRRLL

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TARGET VECTORSTARGET VECTORS

PAULI SCATTERING VECTOR

Advantage: Closer related to physical properties of the scatterer

[ ]( ) [ ][ ]( )PSTrace21SVk ψ==

SET OF 2x2 COMPLEX MATRICES FROM THE PAULI MATRICES GROUP

Note: Also known as k4P

[ ]⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡ −⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡=0j

j02,

0110

2,10

012,

1001

2Pψ

( )[ ]TYXXYYXXYYYXXYYXX SSjSSSSSS

21k −+−+=

General Case: SXY ≠ Syx

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PAULI SCATTERING VECTOR k

COHERENCY MATRIX [T]

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+++−−−−+++−+−

=⋅=

A2jIJjNMjKLjIJBBjFEjGHjNMjFEBBjDCjKLjGHjDCA2

kkT0

0

0

T*

HERMITIAN POSITIVE SEMI DEFINITE MATRIX - RANK 1

COHERENCY MATRIXCOHERENCY MATRIXBISTATIC CASE

( )[ ]TYXXYYXXYYYXXYYXX SSjSSSSSS

21k −+−+= ; ; ;

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HERMITIAN MATRIX - RANK 1

COHERENCY MATRIXCOHERENCY MATRIX

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

MONOSTATIC CASE

COHERENCY MATRIX [T]

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

PAULI SCATTERING VECTOR k

[ ]TXYYYXXYYXX S2SSSS2

1k −+= ;;

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−++++−

=⋅=

BBjFEjGHjFEBBjDCjGHjDCA2

kkT

0

0

0T*

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PHYSICAL INTERPRETATION

SINGLE BOUNCESCATTERING

(ROUGH SURFACE)

DOUBLE BOUNCESCATTERING

VOLUMESCATTERING

TARGET GENERATORS TARGET GENERATORS

2YYXX011 SSA2T +==

2YYXX022 SSBBT −=+=

2XY033 S2BBT =−=

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Coherence

CE t E t

E t E t E t E t=

( ( ) ( ))

( ) ( ) ( ) ( )

*

* *

1 2

1 1 2 2

E1 and E2 vary in conformity C=1, E1 and E2 vary in opposition C=-1

Coherence: γ = =CE t E t

E t E t E t E t( ( ) ( ))

( ) ( ) ( ) ( )

*

* *1 2

1 1 2 2

γ = 0 means incoherence, γ = 1 complete coherence

Continous transition from pure coherence to pure incoherence

If phases of waves random & (directly or in effect) uniformly distributed

0 ≤ ϕ ≤ 2π incoherent. If phase relations between waves are constant coherent

0 ≤ γ ≤ 1

-1 ≤ C ≤ +1Correlation

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Matrizen

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Zerlegung von [T] in 3 Kohärenzmatrizen [Tn],Gewichtung mit entsprechendem Eigenwert λn.

T T e e e ee

nn

n nn

n n

T

n

n

n nj n

n nj n

= ∑ = ∑ FHIK =

F

HGG

I

KJJ= =

λ λα

α βα β

δ

γ1

3

1

3;

cossin cossin sin

mit

0° ≤ αn ≤ 90° : Streumechanismus für jeden Vorgang

-180° ≤ βn ≤ 180° : Objektorientierung gegen Sichtlinie

δ & γ : Phasenwinkel

Mittlerer - Winkel:α α λ α= ∑=

n nn 1

3

2 3

Entropie: λ λ= − ∑=

n nn

H 31

3log

λ λλ λ

=−+

Anisotropie A 2 3:

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DIFFICULT MECHANISM DISCRIMINATION WHEN : H > 0.7

ANISOTROPY(EIGENVALUES SPECTRUM)

λ1 λ2 λ332

32Aλλλλ

+−

=

COMPLEMENTARY TO ENTROPY

DISCRIMINATION WHEN H > 0.7

ROLL INVARIANT

H / A / H / A / aa DECOMPOSITION DECOMPOSITION

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Measure for the homogeneity of a target relative to the radar look direction.

For example: the Amazon forest is a very homogeneous target & would have a low anisotropy value.

In contrast: row crops would have a high anisotrophy value.

λ λλ2 λ3

=−+

Anisotropy A 2 3:

0 ≤ H ≤ 1Measure of the dominance of a given scattering mechanism within a resolutioncell related to the amount of effective scattering mechanisms, normalizedbetween 0 and1.

H = 0: all scattering results from one mechanism (such as a flat surface [singlebounce] or a tall building [double bounce]),

H = 1 represents a completely random scattering mechanisms.

Entropie: λ λ= − ∑=

n nn

H 31

3log

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H provides a measure of the diversity of the scattering mechanisms, degree of randomness statistical disorder

single mechanism H = 0, three mechanisms of equal power H = 1.

difficult mechanism discrimination when : H > 0.7

Eigenvalues Spectrum:

♣

Related to scattering mechanisms, not an orientation.Single bounce: α = 0; Double bounce: α = 90°; Diffuse scattering: α = 45°

Entropy: λ λ= ∑=

n nn

H 31

3logPolarimetric

- Angle:α α λ α= ∑=

n nn 1

3Mean

λ λλ2 λ3

=−+

Anisotropy A 2 3:λ1 λ2 λ3

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38Institut für Hochfrequenztechnk und Radar W. Keydel, Vorlesung IHFT Erlangen Courtesi Yoshio Yamagucci

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Coherence & Covariance Matrices

T kk

k k k k k

k k k k k

k k k k k

k S S k S S k S S S

CoherenceMatrix

Todd odd even odd diff

odd even even even diff

odd diff even diff diff

odd HH VV even HH VV diff HV VH HV

= =

L

N

MMMMM

O

Q

PPPPP= + = − = + =

*

* *

* *

* *

; ;

12

2

2

2

2

CovarianceMatrix C kS kS

T

S S S S S S S

S S S S S S SS S S S S S S

S S S S S S S

HH HH HV HH VH HH VV

HV HH HV HV VH HV VV

VH HH VH HV VH VH VV

VV HH VV HV VV VH VV

= =

L

N

* * *

* * *

* * *

* * *

2

2

2

2

MMMMMM

O

Q

PPPPPP=k S S S Ss HH VV HV VH; ; ;a f

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H-α Space

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0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90

Entropy (H)

Alp

ha(α

)

9

3

LOWENTROPY

MEDIUMENTROPY

HIGHENTROPY

SURFACESCATTERING

VOLUMESCATTERING

MULTIPLESCATTERING

DIPOLE

DIHEDRAL SCATTERERFORESTRY DBLE BOUNCE

BRANCH / CROWNSTRUCTURE

CLOUD OF ANISOTROPICNEEDLES

NO FEASIBLEREGION

PERTURBATION OF 1st ORDERSCATTERING THEORIES DUE

TO 2nd ORDER EVENTS

DEGREE OF ARBITRARINESS(SCATTERING PROCESSES

RANDOM NOISE

1

47

2

65VEGETATION

8

SEGMENTATION OF THE H / α SPACE

H / A / H / A / αα DECOMPOSITION DECOMPOSITION

BRAGG SURFACE SURFACE ROUGHNESSPROPAGATION EFFECTS

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H

C1 Urban dihedral

C2 Dipole volumetric scattering

C3 Surface scattering

C4 Forestry C5 Vegetation

C6 Rough surface & vegetationC7 Forestry crown

C8 Vegetation

α°

C1 Urban -dihedral C4 Forestry C7 Forestry crown

C2 Dipole volumetric scatt.

C5 Vegetation C8 Vegetation

C3 Surface scattering

C6 Rough surface and vegetation

Single mechanism Two mechanisms Three mechanisms

Double bounce

Volume scattering

Surface scattering

Not feasible

Scattering characteristics of regions in H-α plane

0 0.2 0.4 0.6 0.8 10

10

203040

50

60708090

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Unsupervised image classification (left), initial scene (right)

C9 C10 C11 C12 C13 C14 C15 C16

C1 C2 C3 C4 C5 C6 C7 C8 Colour composite of 3 Pauli components(k vector elements are blue, red and green)

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LL--band 1988 band 1988

SAN FRANCISCO BAYSAN FRANCISCO BAY

AIRSAR

DC8P, L, C-Band (Quad)

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


T11=2A0 T33=B0-B T22=B0+B

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


T11=2A0 T33=B0-B T22=B0+B|HH| |HV | |VV|

Sinclair Color Coding Pauli Color Coding

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ENTROPY (H)0.5 1.00

ANISOTROPY (A)0.5 1.00

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48Institut für Hochfrequenztechnk und Radar W. Keydel, Vorlesung IHFT Erlangen-15dB 0dB-30dB

( )dB0 BB + ( )dB0 BB −( )dB0A2

TARGET GENERATORSTARGET GENERATORS((TTiiii) )

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ENTROPY(DEGREE OF RANDOMNESS

STATISTICAL DISORDER)

H P Pi ii

= −=∑ log ( )3

1

3

DISTRIBUTED TARGETλ1 = λ2 = λ3= SPAN / 3

H = 1

PURE TARGETλ1=SPAN λ2=0 λ3=0

H = 0

EIGENVALUES λ1 λ2 λ3 : ROLL INVARIANT

PROBABILITIES P1 P2 P3 : ROLL INVARIANT

H / A /H / A / αα DECOMPOSITION DECOMPOSITION

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0A2 BB0 + BB0 −


ENTROPY (H)0.5 1.00

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0A2 BB0 + BB0 −


0 45° 90°

α PARAMETER

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10n

0

1

2

H0.5 1.00

α0 45° 90°

Alp

ha( α

)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)


POLSAR DATA POLSAR DATA DISTRIBUTIONDISTRIBUTION

IN THEIN THEH /H / αα PLANEPLANE

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Alp

ha( α

)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

C1

C2

C3

C4

C5

C6

C7

C8

10n

00.20.40.60.8

11.21.41.61.8

2

LOW H MEDIUM H HIGH H

SURFACESCATTERING

VOLUMESCATTERING

MULTIPLESCATTERING


Alp

ha( α

)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

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Alp

ha (

α)

0

30

60

90

0 0

0.50.5

11

POLSAR DATA DISTRIBUTION IN THE H / A / α SPACE


Anisotropy (A) Entropy (H)

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0A2 BB0 + BB0 −

H / A / H / A / αα DECOMPOSITION DECOMPOSITION H - α classification

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332211 PPP αααα ++=

ENTROPY

)P(logPH3

1ii3i∑

=

−=

3 ROLL INVARIANT PARAMETERS

ANISOTROPY

32

32Aλλλλ

+−

=

α PARAMETER

( )( )

( )( )⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−

−=

AHAH

AHAH

I

111

1

α PHYSICAL SCATTERING MECHANISM

TYPE OF SCATTERING PROCESS

SEGMENTATION / CLASSIFICATION


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Polarimetric Analysis of Radar Signature ofa Manmade Structure

J.S. Lee, T. Ainsworth,NRL, Washington DC 20375, USA

Ernst Krogager, Danish Defence Research Establishment, Copenhagen,

Denmark

Wolfgang-Martin Boerner University of Illinois at Chicago, IL, USA

IGARSS 2006, Denver, Cororado, 2006

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Pauli Vector, |HH-VV|, |HV|, |HH+VV|

Polarimetric SAR Image

EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge

RAN

GE

FLIGHT

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Store Bridge Signature during Construction

|HH|

(A) |HH| image(B) |HV| image(C) |VV| image

Flight Direction

|HV|

|VV|

3

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Surface and Double Bounce Scatterings

Surface (Bragg) scatteringHH and VV are in phase

Realiter, phase difference of Bragg scattering, albeit small, is a function of incidence angle & dielectric constant.

Dihedral scattering HH and VV is 180° out of phase

Two perpendicular conducting plates

1

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Multi- Bounce Scattering

1 32

d

SingleDouble

Triple

Roundtrip distances:Single bounce return: Double bounce return:Triple bounce return:

θ is the local incidence angle.

)cos(2 θ− dL2L

)cos(2 θ+ dL

L

2

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High-resolution POLSAR signature of a suspension bridge under construction -the deck was not installed.

Pauli Decomposition, |HH-VV|, |HV|, |HH+VV|

Aerial PhotoKrogager SDH Decomposition

• Blue= Sphere Green = Helix Red = Diplane.

RAN

GE

FLIGHT

Polarimetric Target Decomposition

EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge4

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Bridge under construction - deck not installed.

Aerial Photo Dominant scattering mechanisms are extracted by applyingtarget decomposition:

Blue= Surface Green = Dipole Red = Double Bounce.

Cloude and Pottier Decomposition

EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge

Direct bounce from cables

Triple bounce from cables

Double bounce from cables

HEntropy

αAlphaAngle(Rotational invariant)

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BRIDGE RADAR SIGNATURES

(EMISAR C- Band)

|HH+VV|

|HH-VV|

|HV|

After Completion of Bridge Construction

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

RAN

GE

FLIGHT

Polarimetric Target Decomposition – After Completion

SDH

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Entropy

Dominant scattering mechanisms are extracted by applying target decomposition: Blue= Surface Green = Dipole Red = Double Bounce.

Cloude and Pottier Decomposition – After Completion

Angle α

6

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Dominant scattering mechanisms are extracted by applying target decomposition: Blue= Surface Green = Dipole Red = Double Bounce.

Higher Order Multiple Bounces – After Completion

αAlpha

Roundtrip distances:

A: Triple bounces,

B: 5 (or 7) bounces,

C: 7 (or 9) bounces,

D: 9 (or 11) bounces,(…) indicates additional two bounces from the bottom of the deck.

ddL 2)cos(2 ++ θ

)cos(2 θ+ dL

ddL 4)cos(2 ++ θ

ddL 6)cos(2 ++ θ

7

6c

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BRIDGE AND BUOY RADAR SIGNATURES

Polarimetric SAR Image ( |HH-VV|, |HV|, |HH+VV| )

Navigation Map of Storebelt, Denmark

(EMISAR C- Band)

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The Combination of Polarimetry and InterferometrySAR InterferometrySAR Polarimetry

Sensitive to scatterersshape, orientation and dielectric properties

Allows decomposition of different scattering processes

occurring inside the resolution cell

Established technique for terrain topography estimation

allows Location of scattering centers

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

Phase sensitivity

Central Part: Coherence

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Correlation:

Co-pol correlation provides a method to detect depolarization.

If the scattering is dominated by surface scattering, one wouldexpect high correlation and a phase difference approaching 0º.

In contrast, when depolarization occurs, due to volumescattering, for example, the correlation approaches zero and there is a poorly defined phase difference.

http://www.radrsat2.info/polarimetry/rs2_pol_info.asp

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Depolarization

Occurs when the polarization state changes between the transmitted & receivedsignal (changing a HH to a HV response). There are four mechanisms known to cause depolarization:

quasi-specular reflection as a result of the difference between the Fresnelreflection coefficients for a two-dimensional, smoothly undulating surfacemulti-scattering due to target surface roughnessmultiple scattering due to volume scatteringanisotropic properties of the targets

The first three depolarization mechanisms are commonly encounteredin remote sensing applications:

the first mechanism applies only to smoothly undulating surfaceThe third mechanism produces stronger returns than the first and second The fourth mechanism, mainly, is a function of target geometry

http://www.radrsat2.info/polarimetry/rs2_pol_info.asp

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The Combination of Polarimetry and InterferometrySAR InterferometrySAR Polarimetry

Sensitive to scatterersshape, orientation and dielectric properties

Allows decomposition of different scattering processes

occurring inside the resolution cell

Established technique for terrain topography estimation

allows Location of scattering centers

inside the resolution cell

Polarimetric SAR InterferometryPotential to separate in height different scattering processes

occuring inside the resolution cell.


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

Phase sensitivity

Central Part: Coherence

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Combination of Polarimetry and Interferometry

SAR Polarimetry (PolSAR) SAR Interferometry (InSAR)Allows decomposition of different

scattering processes inside resolution cell Allows location of the effective

scattering center inside resolution cell

Polarimetric SAR Interferometry (Pol-InSAR)

Potential to separate in height different scattering processes occurring inside the resolution cell.


Allows the investigation of 3D structure of volume scatterers

InSAR DEMSAR ImagePauli Decomposition RGB

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Coherence Optimisation ExampleTwo Pass Interferometry, L-Band, Δt ~ 10 min, B = 20m, E-SAR

a. HH, Coherence b. 1st Optimisation c. 2nd Optimisation

a. Low coherence for low S/N & volume decorrelation in forest areas, echoes originating from different heights in the forest structure during different flight passes

b. Highest optimisation, interactions with the forest floor are emphasised by the process.

c. lowest optimised coherence optimisation process selects the returns from canopywithin the forest. Joint use of b. & c. allows forest hight estimation

D. G. Corr: Potential of Radar Polarimetry

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L-Band, SIR-C, Siberian Forest, Digital Elevation Image with cuts, Two Pass and Differential POLINT

Documents

8. Grundlagen der SAR Polarimetrie - Pixelplaatkeydel.pixelplaat.de/uploads/File/erlangen 07-08/Polarimetry.pdf · Quellenangabe Institut für Hochfrequenztechnk und Radar W. Keydel,