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Basics of Radar Polarimetry

Wolfgang Keydel

Vorlesung Erlangen

Literatur: Martin Hellmann, SAR Polarimetry, Tutorial http://epsilon.nought.deKeydel, W. (Editor) Radar Polarimetry and Interferometry; Lecture Series RTO-EN-SET-081Radar Interferometry and Polarimetryhttp://ftp.rta.nato.int/public//PubFullText/RTO/EN/RTO-EN-SET-081///EN-SET-081-$$TOC.pdf

Alle Kapitel als Downloads: http://www.rto.nato.int/pubs/rdp.asp?RDP=RTO-EN-SET-081

http://epsilon.nought.de/

http://ftp.rta.nato.int/public//PubFullText/RTO/EN/RTO-EN-SET-081///EN-SET-081-$$TOC.pdf

http://www.rto.nato.int/pubs/rdp.asp?RDP=RTO-EN-SET-081

2Microwaves and Radar Institute, Wolfgang Keydel

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: = =CE t E t

E t E t E t E t

( ( ) ( ))

( ) ( ) ( ) ( )

*

* *

1 2

1 1 2 2

= 0 means incoherence, = 1 complete coherence

Continous transition from pure coherence to pure incoherence

Incoherent: Phases random & (directly or in effect) uniformly distributed

0 ≤ ≤ 2π.

Coherent: phase relations between waves are constant

0 ≤ ≤ 1

-1 ≤ C ≤ +1Correlation


Polarisation Ellipse & Spatial Helixdecomposed

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

Courtesy Shane Cloude


Polarisation Ellipse & Spatial Helixdecomposed

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


Ausbreitung des Wellenvektors

Drehsinnbetrachtung

in Ausbreitungsrichtung

rechts

links

z

x

http://upload.wikimedia.org/wikipedia/de/4/41/Rising_circular.gif


EY

EX

Polarisation: Vektor Nature of Electromagnetic Waves

vertikal

horizontal

EY

EX

z

z

http://upload.wikimedia.org/wikipedia/commons/e/e5/Interne_Reflexion_%28Schema%29.svg


Polarization Ellipse

χ = Ellipticity Angle: 0 ≤ χ ≤ π/4

Ψ= Orientation Angle: - π/2 ≤ ψ ≤ π/2

cos)2tan()2tan(andsin2sin2sin

a

a)tan(andcos

EE

EE2)2tan( 02

0y2

0x

0x0y

withsincosEE

EE2

E

E

E

Eyx000

0x0y

xy

2

0x

x

2

0y

y

y

jjkz0y

jkzyy eee)z(Ee)z(E)z(E y

xjjkz

0xjkz

xx eee)z(Ee)z(E)z(E x

yyxx e)z(Ee)z(E)z(E

ξ

χ

Ψ x

y

majoraxis

minor axis

η

αa ξ

aη

E

EX0

EY0


x

χ

Ψ

y

x

η

Ψ

χ = 45°

x

y

Ψ

χ = 0°

y

Orthogonal Polarizations

Elliptical Circular Linear

Polarization Ratio:

For each Polarization State ρ exists an orthogonal Polarization State ρorth

)2cos()2cos(1

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

E

E )(j

xO

yOyx

1*orth


POLARIMETRIC DESCRIPTORSPOLARIMETRIC DESCRIPTORS

DIFFERENTTARGET POLARIMETRIC

DESCRIPTORS

X

Y

TRANSMITTER: X & YRECEIVER: X & Y

Courtesy Eric Poitier

Examples:k Target VectorE Jones Vektorg Stokes Vector[S] Streu -Matrix[K] Müller-Matrix

(KENNAUGH)[T] Coherency Matrix[C] Covariance Matrix


Jones Vector for completely polarized Waves

yyxx e)z(Ee)z(E)z(E

Containes complete information about the Polarization Ellipse, except handleness.

Two plane waves propagating in opposite directiond have the same Jones Vector representation

Subscripts „+“ & „-“ compensate this lack using direction of Propagation Vektor k

Using the Polarisation Ratio the Jones Vector can be written as

1E

E

EE x

y

x

xy

sin

cos

cossin

sincos0

00

0

jeE

eE

eE

E

EE j

j

y

jx

y

x

y

x


Different Polarization States

Courtesy Eric Pottier

x x

xx

y

yy

y

12Microwaves and Radar Institute, Wolfgang KeydelCourtesy Eric Poitier

x x

xx

y

y y

y

Jones Vector Descriptions for Characteristic Polarization States Propagation

Direction out of Page


Change of Polarization Basis

0for

newbasistheofvectorstheareUofcolumnsThe

e,eande,e:basesonpolarizatilorthonormaTwo

1Y

y2y1x2x1

eEeEeEeEE:Field-E y2y2y1y1x2x2x1x1

1

1

1

1U

x

*x

*xx

ee

ee

1

1U

jjx

j*x

j

*xx

1Y1Y

1Y1Y

e,e y2y1

1

ρ

ρρ1

1eeand

ρ

1

ρρ1

1ee

*x

*xx

jy2

x*xx

jy1

Y2Y1

:e,ebasis-YforrsBasisvecto y2y1

e,ebasis-Xforratioonpolarizatiingcorrespondρ x2x1x

EUE

UMatrixvia 2x2EEvectorcomplexElement2oftionTransforma

2x,1x2y,1y

2y,1y2x,1x

E

EEand

E

EE:VectorsonesJ

2y

1y

2y,1y

2x

1x

2x,1x


The Stokes Vector

;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 23

22

21

20

>

Completely polarized waves:

sin2

cos2

)Im(2

Re2)(

00

00

2

0

2

0

2

0

2

0

*

*

22

22

3

2

1

0

yx

yx

yx

hv

yx

hx

yx

yx

EE

EE

EE

EE

EE

EE

EE

EE

g

g

g

g

Eg

)2sin(g

)2cos()2sin(g

)2cos()2cos(g

g

g

0

0

0

0


Stokes Vektor Decomposition

Degree of Polarization:o

23

22

21

g

gggp

Decomposition into completly polarized & unpolarized Component

21

21

21

20 gggg General Case:

0

0

0

p1

g

g

g

g

3

2

1

0

)2sin(p

)2cos()2sin(p

)2cos()2cos(p

p

g0

g

All 4 Parameter derivable from intensity measurements

Orthogonal Polarization States located on diametrally oppositepositions on the Poincaré Sphere


Poincare Sphere

http://www.wave.ie.niigata-u.ac.jp/pol/pol_07.html

http://www.wave.ie.niigata-u.ac.jp/pol/pol_09.html


X

Y

T

RX

AX

RY

AY

YY

XY

YX

XX

S

S

S

SS

YXS

XXS

YYS

XYS

YXS

XXS

YYS

XYS

X Y X Y

T

RX

RY

SINCLAIR MATRICES

SCATTERING POLARIMETRY

SCATTERING POLARIMETRYSCATTERING POLARIMETRY

TRANSMITTER: X & YRECEIVERS: X & Y


Radar Polarimetry

Full utilization of the vector nature of Electromagnetic Waves

via

Orientation of the Electric Vector in anElectro Scattering Matrix

EHr

EVr S

EHt

EVt

EHt

EVt

SHH SHVSVH SVV

Monostatic Radar Case: SHV= SVH

Relative Scattering Matrix

5 independent Parameter

4 complex coeffizients, 8 independent Parameter

Si, k

i ke

ji k

,

, ,=

0

… α = jk +E e-j(ωt +φ)kre -αr

E0

Radar Equation


EMW Reflection

ISHHI ≥ ISHVI

ISVVI ≥ ISVHI

<Re(S*HHSVV)> ≥ < ISHVI2 >

Phase (S*HHSVV) ≈ 0

OddReflections

•

ISHHI ≥ ISHVI

ISVVI ≥ ISVHI

<Re(S*HHSVV)> ≥ < ISHVI2 >

Phase (S*HHSVV) ≈

•

•

EvenReflections


Eigenschaften Streumatrix

|SHH |

|SHH |

|SHV |

|SHH |2

|SHH |2

|SHV |2 |φHV |

|φVV |

SHH SHVSVH SVV

Elemente

Invariante

1 0

0 2

Spur [S(HV)] = |SHH |2 +2 |SHV |2+ |SVV |2 = |1|2 + |2|

2

| Det [S(HV)] | = |SHHSVV – SHV2| = | 1 2 |

Si, k

i ke

ji k

,

, ,=

0


BasismatrizenEine generische Matrix ist in Basismatrizen zerlegbar;

a S S b S S c S SHH VV HH VV HV VH ; ;

a b S a b SHH VV ;

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

SS S

S S

HH HV

VH VV

a b c

c a ba b c

1 0

0 1

1 0

0 1

0 1

1 0

Pauli Matrizen


Depolarization Scheme


Pauli Matrices

2

2

line

sin2sin2

1

2sin2

1cos

S

Sphere Statisical Volume

01

10Sdiff

,

10

01S

odd

Wire

cos2αsin2α

sin2αcos2αS

even

Diplane

1j

j1e

2

1S 2j

helix

Helix


Pauli Matrices

RoughSurfacePlate,

Sphere, Dihedral;

TiltedDihedral;

Vegetation

01

10Sdiff

,

10

01S

odd

cos2αsin2α

sin2αcos2αS

even

Single Bounce,odd

Double Bounce,even

Volume Scattering,diffuse

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

α


01

10S,

cos2αsin2α

sin2αcos2αS,

10

01S dfiffus21


Dihedral with 45-degree tilt

Even-bounce, π/4-TiltDihedral

DihedralEven-bounce

Surface, sphere,Corner reflectors

Odd-bounce

Scatteringmechanism

Scattering typePauli matrix

1 0

0 1

1 0

0 1

0 1

1 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


Transformation from linear to circular Basis

VVHHRL

VVHHHVLL

VVHHHVRR

SS2

j´S

SS2

1jSS

SS2

1jSS

Circular Basis Radar Responses

NOYESNOLeft Helix

NONOYESRight Helix

NOYESYESDiplane

YESNONOSphere

LRRRLL

Microwaves and Radar Institute, Wolfgang Keydel

HERMITIAN MATRIX - RANK 1

COHERENCY MATRIXCOHERENCY MATRIX

TXYYYXXYYXX S2SSSS2

1k

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

MONOSTATIC CASE

COHERENCY MATRIX [T]

PAULI SCATTERING VECTOR k

[T] is closer related to Physical and Geometrical Properties of the Scattering

Process, and thus allows a better and direct physical interpretationCourtesy Eric Poitier

BBjFEjGH

jFEBBjDC

jGHjDCA2

kkT

0

0

0T*

Microwaves and Radar Institute, Wolfgang Keydel

PHYSICAL INTERPRETATION

SINGLE (odd) BOUNCESCATTERING

(ROUGH SURFACE)

DOUBLE (even) BOUNCESCATTERING

VOLUMESCATTERING

TARGET GENERATORSTARGET GENERATORS

Courtesy Eric Poitier

2

YYXX011 SSA2T

2

YYXX022 SSBBT

2

XY033 S2BBT


Coherence & Covariance Matrices

CoherenceMatrix

CovarianceMatrix C k k

S S S S S S S

S S S S S S S

S S S S S S S

S S S S S S S

S S

T

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

* * *

* * *

* * *

* * *

2

2

2

2

k S S S Ss HH VV HV VH; ; ;

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

*

* *

* *

* *

; ;

1

2

2

2

2

2

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


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

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

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

& γ : Phasenwinkel

Mittlerer - Winkel:

n nn 1

3

2 3

Entropie:

n nn

H 31

3

log

Anisotropie A 2 3:

T T e e e e

e

nn

n nn

n n

T

n

n

n nj n

n nj n

1

3

1

3

;

cos

sin cos

sin sin

mit


Normalized Polarimetric Entropy, H ; Diversity of scattering mechanisms

H = -Σiλilog3 λi ….i = 1…3

mean α related to „Form“ scattering mechanismα = -Σiλi αi

simple

single (odd)bounce

Plate,Sphere

double (even)bounce

Diplane

multiple bounce

random

10H

α

45°0° 90°

anisotropic odd anisotropic even

isotropic evenisotropic odd Dipol


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 (odd) bounce: α = 0; Diffuse scattering: α = 45; Double (even) bounce: α = 90°

Polarimetric Entropy:

i ii

H 31

3

log

- Angle:

n nn 1

3Mean

Anisotropy A 2 3:


Measure for a targets homogeneity relative to the radar look direction.

Example: Amazon forest is a very homogeneous target ===> low anisotropy.

In contrast: row crops ===> high anisotrophy value.

Anisotropy A 2 3:

0 ≤ H ≤ 1Measure of the dominance of a given scattering mechanism within a resolution cell related

to amount of effective scattering mechanisms, normalized between 0 and 1.

H = 0: all scattering results from one mechanism (single bounce, double bounce),

H = 1 completely random scattering mechanisms ore 3 mechnisms of equal power resp.

Entropie:

n nn

H 31

3log


DIFFICULT MECHANISM DISCRIMINATION WHEN : H > 0.7

ANISOTROPY(EIGENVALUES SPECTRUM)

32

32A

COMPLEMENTARY TO ENTROPY

DISCRIMINATION WHEN H > 0.7

ROLL INVARIANT

H / A /H / A / aa DECOMPOSITIONDECOMPOSITION


H

C1 Urban -dihedral C4 Forestry C7 Forestry crown

C2 Dipolevolumetric scatterg

C5 Vegetation C8 Vegetation

C3 Surfacescattering

C6 Rough surfaceand vegetation

Single mechanism Two mechanisms Three mechanisms

Double bounce

Volumescattering

Surfacescattering

Not feasible

Scattering characteristics of regions in H-α plane

C8 Vegetation

C1 Urban dihedral

C2 Dipole volumetric scattering

C3 Surface scattering

C4 Forestry

C5 Vegetation

C6 Rough surface & vegetation

C7 Forestry crown

α°

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90


Comparision of unsuperwised classifications over a cultural & forested region

Left: Scattering vector. Right: Scattering mechanisms (H – α)

C8 Vegetation

C1 Urban dihedral

C2 Dipole volumetric scattering

C3 Surface scattering

C4 Forestry

C5 Vegetation

C6 Rough surface & vegetation

C7 Forestry crown


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)


The Combination of Polarimetry and Interferometry

SAR InterferometrySAR Polarimetry

Sensitive to scatterersshape, orientation and dielectric properties

Allows decomposition of differentscattering processes

occurring inside the resolution cell

Established technique forterrain topography estimation

allowsLocation of scattering centers

inside the resolution cell

Polarimetric SAR Interferometry

Potential to separate in height different scattering processesoccuring 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


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

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