SAR Polarimetrie und Pol-SAR-Interferometrie: Theorie und ... · Short History of Radar...

1

Folie [email protected] - 05.02.2007

Arbeitsgruppe Pol-InSARIrena Hajnsek, Kostas Papathanssiou, Helmut Schön, Raffael Zandona Schneider, Luca Marotti, Florian Kugler, Jayanti Sharma, Seungkuk Lee, Thomas Jagdhuber, Angelo Coscia

Microwaves and Radar InstituteGerman Aerospace Center

HH HV

VH VV

SAR Polarimetrie und Pol-SAR-Interferometrie: Theorie und Praxis in der Radarfernerkundung

Folie 2Microwaves and Radar Institute

Overview of the Lecture

Part 1Short introduction into SAR

Part 2Basics and principles of SAR polarimetryMain applications of SAR polarimetry

Part 3Basics and principles of SAR interferometryDerivation of forest heights

Every part will be illustrated with examples and exercises using PolSARPro !

2


SAR

Part 1:

Short introduction into SAR


Electromagnetic Spectrum including the attenuation caused by water vapor in the atmosphere

Electromagnetic Spectrum

3


Radar vs Optic‘s of Oberpfaffenhofen


Range distance ro

object

oc (velocity of light)

Tx

Rx

transmit

t (time)

Total time delay =o

o

cr . 2

• Received echo signal (back-scattered signal of imaged object):

receive

Radar Measurement Principle

4


Transmitter

Receiver

Antenna

Circulator

Data Recording

Radar Pulse

• Transmitter generates a high power pulse• Circulator or Switch - switches transmitted pulse to antenna,

returned echoes to receiver• Antenna directs transmitted pulses towards the target area• Receiver amplifies the received signal and converts to base band

• Transmitter generates a high power pulse• Circulator or Switch - switches transmitted pulse to antenna,

returned echoes to receiver• Antenna directs transmitted pulses towards the target area• Receiver amplifies the received signal and converts to base band

Basic Radar Block Diagram


• Pulsed radar system

• Two-dimensional imaging (azimuth x slant range)

Side-Looking Imaging Geometry

yx

Swath

Azimuth

Range

z

Illuminated area

Antenna

Tx TxRx Rx

T = 1/PRF

τ

PRF = Pulse Repetition Frequency

τ• Timing of the Radar:

5


• Radar reflectivity (backscattered signal) of the target as a function of position.

• radar transmits a pulse (travelling velocity is equal to velocity of light)

• some of the energy in the radar pulse is reflected back towards the radar.

This is what the radar measures.

It is known as radar backscatter σo(sigma nought or sigma zero).

What does the Radar measure ?


E-SAR X-band Real-time Image, 3 x 3 m Resolution, 6 Looks

Single Channel Radar Image

6


X-Band SAR Image of Munich

E-SAR, Test Site Munich - 1m x 2m resolution


• Normalized radar cross-section (backscattering coefficient) is given by:

σo (dB) = 10. Log10 (energy ratio)

whereby

received energy by the sensor“energy reflected in an isotropic way”

energy ratio =

i.e. The backscattered coefficient can be a positive number if there is a focussing of backscattered energy towards the radar

orThe backscattered coefficient can be a negative number if there is a focussing of backscattered energy way from the radar (e.g. smooth surface)

What does the Radar measure ?

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Backscattering Coefficient σo

Levels of Radar backscatter Typical scenario

• Very high backscatter (above -5 dB) Man-Made objects (urban)Terrain Slopes towards radarvery rough surfaceradar looking very steep

• High backscatter (-10 dB to 0 dB) rough surfacedense vegetation (forest)

• Moderate backscatter (-20 to -10 dB) medium level of vegetationagricultural cropsmoderately rough surfaces

• Low backscatter (below -20 dB) smooth surface calm water, roadvery dry terrain (sand)


Polarimetric

SAR

Polarimetric SAR

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Scattering PolarimetryWave Polarimetry

• Polarisation Ellipse

• Stoke Vector

• Jones Vector

• Polarisation State

• Scattering Matrix andMeasurements

• Backscattering Vector

• Backscattering Matrices

• Interpretation of ScatteringMechanisms

Decomposition Theorems

HistoricalIntroduction

• Pauli Matrice Decomp.

• Sphere-Diplane-HelixDecomp.

• Model Based Decomp.

• Eigenvector Decomp.

Part 2


Part 2

Application of Polarimetric Radar Remote Sensing

• Terrain correction for quantitative surface parameter inversion

• Segmentation / Classifications (Agricultural Area, Urban Area,Sea Ice, Forestry, Oceanography)

• Modeling and Inversion of Surface Parameters


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Surface Roughness

Soil MoistureScattering Amplitudes

Vegetation BiomassAmplitude ratios

Surface SlopesRelative Phase Angles

Vegetation HeightPolarimetric Coherence

Tree Species

Snow Hydrology

Ice Thickness

Physical Parameters

Motivation for Radar Polarimetry in Remote Sensing

Radar Parameters


Single Polarised versus Quad-Polarised- Adding Information

L-HH L-Band R=HH-VV G=2HV B=HH+VV

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Lexicographic Image @ C-band

Folie 20Microwaves and Radar InstituteRed=HH-VV, Green= 2HV, Blue=HH+VV

ESAR / Alling, Germany L-band

March July

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Folie 21Microwaves and Radar InstituteRed=HH-VV, Green= 2HV, Blue=HH+VV

Dresden, Germany / HH Polarisation

ESAR / L-band


Scattering Classification Freeman/Durden & Wishart Segmentation

ESAR / L-band

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SVALEX 2005 SVALBARD - Norway Sea Ice @ L-band

Lexicographic-RGB Image @ L-band Red=HH, Green= HV, Blue=VV)


Test Area Plaatgat (Dutch Plaatgat) 2002

10 km

Ameland

Schiermonnikoogisland

SchiermonnikoogIsland

Pauli-RGB Image @ L-band Red=HH-VV, Green= 2HV, Blue=HH+VV

Ocean Topography

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Soil

Moisture [mv]Dielectric Constant0

80

Soil Moisture Estimation Results: AQUIFEREX Campaign (Tunesia) Nov. 2005

0

90

ESAR / L-band


What does polarisation means ?

For all vector waves polarisation refers to thebehaviour in time of the wave field vectors

observed at a fixed point in space. (AZZAM & BASHARA)

Direction of Wave Propagation ---> kDirection of Wave Propagation ---> k

Elliptical Polarisation Linear Polarisation

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Short History of Radar Polarisation Part I

Before the definition of the polarisation different polarisation effects has been observed in nature:

1. The Vikings (800 b.c.) used a dichromic mineral to navigate in the absence of light, so that the diffuse light could be bundled to determine the position of light

2. The first discovery of polarised light has been made by Christian Hygens(1677) and Erasmus Bertolinus (1669) looking through a crystal doublet, where the incident light has been split into ordinary and extraordinary rays;

3. Malus (1808) could prove that polarisation is a intrinsic property and not something added by a crystal

A transition from the early discovery of polarisation to the present-day has been made by introducing the Theory of Electromagnetism. In this domain numerous names can be added – Amper, Faraday, Stokes etc.

Finally, Maxwell tied the previous work together with a consistent formulation to the laws of macroscopic electromagnetics.


G. Sinclair (1950)

Radar Polarisation

G.A. DESCHAMPS(1952)

J.R. HUYNEN(1960)

E. M. KENNAUGH(1951)

W.M. BOERNER(1970)

Optimal polarisation for radar target detection

Geomteric presentation of the Stokes parameters -

Poincare Sphere

First Target Decomposition Theorems

Distribution of multi-polarimetry and multi-

frequency for Application

Short History of Radar Polarisation Part IIThe first use of radio and microwave frequencies started in the 1930s and advanced considerably in the second world war. The first radars typically received a signal of the same polarisation and had no full polarisation capability.

The radar target acts as a polarisation transformer and expressed the properties of a coherent target by a 2x2 scattering matrix.

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• Polarisation Ellipse

• Stokes Vector (real wave descriptor)

• Jones Vector (complex wave descriptor)

• Polarisation state in the real and complexdomain

Wave

Polarimetry

Wave Polarimetry


Plane Waves

Wave equation: 0rEt

rE 2

2

002 =

∂∂

+ )()( rrrr μμεεωΔ

)exp()( rkiErE rrrrr ⋅=

Linear, source-free, homogeneous, isotropic media:

)()(),( trkftrkftr ωωΨ +⋅+−⋅= −+

rrrrr

Er

… complex constant amplitude vector

Real electric field vector: })trk(iexpERe{})texp()r(ERe{)t,r(E ωω −⋅=−=rrrrrr

Complex electric field vector:

Constant phase front of : Plane orthogonal to !!!),( trE rr →=⋅→ .constrk rrkr

kr

… wave vector μμεεω 00k =||r

Solutions:

Light waves are electromagentic in nature, where the electric component is used to describe the polarisation state

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Wave Polarisation

)exp( hhh iaEhE δ=⋅=rr

)exp( vvv iaEvE δ=⋅=rr

)cos()}(expRe{)}(expRe{),( hhhhhh atrkiatrkiEtrE δτδωω +=+−⋅=−⋅= rrrrr

trk ωτ −⋅= rr)cos()}(expRe{)}(expRe{),( vvvvvv atrkiatrkiEtrE δτδωω +=+−⋅=−⋅= rrrrr

Real field representation:

Complex field representation:

Plane Wave Propagating in the kr

+ direction

Right Handed Orthonormal K.S. )( hvkrrr

vh EvEhEvvEhhE rrrrrrrrr+=⋅+⋅= )()(

),(),(),( trEvtrEhtrE vhrrrrrr +=

|| vv Ea =

|| hh Ea =

Real Amplitudes

Real Amplitudes

Planewave

Phase difference

Direction Projection (length of the vector)

The definition of polarisation requires a reference coordinate system and a directionof propagation


Polarisation Ellipse

)cos(),( hhh atrE δτ +=r

hv δδδ −=

Electric Field Vector:

and where

The field-vector moves in time along an ellipse known as the polarisation ellipse),( trE rr

General representation of a rotated ellipse !!!

)cos(),( vvv atrE δτ +=r

),(),(),( trEvtrEhtrE vhrrrrrr +=

0aaa1aa

aaa12

vh

2

2vvh

vh2h ≥=

−−

)(sin

/)/(cos)/(cos/

det δδ

δ

δδ 2

vh

vh2

v

2v

2h

2h

aatrEtrE2

atrE

atrE sin),(),(cos),(),(

=−+rrrr

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Polarisation EllipseThe shape of the polarisation ellipse describes the polarisation state of the plane wave:

Orientation angle ψ : Major Axis Inclination Angle

Ellipticity angle χ : ±=χtan Minor Ellipse AxisMajor Ellipse Axis

Polarisation AnglesDeschamps Parameters

⎟⎟⎠

⎞⎜⎜⎝

⎛=

h

v

aaa arctan

hv δδδ −=

22πψπ

≤≤−44πχπ

≤≤−Range: and

Phasedifference:

Amplitude:


Polarisation Ellipse

Orientation angle ψ :

Ellipticity angle χ :

Horizontal Vertical Linear at θº Left Circular Right Circular

0º 90º θº -90º - 90º -90º - 90º

0º 0º 0º -45º 45º

Elliptical Circular Linear

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Wave Polarisation and Polarisation Ellipse

Direction of Wave Propagation ---> k

Elliptical Polarisation

Circular Polarisation

Linear Polarisation

Linear Polarisation

h

v

h

v

h

v

h

v


Orthogonal Polarisation States

Horizontal and Vertical

Left Elliptical and Right Elliptical Left Circular and Right Circular

Linear at y and Linear at y + π/2

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Polarisation HandednessThe rotation sense is defined by looking into the direction of wave propagation:

Left Handed Rotation

Ellipticity angle χ < 0

Right Handed Rotation

Change of propagation direction implies a permutation of polarisation handedness !

Ellipticity angle χ > 0

Deschamps angle δ > 0 Deschamps angle δ < 0

… clockwise in propagation direction… anti-clockwise in propagation direction

IPU Convention:


Polarisation Handedness

“…Circularly polarized waves have either a right-handed or left –handed sense, which is defined by convention. The TELSTAR satellite sent out circularly polarized microwaves. When it first passed over the Atlantic,

the British station at Goonhilly and the French station at PleumeurBodou both tried to receive its signals. The French succeeded because

their definition of polarization agreed with the American definition. The British station was set up to receive the wrong (orthogonal) polarisationbecause their definition of sense…was contrary to ‘our’ definition…”

from J R Pierce “Almost Everything about Waves”, Cambridge MA, MIT Press, 1974, pp 130-131

“…Circularly polarized waves have either a right-handed or left –handed sense, which is defined by convention. The TELSTAR satellite sent out circularly polarized microwaves. When it first passed over the Atlantic,

the British station at Goonhilly and the French station at PleumeurBodou both tried to receive its signals. The French succeeded because

their definition of polarization agreed with the American definition. The British station was set up to receive the wrong (orthogonal) polarisationbecause their definition of sense…was contrary to ‘our’ definition…”

from J R Pierce “Almost Everything about Waves”, Cambridge MA, MIT Press, 1974, pp 130-131

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Wave Description

Monochromatic Plane Waves are completely described by four parameters:

- Two parameters for the description of the polarisation state of the wave

- The wave amplitude or the wave intensity

- A initial absolute phase reference


Stokes Vector for Monochromatic Waves

4

vh

vh

2v

2h

2v

2h

3

2

1

0

R

EE2EE2EEEE

qqqq

q ∈

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−+

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

∗

∗

}Im{}Re{||||||||

:r

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡++

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

δδ

δ

sincos

),,(

vh

vh

2v

2h

2v

2h

3

2

1

0

vh

aa2aa2

aaaa

qqqq

aaqr

23

22

21

20 qqqq ++=

3210 qqqq ,,, are wave intensities:

0q total wave intensity321 qqq ,, polarised wave intensity

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

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

),,(

χχψχψ

χψ

2a22a22a

a

qqqq

aq

2

2

2

2

3

2

1

0

r

Only three from the four Stokes elements are independent:

Stokes Vector:

Wave polarisation state estimation via intensities measurements only !!!

The total wave energy is polarised

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Poincaré Sphere

23

22

21

20 qqqq ++=

North Pole: Right Circular Polarisation

South Pole: Left Circular Polarisation

Southern Hemisphere: Left Handed Polarisations

Northern Hemisphere: Right Handed Polarisations

Aquator: Linear Polarisations

321 qqq ,, : Cartesian coordinates of a point on a sphere with radius 0q

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

3

2

1

0

qqqq

q :rStokes Vector: with Equation of Sphere in R3

Poincaré Sphere:


Jones Vector

vh EvEhEvvEhhE rrrrrrrrr+=⋅+⋅= )()(

2vv

hh

v

h Ciaia

EE

E ∈⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

)exp()exp(

δδr

nnmmnnmm EEEEE εεεεεε rrrrrrrrr+=⋅+⋅= )()(

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

)exp()exp(

nn

mm

n

m

iaia

EE

Eδδr

vh EE , are the complex projections onto vh rr,

Jones vector:

Jones vector:

nm EE , are the complex projections onto nm εε rr ,

The description may be considered as a component representation in the 2-dim complex vector space with basis },{ vh rr

referred to the orthonormal basis},{ nm εε rr

Generalisation: Projection of onto two arbitrary orthonormal polarisation states nm εε rr ,Er

The is represented as a linear combination of two orthogonal linear polarisation h and v.Er

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Jones Vector

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ −−=⎥

⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

χχ

ψψψψ

φδδ

sincos

cossinsincos

)exp()exp()exp(

iiA

iaia

EE

E 0nn

mm

n

mrJones vector:

Thus, it describes completely the shape of the polarisation ellipse, the sense of rotation of the field vector and the wave intensity. But, it contains not the information about the direction of wave propagation and so about the polarisation handedness of the wave.

The Jones vector contains four parameters in terms of 2 complex scalars:

f( Polarisation Angles )f(Deschamps Parameters)

Important: The wave is a vector function with a physical meaning independently of any reference frame. But its representation depends on the chosen reference basis.

Wave intensity:= 2n

2m EEEE |||| +=⋅+

rr


Directional Jones Vector

)}(expRe{),( trkiEtrE ω−⋅+= ++

rrrrr)}(expRe{),( trkiEtrE ω−⋅−= −−

rrrrr

∗± = m

rrEETime reversal = Complex conjugation:

Plane Wave Propagating in the kr

− directionPlane Wave Propagating in the kr

+ direction

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

)exp()exp(

vv

hh

v

h

iaia

EE

Eδδr

Jones vector: ⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

)exp()exp(

vv

hh

v

h

iaia

EE

Eδδr

Jones vector:

Directional Jones vector (IPU Convention):

The Jones vector is insufficient to describe the direction of wave propagation !!!

and

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Complex Polarisation Ratio

Ciaiaa

EE

mnm

n

m

n ∈=−== )exp(tan)(exp: δδδρ

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

χψχχψχψρ

212i22

++

=⎟⎠

⎞⎜⎝

⎛−

= ∗ρρρρψ

12

21 }Re{arctan)(

⎟⎠

⎞⎜⎝

⎛−

= ∗ρρρρχ

12

21 }Im{arcsin)(

2n

m CEE

E ∈⎥⎦

⎤⎢⎣

⎡=

r

Jones vector:

Complex Polarisation Ratio:

where is a linear reference basis},{ nm εε rr

Complex Space Polarisation Description Real Space Polarisation Description


Complex Polarisation Ratio: Geometrical Interpretation

)cos()cos()sin()cos()sin()(exp:

χψχχψδδρ

212i22i

aa

EE

mnm

n

m

n

++

=−==

Right Circular Polarisation

Positive Imaginary Part: Right Handed Polarisations

Real Axis: Linear Polarisations:

Negative Imaginary Part: Left Handed Polarisations

Left Circular Polarisation

i=:ρ

i−=:ρ

1

1−

Complex Polarisation Ratio:

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Partially Polarised Waves

Polarisation ellipse varies in time

Partially polarised waves

Wave coherency matrix (Complex domain)

Polarisation can be defined only in the sense of statistical average

Generalised Stokes vector (Real domain)Partially polarised wave descriptors:

Amplitude and phase of the electric field vector become random processes

Quasi-Monochromatic waves:

wave packets of incoherent waves with different frequencies over a narrow

frequency band


Monochromatic vs. Partially Polarised Waves

Direction of Wave Propagation --->

25


Partially Polarised Waves: Coherency Matrix

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

)exp()exp(

nn

mm

n

m

iaia

EE

Eδδr

Jones vector: representation in the reference basis},{ nm εε rr

⎥⎦

⎤⎢⎣

⎡><><><><

=⎥⎦

⎤⎢⎣

⎡∗∗

∗∗

nnmn

nmmm

2221

1211

EEEEEEEE

JJJJ

:→>⋅=< +EEJrr

:][Coherency Matrix:

By definition: 2x2 hermitian positive semi-definite matrix

⎥⎦

⎤⎢⎣

⎡−+−+

=⎥⎦

⎤⎢⎣

⎡

1032

3210

2221

1211

qqiqqiqqqq

JJJJ

Diagonal Elements:

Off-Diagonal Elements: cross-correlation between nm EE and

intensities of =→ ])([JTraceEE nm and Total wave intensity

Coherency Matrix=f(Stokes Vector) Stokes Vector=f(Coherency Matrix)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−+

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

}Im{}Re{

:

12

12

2211

2211

3

2

1

0

J2J2JJJJ

qqqq

qr


Partially Polarised Waves: Coherency Matrix

Completely polarised wave: … i.e. maximum correlation between

Completely unpolarised wave: … i.e. absence of any polarised structure in the wave

>>=<< ∗∗nnmm EEEE

0EEEE mnnm >=>=<< ∗∗1J

1001

IJ 0 =→⎥⎦

⎤⎢⎣

⎡=→ ])det([][

Partially polarised wave: … i.e. certain degree of correlation between

Coherency Matrix:

0JEEEEEEEE mnnmnnmm =→= ∗∗∗∗ ])det([))(())((

nm EE and

nm EE and

0JEEEEEEEE

Jnnmn

nmmm >→⎥⎦

⎤⎢⎣

⎡><><><><

=∗∗

∗∗

])det([][

Degree of Polarisation:

⎟⎠

⎞⎜⎝

⎛−= 2JTrace

J41m]))([(])det([⎥

⎦

⎤⎢⎣

⎡><><><><

=∗∗

∗∗

nnmn

nmmm

EEEEEEEE

J :][

1m =DoP:

1m0 <<DoP:

0m =DoP:

Polarised Wave PowerTotal Wave Power

26


Wave Description

Monochromatic Plane Waves are completely described by four parameters:

- Two parameters for the description of its polarisation state

- The wave amplitude which defines the size of the polarisation ellipse


Partially Polarised Plane Waves are completely described by five parameters:

- Two parameters for the description of the polarisation state

- The degree of polarisation

- The wave amplitude which defines the size of the polarisation ellipse



Wave and Polarisation Descriptors

Real Domain Complex Domain

Wave Descriptor:

Polarisation State Descriptor:

Wave Descriptor:

Polarisation State Descriptor:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

3

2

1

0

qqqq

q :rStokes Vector:

⎥⎦

⎤⎢⎣

⎡=

n

m

EE

E :r

Jones vector:

Polarisation Angles

Deschamps Parameters

m

n

EE

=:ρComplex Polarisation Ratio:

I. Monochromatic Waves:

II. Partially Polarised Waves:

Monochromatic & Partially Polarised Waves:

>⋅=< +EEJrr

:][Wave Coherency Matrix:

27


Scattering Polarimetry

• SCATTERING MATRIX AND MEASUREMENTS• Backscattering Vector


• Interpretation of Scattering Mechanisms

Scattering

Polarimetry


The Scattering Problem: Matrix Representation

Scattering in the far-zone region:

Mapping of the 2-dim incident vector into the 2-dim scattered vector

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡)()(

)()()()()exp(

)()(

rErE

rSrSrSrS

rri

rErE

iv

ih

VVVH

HVHHsv

sh

r

r

rr

rr

r

rκ

⎥⎦

⎤⎢⎣

⎡=

)()(

)(rErE

rE iv

ihi

hv r

rrr

⎥⎦

⎤⎢⎣

⎡=

)()(

)(rErE

rE sv

shs

hv r

rrr

Incident Field Scattered Field

Jones Vector: Jones Vector:

2x2 Complex Scattering Matrix

)(rEihvrr

)(rEshvrr

28


Coherent Scattering Matrix

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡iv

ih

VVVH

HVHHsv

sh

EE

SSSS

rri

EE )exp(κ

⎥⎦

⎤⎢⎣

⎡=

)exp(||)exp(||)exp(||)exp(||)exp(][

VVVVVHVH

HVHVHHHH

iSiSiSiS

rriS

φφφφκ

[S] is independent on the polarisation of the incident wave !!!

… also known as the Jones Matrix in the Bistatic and Sinclair Matrix in the Monostatic case

IJS

Complex Scattering Amplitudes:

=f(Frequency,Scattering Geometry)

and depends only on the physical and geometrical properties of the scatterer

⎥⎦

⎤⎢⎣

⎡−

−−=

||)(exp||)(exp||)(exp||)exp()exp(][

VVVVVHVH

VVHVHVVVHHHHVV

SiSiSiS

ririS

φφφφφφφκ

Seven Parameters: 4 Amplitudes & 3 PhasesAbsolute PhaseFactor

Total Scattered Power: 2VV

2VH

2HV

2HH SSSSSSTraceSSpanTP ||||||||)]][([])([ +++=== +


Bistatic Measurement of the Scattering Matrix

⎥⎦

⎤⎢⎣

⎡

VVVH

HVHH

SSSS

⎥⎦

⎤⎢⎣

⎡

VVVH

HVHH

SSSS

VVHVVHHH SSSS VVHVVHHH SSSS

29


Monostatic Measurement of the Scattering Matrix

⎥⎦

⎤⎢⎣

⎡

VVVH

HVHH

SSSS

⎥⎦

⎤⎢⎣

⎡

VVVH

HVHH

SSSS

VVHVVHHH SSSS VVHVVHHH SSSS


VH VV

HH HV

Azim

ut

Range

E-SAR / Test Site: Oberpfafenhoffen

Scattering Amplitude Images

30


Polarimetric Airborne SAR Sensors

AIRSARNASA / JPL (USA)

DC8P, L, C-Band (Quad)

AES1AeroSensing (D)

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

DOSAREADS / Dornier GmbH (D)

DO 228 (1989), C160 (1998), G222 (2000)S, C, X-Band (Quad), Ka-Band (VV)

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)

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)

STORMUVSQ / CETP (F)

Merlin IVC-Band (Quad)

RENEUVSQ / CETP (F)Écureuil AS350

S, X-Band (Quad)

SAR580CCRS (CA)

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


Experimental SyntheticAperture Radar System

E-SAR

P-Band (λ 68 cm)

L-Band (λ 23 cm)

X-Band (λ 3 cm)

C-Band (λ 5 cm)

System Engineer Ralf Horn

31


Single polarization channel

SRTM, February 2000

Receive

Transmit

Shuttle Polarimetric SAR Interferometry

SIR-C Mission: First Ever PolarimetricInterferometry L/C-Band Quad Pol - April 1994 10 days/October 1994 10 days

*last 3 day repeat pass interferometry (1 day repeatcycle) Time baseline of 1, 2, 3 days and 6 month

X-band6 m Receive AntennaC-band8 m Receive Antenna

X-band and C-band12m Transmit and Receive Antennas

Baseline:60 m long Mast, 45 deg off nadir

Orbit height: 233 kmInclination: 57 degX-band look angle: 52 degX-band swath: 50 km


2300 kgWeight

25 m x 25 mResolution100 kmSwath Width

10,74 m x 2,16 m

AntennaSize~ 23°Incident

Angle

19 MHz Bandwidth~780 kmAltitude

1,275 GHzFrequencyJune 26, 1978Launch

First Civilian SAR Satellite: SEASAT (1978)

32


• SEASAT 1978 L-Band (1.25 GHz) HH

• ERS 1/2 1991/95 C-Band (5 GHz) VV

• ALMAZ 1 1991/92 S Band (3 GHz) HH

• JERS-1 1992 L-Band HH

• RadarSat 1995 C-Band HH

• ENVISAT (ASAR) 2002 C Band HH,VV(VH)

• ALOS (PALSAR) 2006 L-Band QuadPol

• Radarsat II 2007 C-Band QuadPol

• TerraSAR 2006 X-Band QuadPol

Satellite SAR Systems


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

RadarSAT-1Canadian Space Agency (CSA)

C-Band, 1995-today

ERS-2European 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

ALOS / PALSARJapanese Space Agency (NASDA)

L-Band (quad), 2005

TerraSAR-XGerman Aerospace Center (DLR) / Astirum

X-Band (quad), 2006

RadarSAT-IICanadian Space Agency (CSA)

C-Band (quad), 2006

SAR-LupeBWB, GermanyX-Band, 2005

Spaceborne SAR Systems

33


Wavelength 0.236 m

Chirp Bandwidth 14 MHz

Peak Transmit Power 2 kW

Duty Cycle 3,5 % (7 % / 2)

Noise Figure 4 dB

Antenna Size (Tx , Rx) 8.9 m x 3.1 m

Quantisation 5 bit (BAQ)

Launch date Januar 2006Weight 4000kgSolar Power ~7Kw@EOLOrbit Sun SynchronousAltitude 691.65 kmRevolution 14+27/46Yaw steering ONInclination 98.16 degreesAttitude error 0.4e-4°


Frequency Frequency range Application Example

band

• VHF 300 KHz - 300 MHz Foliage/Ground penetration, biomass

• P-Band 300 MHz - 1 GHz Biomass, penetration

• L-Band 1 GHz - 2 GHz Agriculture, forestry, soil moisture

• C-Band 4 GHz - 8 GHz Ocean, agriculture

• X-Band 8 GHz - 12 GHz Agriculture, ocean, high resolution radar

• Ku-Band 14 GHz - 18 GHz Glaciology (snow cover mapping)

• Ka-Band 27 GHz - 47 GHz High resolution radars

Commonly used Frequency Bands

34


X-SAR/SIR-C Mission, DLR/NASA, 199

Attenuation due to Clouds and Rain Cells at X-Band


Frequency and Polarisation Diversity

C-bandR: HH G: HV B: VV

L-bandR: HH G: HV B: VV

P-bandR: HH G: HV B: VV

35


C-bandR: HH G: HV B: VV

L-bandR: HH G: HV B: VV

P-bandR: HH G: HV B: VV

Environmantal Monitoring

LARSEN B collapse observed in 2002 by ERS /Envisat

Envisat Radar monitoring Antarctica Ice and Sea-Ice extent (April-to June 2004)


Oil Spil Monitoring / Detection

36


Flooding Monitoring - German Flood Event (Summer 2002)

ASAR Alternating Polarization mode - Swath IS2 - 19 August 2002 R: |HH| G: |HV| B: |HH|-|VV|



• Scattering Matrix and Measurements

• BACKSCATTERING VECTOR• Backscattering Matrices

• Interpretation of Scattering Mechanisms

Scattering

Polarimetry

37


Scattering Vector

⎥⎦

⎤⎢⎣

⎡=

VVVH

HVHH

SSSS

S][Scattering Matrix:

Scattering Vector: 4T

43214 CkkkkSTrace21SVk ∈=== ][)]([])([: Ψ

r

.])?([.V … Matrix Vectorisation Operator

Ψ … Complete Set of 2x2 Basis Matrices

Vectorial formulation of the Scattering Problem in terms of system vectors

2VV

2VH

2HV

2HH44

24 SSSSSSpankkk ||||||||])([|||| +++==⋅= +

rrrFrobenious Norm of :4k

r

2VV

2VH

2HV

2HH SSSSSSpanTP ||||||||])([ +++==Frobenious Norm of :][S


Ψ … any complete set of four matrices leaving the norm of invariant4kr

Lexicographic & Pauli Scattering Vectors

⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=

1000

20100

20010

20001

2L ,,,Ψ

⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡ −⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

0ii0

20110

21001

21001

2P ,,,Ψ

TVVVHHVHH4 SSSSk ][=

r

TVHHVVHHVVVHHVVHH4 SSiSSSSSS

21k ])([ −+−+=

r

)]([])([: ΨSTrace21SVk4 ==

r

Lexicographic Scattering Vector:

Pauli Scattering Vector:

Lexicographic Matrix Set:

Pauli Matrices Set:

Scattering Vector:

Advantage: Directly related to the system measurable

Advantage: Closer related to physical properties of the scatterer

38


4-dim Scattering Vector Transformations

L44P4 kDkvv

][= P41

4L4 kDkvv

−= ][

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

VV

VH

HV

HH

L4

SSSS

kr

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+−+

=

)( VHHV

VHHV

VVHH

VVHH

P4

SSiSSSSSS

21k

r

Lexicographic Scattering Vector: Pauli Scattering Vector:

Unitary Transformation:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−=

0ii0011010011001

21D4][

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−== +−

0011i100i1000011

21DD 4

14 ][][

and

and

where is a 4x4 special unitary matrix in order to preserve the norm of : ][ 4D 4kr


⎥⎦

⎤⎢⎣

⎡−

−−=

||)(exp||)(exp||)(exp||)exp()exp(][

VVVVXXXX

VVXXXXVVHHHHVV

SiSiSiS

ririS

φφφφφφφκ

Five Parameters: 3 Amplitudes & 2 PhasesAbsolute PhaseFactor

BackscatteringIn the case of monostatic backscattering from reciprocal scatterers:

BSAXX

BSAVH

BSAHV SSS == )( FSA

XXFSA

VHFSAHV SSS =−=Reciprocity Theorem

→⎥⎦

⎤⎢⎣

⎡=

VVXX

XXHH

SSSS

S][

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

VV

XX

XX

HH

L4

SSSS

kr

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−+

=

0S2

SSSS

21k

XX

VVHH

VVHH

P4

r

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

VV

XX

HH

L3

SS2

Skr

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=

XX

VVHH

VVHH

P3

S2SSSS

21k

r

3-dim Lexicographic and Pauli Scattering Vectors:

Note: The factor is required to keep the vector norm of invariant L3kr

2

The scattering problem can be addressed in the 3-dim complex space:

39


3-dim Scattering Vector Transformations

L33P3 kDkvv

][= P31

3L3 kDkvv

−= ][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

VV

XX

HH

L3

SSS

kr

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=

XX

VVHH

VVHH

P3

S2SSSS

21k

r

Lexicographic Scattering Vector: Pauli Scattering Vector:

Unitary Transformation:

and

and

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=020101

101

21D3][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−==−

011200

011

21DD T

31

3 ][][

where is a 4x4 special unitary matrix in order to preserve the norm of : ][ 3D 3kr





• BACKSCATTERING MATRICES• Interpretation of Scattering Mechanisms

Scattering

Polarimetry

40


Partial ScatterersDeterministic Scatterers Partial Scatterers

Completely described by [S] Cannot be described by a single [S]

• Change the polarisation state of the wave • Change the polarisation state of the wave

• Do not change the degree of polarisation and also change the degree of polarisation

Scatterers with Space or Time VariabilityPoint Scatterers

MonochromaticIncident Wave

MonochromaticScattered Wave

Depolarisationdescribed by second order statistics


Covariance and Coherency Matrices in BackscatteringCovariance Matrix [C]:

>⋅=< ∗L3L33 kkC

rr:][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

><><><><><><

><><><=

∗∗

∗∗

∗∗

2

2

2

3

||22||22

2||:][

VVHVVVHHVV

VVHVHVHHHV

VVHHHVHHHH

SSSSSSSSSS

SSSSSC

Coherency Matrix [T]:

>⋅=< +P3P33 kkT

rr:][

Pauli Scattering Vector:

[ ]TXXVVHHVVHHP3 S2SSSS2

1k −+=r

Lexicographic Scattering Vector:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

><>−<>+<>−<>−<>+−<>+<>−+<>+<

=∗∗

∗∗

∗∗

2HVVVHHHVVVHHHV

HVVVHH2

VVHHVVHHVVHH

HVVVHHVVHHVVHH2

VVHH

3

S4SSS2SSS2SSS2SSSSSSSSS2SSSSSS

T||)()()(|)(|))(()())((|)(|

:][

TVVXXHHL4 SS2Sk ][=

r

and are by definition 3x3 hermitian positive semi-definite matrices][][ 33 TCand contain in general 9 independent parameters

41


Covariance vs. Coherency Matrix

[T] and [C] are unitarily similar (i.e., they have the same eigenvalues)

• [T] allows a physical interpretation of the scattering process

• Mean scatterer orientation can be more easily obtained from [T]

• [T] is diagonal for azimuthally symmetric media while [C] is not

• [T] is fundamentally related to the Mueller matrix and Stokes vector

[T] is closer related to physical / geometrical properties of the scattering process than [C]

• Polarimetric Scattering Amplitudes

• Polarimetric Phase Angles

• Polarimetric Correlations

Both contain information about:


Covariance 2 Coherency Matrix Transformation

( )( )

( ) ( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−+−−−+−−++−+−+++

=

45225

5233616331

5263313361

c2cc2cc2cc2cccccccccc2cccccccc

21T

**

***

***

][

( )( ) ( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−+−−−−−+−+−++++

=

2241532241

53653

2241532241

tttttt2tttttt2t2tt2

tttttt2tttt

21C

****

****

**

][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

653

542

321

ccccccccc

C**

*][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

653

542

321

ttttttttt

T**

*][

Covariance 2 Coherency Matrix Transformation:

Coherency 2 Covariance Matrix Transformation:

133

13LL33LL3PP DCDDkkDDkkDkkT −−++++ =⋅=⋅=⋅= ]][][[][][][][][

vvvvvv

]][[][][][][][][ 31

33PP1

33PP1

3LL DCDDkkDDkkDkkC −+−+−+ =⋅=⋅=⋅=vvvvvv

L33P3 kDkvv

][= P31

3L3 kDkvv

−= ][⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=020101

101

21D3 ][and where

42


Mueller Matrix

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−+

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

}Im{}Re{||||||||

:

sv

sh

sv

sh

2sv

2sh

2sv

2sh

s3

s2

s1

s0

s

EE2EE2EEEE

qqqq

qr

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡−+

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

}Im{}Re{||||||||

:

iv

ih

iv

ih

2iv

2ih

2iv

2ih

i3

i2

i1

i0

i

EE2EE2EEEE

qqqq

qr

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

i3

i2

i1

i0

33323130

23222120

13121110

03020100

s3

s2

s1

s0

qqqq

mmmmmmmmmmmmmmmm

qqqq

is qMq rr ][=

… also known as Stokes Matrix or Kennaugh Matrix in the Monostatic case (BSA convention)

[M] is a 4x4 real matrix

Stokes vectorfor the incident field

Stokes vectorfor the scattered field

The absolute phase of the scattering matrix is not preserved in [M] :-(

RSSSSfm VVVHHVHHij ∈= )(


Mueller Matrix

Ti3

i2

i1

i0

i qqqqq ][:=r

Monochromatic incident wave Monochromatic scattered wave

Monochromatic incident wave Depolarised scattered wave

[M] contains the same information as [C] or [T]: 9 independent parameters

[M] contains the same information as [S]: 5 independent parameters

[M] is symmetric for backscattering problems in the BSA convention

Ti3

i2

i1

i0

i qqqqq ][:=r

Ts3

s2

s1

s0

s qqqqq ][:=r

Ts3

s2

s1

s0

s qqqqq ][:=r

is qMq rr ][=

is qMq rr ][=

1m= 1m0 <<DoP: DoP:

1m=DoP: 1m=DoP:

Non Depolarising Scattering

Depolarising Scattering

43


Scatterer Descriptors

Scattering Matrix

Mueller Matrix

Coherency Matrix Covariance Matrix






• INTERPRETATION OF SCATTERING MECHANISMS• Directly from the Scattering Matrix

• Model based

Scattering

Polarimetry

44


Interpretation of Scattering Mechanisms

⎥⎦

⎤⎢⎣

⎡=

VVHV

HVHH

SSSS

S][ [ ]TxxVVHHVVHHP S2SSSS2

1k −+=v

PP

kk1ev

vv =

( )( )( ) ⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡==

XX

VVHH

VVHH

P3

2

1

PP S2

SSSS

k21

ii

ik

k1e vv

vv

φβαφβα

φα

expsinsinexpcossin

expcos

Scattering Matrix: Scattering Vector:

Unitary Representation:

Parameterisation of in terms of five angles:ev 321 φφφβα ,,,,



e00

001e vv

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

βΔβΔβΔβΔ

cossinsincos' e

10000

e vv

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −= αΔαΔ

αΔαΔcossinsincos

'

( )( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

001

10000

00

001

i000i000i

e

3

2

1

αααα

ββββ

φφ

φcossinsincos

cossinsincos

expexp

expv

Point Reduction Theorem:

Change of Scattering Mechanism:

45



⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

010

001

100001010

100010001

e'v

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

02121

001

1000212102121

100010001

e'v

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

001

10000

00

001e αα

αα

ββββ cossin

sincos

cossinsincos'v

H-DipolScatterer

Dihedral Scatterera=90º and β=0º

a=45º and β=0º

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

HV

VVHH

VVHH

P S2SSSS

k21

001

e vv

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−=

02121

001

1000212102121

100010001

e'v V-DipolScatterer

a=45º and β=180º

where


Scattering Processes: Fresnel Scattering

θεθθεθ

2

2

HRsincossincos

−+−−

=θεθεθεθε

2

2

VRsincossincos

−+−−

=

⎥⎦

⎤⎢⎣

⎡=

V

H

R00R

S][

Fresnel Reflection Coefficients:

Scattering Matrix:

… where e is the dielectric constant of the surface

and

HH

VV

Incidence Angle [Degree]

Am

plitu

de

ε = 20.

46


Scattering Processes: Bragg Scattering

θεθεθεθε

2

22

V11Rsincos

)]sin()[sin(−++−−

=

Bragg Scattering Coefficients:

Scattering Matrix:

… where ε is the dielectric constant of the surface

⎥⎦

⎤⎢⎣

⎡=

V

H

R00R

S][

θεθθεθ

2

2

HRsincossincos

−+−−

= and

VV

HH


Am

plitu

de

ε = 20.


Scattering Processes: Dihedral Scattering

⎥⎦

⎤⎢⎣

⎡−

=⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−

= ϕϕ iPTPS

STSS

PT

ST

PS

SSi eRR0

0RRR0

0RR00R

e001

1001

S][

θεθθεθ

2S

2S

SSRsincossincos

−+

−−=

θεθεθεθε

2SS

2SS

PSRsincossincos

−+

−−=

θεθθεθ

2T

2T

STRsincossincos

−+−−

=θεθεθεθε

2SS

2SS

PSRsincossincos

−+

−−=

Fresnel Coefficients:

Scattering Matrix:

and

and

HH

VV


Am

plitu

de

ε = 20.

47


→⎥⎦

⎤⎢⎣

⎡=

dbba

S][⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=c2baba

21k

v

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

10000

R3 αααα

α cossinsincos

:)(

kRRRk 333

vv)]([)]([)]([),,( γβαγβα =

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −=

ββ

βββ

cossin

sincos:)(

001

0R3 [ ]

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

10000

R3 γγγγ

γ cossinsincos

:)(

Scattering Processes: Volume Scattering

πα 20 ≤≤

πβ ≤≤0

πγ 20 ≤≤

Rotation about x-axisRotation about y-axisRotation about z-axis

),,(),,(][ γβαγβα +⋅= kkTvv

Coherency Matrix:



⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

z

y

x

000000

ρρ

ρΡ ][

11L4V

rii ))/(( −+=

επρ

∫∞

+++=

0

23z

23y

23x

zyxi ds

2ls2ls2ls2

8lllL /// )/()/()/(

/)(

zyxzyx l

1l1

l1LLL :::: =

1m

2m11L11LA

r

r

ry

rxP ++

+=

+−+−

=εε

εε

)()(:

ll

LLm

x

y

y

x ==:

1LLL zyx =++

2l

2l

2l

43V zyxπ=where is the particle volume and

with

Principal Polarisability Matrix:

Particle Anisotropy: Particle Shape Ratio:

∞≤≤m0

1m<

1m> oblate spheroids

prolate spheroids

48



T3

T3

T3333 RRRPRRRP )]([)]([)]([][)]([)]([)]([),,]([ αβγγβαγβα =

∫∫∫=α β γ

γβαγβαγβα dddpppPT )()()(),,]([][

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

b000b0001

aT][)(

)(2PP

2P

A7A6221Ab++

−= 50b0 .≤≤

Special Case:Random Volume

p(α )

-π π

p(γ )

-π π

p(β )

-π / 2 π / 2

where

Coherency Matrix:

where )(),(),( γβα ppp are the pdf’s for the corresponding angle distributions



A=0.01

A=0.20

A=0.40

A=0.60

A=0.80

A=1.00

H/a Loci for varying particle

shape and width of distribution

Prolate Particles

oriented volume random volume

dipole

sphere

49

Microwaves and Radar Institute

[S]

COHERENTDECOMPOSITION

E. KROGAGER(1990)

W.L. CAMERON(1990)

[K]

[T] [C]

TARGETDICHOTOMY

EIGENVECTORS BASEDDECOMPOSITION

MODEL BASEDDECOMPOSITION

EIGENVECTORS / EIGENVALUES ANALYSIS&

MODEL BASED DECOMPOSITION

EIGENVECTORS / EIGENVALUES ANALYSISENTROPY / ANISOTROPY

S.R. CLOUDE - E. POTTIER(1996-1997)

A.J. FREEMAN(1992)

W.A. HOLM(1988)

S.R. CLOUDE(1985)

J.J. VAN ZYL(1992)

AZIMUTHAL SYMMETRY

J.R. HUYNEN(1970)

R.M. BARNES(1988)




Decomposition

Theorems• PAULI MATRICES DECOMP.

• Sphere-Diplane-Helix Decomp.



50


Pauli Matrices Decomposition

⎥⎦

⎤⎢⎣

⎡ −+⎥

⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−

+⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡−+−+

=⎥⎦

⎤⎢⎣

⎡=

0ii0

d0110

c1001

b1001

abaidcidcba

SSSS

SVVVH

HVHH][

⎥⎦

⎤⎢⎣

⎡=

1001

aSa][

⎥⎦

⎤⎢⎣

⎡−

=1001

bSb][

⎥⎦

⎤⎢⎣

⎡=

0110

cSc][

⎥⎦

⎤⎢⎣

⎡ −=

0ii0

dSd ][

Single Scattering:

Dihedral Scattering ( … rotated by π/2 about the LOS )

Dihedral Scattering:

Transforms all polarisation states into their orthogonal states (disappears in backscattering)

VVHH SS =

VVHH SS −=


Azi

mut

h

Range


HH

C-band

SIR-C / Test Site: Kudara,Russia

VV HV

51



HH

L-bandSIR-C / Test Site: Kudara,Russia

VV HV

Azi

mut

h

Range


Pauli Images

C-band L-band


HH+VV

HH-VV

2HV

RGB-Coding:

52



Decomposition

Theorems• Pauli Matrice Decomp.

• SPHERE-DIPLANE-HELIX DECOMP.




Sphere-Diplane-Helix Decomposition

⎥⎦

⎤⎢⎣

⎡=

1001

SS ][Single Scattering:

Helix Scattering :

Dihedral Scattering: ⎥⎦

⎤⎢⎣

⎡=

)2cos(-)2sin()2sin()2cos(

][θθθθ

DS

⎥⎦

⎤⎢⎣

⎡−

=1i

i1SH ε

ε][

|| aAS =

|}Im{||| cb2AH ′=

VVHH

HVHVVVHHVVHH SS

SbccScSSbSSa

−==′=−=+=where:

22D cc1bA |}Re{||)}Im{|(|| ′+′−=

( ){ }][][)exp(][)exp(][ HHDDRSSVVVH

HVHH SASAiSAibac

cbaSSSS

S ++=⎥⎦

⎤⎢⎣

⎡−

+=⎥

⎦

⎤⎢⎣

⎡= φφ

53


Sphere-Diplane-Helix Images

C-band L-band


Sphere

DiplaneHelix

RGB-Coding:



Decomposition

Theorems




• EIGENVECTOR DECOMP.

54


Eigenvector Decomposition

Dr. Shane R. CloudeAEL Consultants

Prof. Dr. Eric PottierUniversity of Rennes 1

Cloude S R "Uniqueness of Target Decomposition Theorems in Radar Polarimetry", in Direct and Inverse Methods in Radar Polarimetry, Part 1, NATO-ARW, Eds. W.M. Boerner et al, KluwerAcademic Publishers, ISBN 0-7923-1498-0, pp 267-296, 1992

Cloude S R , E. Pottier, "A Review of Target Decomposition Theorems in Radar Polarimetry", IEEE Transactions on Geoscienceand Remote Sensing, Vol. 34 No. 2 March 1996, pp 498-518



Coherence Matrix: >⋅=< +P3P33 kkT

rr:][

Diagonalisation: 1333 UUT −= ]][][[][ Λ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

333231

232221

131211

3][eeeeeeeee

U⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=Λ

3

2

1

000000

][λ

λλ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡==

∗∗∗

∗∗∗

∗∗∗

+−

332313

322212

312111

31

3 ][][eeeeeeeee

UU

][][][)()()()(][ 33

23

13333222111

3

1iiii3 TTTeeeeeeeeT ++=⋅+⋅+⋅=⋅= +++

=

+∑ rrrrrrrr λλλλ

0321 ≥≥≥ λλλ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

33

23

13

3

32

22

12

2

31

21

11

1

eee

eeee

eeee

e rrr

where:

3 real positive eigenvalues 3 orthonormal eigenvectors

][][][ 321 SSS

55


Scattering Entropy / AnisotropyCoherency Matrix Diagonalisation:

][][][)()()()(][ 33

23

13333222111

3

1iiii3 TTTeeeeeeeeT ++=⋅+⋅+⋅=⋅= +++

=

+∑ rrrrrrrr λλλλ

32

32

32

32

PPPPA

+−

=+−

=λλλλ:

321

iiP

λλλλ++

=:i3

3

1ii PPH log: ∑

=

= with:Scattering Entropy:

Scattering Anisotropy:

Totally Polarised Scatterer

Totally Unpolarised Scatterer

→= 0H

→= 1H1H0 ≤≤ where:

→= 0A

→= 1A1A0 ≤≤

2 Equal Secondary Scattering Processes

Only 1 Secondary Scattering Processwhere:


Scattering Entropy Images

C-band L-band

H=0

H=1


56


Scattering Anisotropy ImagesSIR-C / Test Site: Kudara,Russia

C-band L-band

A=0

A=1


Eigenvector Decomposition: Scattering Mechanisms

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

|||

|||][ 3213 eeeU rrr

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

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

)exp()cos()exp()cos()exp()cos(][

333222111

333222111

332211

3

iiiiii

iiiU

εβαεβαεβαδβαδβαδβα

γαγαγα

][][][)()()(][][][][ 33

23

13333222111

1333 TTTeeeeeeUUT ++=⋅+⋅+⋅== +++− rrrrrr λλλΛ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

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

)exp()cos(

εβαδβα

γα

ii

ier

1st Scattering Mechanism

2nd Scattering Mechanism

3rd Scattering Mechanism

57


Mean Scattering Parameters

Coherency Matrix Diagonalisation:

321

iiP

λλλλ++

=:

Mean α-Angle:

Mean β-Angle:

Mean γ-Angle:

Mean δ-Angle:

332211 PPP αααα ++=

332211 PPP ββββ ++=

332211 PPP γγγγ ++=

332211 PPP δδδδ ++=

)()()(][ +++ ⋅+⋅+⋅= 3332221113 eeeeeeT rrrrrr λλλ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=


)exp()cos(

εβαδβα

γα

ii

ier

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=


)exp()cos(

iii

iii

ii

i

ii

ie

εβαδβα

γαr

Eigenvectors: Appearance Probabilities:

Mean Scattering Mechanism

Mean ε-Angle: 332211 PPP εεεε ++=


α-Angle Images

C-band L-band

a=0°

a=90°

a=45°


58


Alpha Parameter for Surface Scattering

Range of a with moisture content


ALOS-PalSAR: Quad-Pol @ 23.5° / Test Site: ALPSRP022952640 ALPSRP029662640

30.06.2006 15.08.2006

SNR

HHVV Phase

HHVV Phase

SNR

59



Decomposition

Theorems




• MODEL BASED DECOMP.


Target Decomposition for Targets with Reflection Symmetry

JACOB J. VAN ZYL (1992)

ANTHONY FREEMAN (1992)

Model Based Decomposition

MODEL BASED DECOMPOSITION

EIGENVECTOR / MODEL BASEDDECOMPOSITION

60


Freeman Decomposition I.

][][][][ VDS TTTT ++=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

000010

fT

2

SS βββ

][⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

−=

000010

fT

2

DD ααα

][⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

100010002

fT VV ][

Vegetation Scattering : Bragg-Scattering + Dihedral Scattering + Random Volume of Dipols

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡++−

−++=

V

VDSDS

DSV2

D2

S

f000ffffßf0fßff2fßf

T ααα

][4 Equations

for 5 Unknowns

where and

Re(HHVV)-fv/3 > 0 Single bounce is dominant alpha =1

Re(HHVV)-fv/3 < 0 Double bounce is dominant beta =1


Freeman Decomposition II.

][][][ / VDS TTT +=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=

θθθθβ

ββ

θθθθ

220220

001

000010

220220

001fT

2

SDS

cossinsincos

cossinsincos][ /

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

m000m0001

fT VV ][

Oriented Bragg or Dihedral Scattering + Random Volume of Spheroids

5 Equations for 5 Unknowns

m - shape of particles in cloud (m = 0 spheres, m = 0.5 dipoles)

θ - ground azimuth slope

β -ground scattering amplitude(single or double bounce)

and

61


|HH-VV|, |HV|, |HH+VV| Freeman/Durden, PD, PV, PS

Freeman Decomposition


Modified three component model – adding the HELIX

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡±=10

10000

21][

jjT Helix

m

Reflection symmetry is not anymore assumed, as for the Freeman three component model

Y. Yamaguchi, et al., “Four-component scattering model for polariemtric SAR image decomposition,”IEEE TGRS, vol.43, no. 8, 2005

Four Component Model Based Decomposition

62


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

POLARIMETRIC SIGNATURE

RAN

GE

FLIGHT

A MANMADE STRUCTURE - AN EXAMPLE

EMISAR C-Band Polarimetric SAR Image of Store Belt BridgeLee, J.-S.; Krogager, E.; Ainsworth, T.L.; Boerner, W.-M. ,‘Polarimetric Analysis of Radar Signature of a Manmade Structure ‘

IEEE, TGARS Letters, vol.3, issue 4, pp. 555- 559


Denmark Storebelt Bridge Signature

|HH|Flight Direction

|HV|

|VV|

63


1 32

d

Single Double

Triple

Double

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

Independent of height

Multi Bounce Scattering


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

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

Aerial Photo Krogager SDH DecompositionBlue= Sphere Green = Helix Red = Diplane.

RAN

GE

FLIGHT

Polarimatric Target Decomposition

EMISAR C-Band Polarimetric SAR Image of StoreBelt Bridge

64


Bridge under construction - deck not installed

Aerial Photo Dominant scat. mech. are extracted by applying decomp.:Blue= Surface Green = Dipole Red = Double Bounce.

Cloude and Pottier Decomposition

Direct bounce from cables

Triple bounce from cables

Double bounce from cables

Entropy

Alpha(Rotational invariant)



|HH+VV|

|HH-VV|

|HV|

After Completion of Bridge Construction

Denmark Storebelt Bridge Signature


65


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

RAN

GE

FLIGHT

Polarimetric Target Decompisition – AFTER COMPLETION

SDH


Entropy

Dominant scat. mech. are extracted by applying decomp: Blue= SurfaceGreen = DipoleRed = Double Bounce

Cloude & Pottier Decomposition – AFTER COMPLETION

Angle α

66


Bridge & Buoy Radar Signatures

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

Navigation Map of Storebelt, Denmark

(EMISAR C- Band)


·Agriculture/Land-UseCrop Classification/Moisture Content EstimationUrban Area mappingUrban Topography for Mobile comms

·ForestryBiomass Estimation: (Saturates For High Biomass)

C-band saturation at 50 tons/hectareL-band saturation at 100 tons/hectareP band saturation at 200 tons/hectare

DeforestationForest Canopy Height EstimationTree Species DiscriminationForest Re-growth Monitoring

·GeologyPlayas :Smooth Natural Surfaces(rms = 1cm)Alluvial fans, Sand Dunes, MorainesSedimentary Rock formationsLava Flows (extreme in surface roughness)Weathering Erosion StudiesSurface Roughness Estimates

·HydrologyFlood mapping/Forest InundationSnow HydrologySoil Moisture

·Sea Ice/OceanographyIce Roughness/Thickness StudiesPolar Ice Cap StudiesExtra-Terrestrial Ice/Water Studies

·MeteorologyRain rate estimationWater/Ice particle studies

Severe Storm/Flood warning

·Topography/CartographyDirect Surface Slope EstimationAccurate DEM GenerationDifference of DEMS for Vegetation mapping

·Humanitarian DeminingSurface Penetrating Radar (SPR)SAR for Mine Field Detection

Applications of Radar Polarimetry

67


Part II

Application of Polarimetric Radar Remote Sensing

• Terrain correction for quantitative surface parameter inversion

• Segmentation / Classifications (Agricultural Area, Urban Area,Sea Ice, Forestry, Oceanography)

• Modeling and Inversion of Surface Parameters



Zeulenroda L-band fully polarimetric

Zeulenroda X-Band DEM

68


Orientation Angle EstimationLee, J.-S., Schuler, D. L. & Ainsworth, T. L, » Polarimetric SAR Data Compensation for Terrain AzimuthSlope Variation » , IEEE Transactions on Geoscience and Remote Sensing, 1999

Q = orientation angle f = radar look angleN = tilted surface normal tan w, tan g = azimuthal/range slopex and y = horizontal plane V and H = polarisation plane

Using Circular Polarisation Method

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=⋅= +

333231

232221

131211

33

TTTTTTTTT

kkTvv

⎪⎩

⎪⎨

⎧

≥+=

≤=+=

42

44 πθπθθ

πθθθπφθfor

for

{ }⎟⎟⎠

⎞⎜⎜⎝

⎛−

=2233

232arctan

TTTRE

φ

Coherencymatrix:

Orientation angle:

Where angle f is:

N

z

y

x

f

QH

V Radar-basis

Scattering-basis

( )φφγ

ωsincostan

tantan+

−=Θ


Zeulenroda Orientation Angle from the X-band DEM

Zeulenroda Orientation Angle from the polarimetric L-band

69


SAR L-band, VV-pol Image

Ocean Internal Wave Detection - Orientation Angle (New York Bight Dataset)

Orientation Angle Image

AIRSAR Data: CM3474, 07/16/92Azimuth Direction

Ran

ge D

irect

ion

IW INDUCED CHANGES

NEWMETHOD

Courtesy of Dale Schuler


Dihedrals

Oberpfaffenhofen Dihedral ExperimentOrientation difference:Position: 5.0°Measured: 4.03°

Orientation

Line of SightRotation

70


Segmentation

/

Classification

Segmentation/ Unsupervised Classification

• H/a/A Unsupervised Classification

• Wishard Classifiction

• Freeman-Durden Classification

• L-band and X-band Classification

Prof. Eric Pottier - University of Rennes 1

Dr. Jong-Sen Lee – Naval Research Laboratory


POL-SAR PROCESSINGPHENOMENOLOGIC

QUALITATIVE ANALYSIS

BASIC THEORY

SPECKLE FILTERING

POLARIMETRICTARGET

DECOMPOSITION

POLARIMETRICCLASSIFICATIONMONO/DUAL FREQUENCY

ScatteringMatrix

Unsupervised Classification

(Preserving Scattering Mechanisms)

71


0.5 1.00 0 45° 90°

ENTROPY (H) ALPHA ( α )

H / A / α DECOMPOSITION

2 0A B B0 + B B0 −

WEIHERBACHTALL-band 1998 ANISOTROPY (A)

0.5 1.0 0


10n

0

1

2H

0.5 1.00

α

0

45° 90°

POLSAR DATA DISTRIBUTION

IN THEH / α PLANE

Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

H / A / α DECOMPOSITION

72


Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

C1

C2

C3

C4

C5

C6

C7

C8

Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

H / A / α DECOMPOSITION 10

n

00.20.40.60.8

11.21.41.61.82

LOW H MEDIUM H HIGH H

SURFACESCATTERING

VOLUMESCATTERING

MULTIPLESCATTERING


H /α CLASSIFICATION

C1 C2 C3 C4 C5 C6 C7 C8

H / α Classification SpaceSub-divised into 9 basic zones

Location of the boundariesis arbitrary and generically

Degree of arbitrariness on thesetting of these boundaries

Segmentation is offered merelyto illustrate the unsupervisedclassification strategy and to emphasize the geometrical

segmentation of physical scatteringprocesses

73


1994 LEE et al. PROPOSED A SUPERVISEDALGORITHM BASED ON THE COMPLEXWISHART DISTRIBUTION FOR THECOMPLEX COVARIANCE / COHERENCY MATRIX.

1998 LEE et al. DEVELOPED A COMBINED UNSUPERVISEDCLASSIFICATION METHOD THAT USES THE H / a PLANEWHICH INITIALLY CLASSIFIES THE POLSAR IMAGE. THISSEGMENTED IMAGE IS THEN USED AS TRAINING SETS FORTHE INITIALIZATION OF THE SUPERVISED WISHARTCLASSIFIER.

1999 INTRODUCTION OF THE ANISOTROPY (E. POTTIER - J.S.LEE)IMPROVEMENT OF THE CAPABILITY TO DISTINGUISHBETWEEN DIFFERENT CLASSES WHOS CENTERS END INTHE SAME ENTROPY (H) AND ALPHA (α) ZONE.

WISHART CLASSIFIER

Dr J.S. LEEN.R. L US -NAVY


PROVIDE INITIAL [Tm](0)

FOR EACH CLASS

[ ]( ) [ ]∑=

=

=mNk

1kk

m

0m T

N1T

Cluster Center of the class m(Lee 1998)

CLASSIFY THE WHOLE IMAGEWITH THE DISTANCE PROCEDURE

[ ] [ ] [ ]( ) [ ]( ) mjTdTdifTT jmm ≠∀<∈

COMPUTE [Tm](k+1) FOR EACH CLASSUSING THE CLASSIFIED PIXELS OF STEP 2

[ ]( ) [ ]∑=

=

+ =mNj

jj

m

km T

NT

1

1 1

TERMINAISONCRITERION ?

Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

H / α WISHART Segmentation

74


During the classification,the clustercenters can move out their zones

or several clusters may end in the same zone

Identification of the terrain typemay cause some confusion due to

the color scheme

The combined Wishart classifier isextended and complemented with the

introduction of the Anisotropy (A)

H/α - WISHART CLASSIFIER

C1 C2 C3 C4 C5 C6 C7 C8


Alp

ha (

α)

0

30

60

90

0 0

0.50.5

11

Entropy (H) Anisotropy (A)

POLSAR DATA DISTRIBUTIONIN THE

H / A / α CLASSIFICATION SPACE

75


Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

Alp

ha (

a)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

A > 0.5l2 >> l3

THE 2 COMPLEMENTED H / α PLANES10

n

0

2

3

1

10n

0

2

3

1

10n

0

2

3

1

1 SCATTERINGMECHANISM

3 SCATTERINGMECHANISMS

2 SCATTERING MECHANISMS(1+e) (e+e)

A < 0.5l2 == l3


2 Successive k - mean Classification procedures

21>A

8 Training sets

16 New Training sets

Introduction of the Anisotropy (A)information once the first classification

procedure has met its termination criterion

21<A 2

1>A

H/A/α - WISHART CLASSIFIER

76


C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

4th ITERATION

H/A/α - WISHART CLASSIFIER

2 0A B B0 + B B0 −

WEIHERBACHTAL DLR - ESAR


Unsupervised Classification Preserving Scattering Mechanisms

Polarimetric SAR (POLSAR) classificationComplex Wishart distribution (Lee et al., 1994)Wishart + Entropy/Alpha (Lee et al., 1999)Wishart + Entropy/Alpha/Anisotropy (Pottier and Lee, 2000)Deficiency: Wishart classifier is a statistic operator. Pixels in a class can be mixed in scattering mechanisms

A new approachPreserving scattering property of each pixel based on Freeman and Durden decomposition:

Double bounceSurfaceVolume (Canopy)

Better stability in convergenceAutomated color rendering

Dr J.S. LEEN.R. L US -NAVY

77


Classification Based onFreeman and Durden Decomposition

Freeman and S.L. Durden, “A Three-Component Scattering Model for Polarimetric SAR Data”

IEEE TGRS, vol. 36, no. 3, May 1998

|HH-VV|, |HV|, |HH+VV| Freeman and Durden

Volume(Canopy)

Double-Bounce

RoughSurfaceSurface


Freeman/Durden + Wishart

The proposed algorithm• Divide the image by Freeman/Durden decomposition into

three categories based on the• Merge clusters within each category by the Wishart between-

class-distance

• To preserve polarimetric scattering properties, • Double bounce

• Surface

• Volume (Canopy)

• Automatic color rendering by scattering characteristics

),,( SVD PPP

78


• Initial ClusteringFiltering POLSAR Image (lee et al., 1999), if needed.1. Decompose each pixel by Freeman and Durden decomposition into one of

three categories by its dominant scattering mechanism D // V / S3. Divide pixels in each category into 30 groups (initial clusters) with equal

number of pixels.Cluster Merging4. Merge initial clusters within each category by the Wishart between-class-

distance (Lee et al., 1999)5. Merge small cluster first, and limit the size of each cluster by

M= total Number of Pixels and N is the desired number of clustersWishart Classification6. Compute averaged covariance matrices (class centers).7. Within each category, apply the Wishart classification for 2 to 4 iterations for

scattering mechanism preservation.• Automated Color Rendering

8. Assign color for each final class according to its category (D/V/S) 9. Within each category, color intensity of a class is proportional to its averaged

power.

Implementation

dNMN /2max =


Procedure – Flow Chart PolSARCovariance

FREEMAN DECOM.

Pixels inSURFACECategory

Pixels inVOLUMECategory

Pixels inD. BounceCategory

Classify into Five Classes

Select pixels within 9x9

window

Apply Adaptive Speckle filtering



window




window


Unsupervised

Classification

Filtering

Pixels inMIXED

Category



window


Alternatively

CPPPPPPMax

SVDBSVDB ≤

++),,(

79


DLR E-SAR L-Band Data

Freeman/Durden Decomposition Classification Map

Experimental Results – Oberphaffenhofen

Image size : 1536 x 1280PolSAR Speckle Filtering Applied


DLR E-SAR L-Band Data

Freeman Decomposition Classification Map

Experimental Results – Oberphaffenhofen

80


X-Band PI-SAR Classification - Tsukuba

Unsupervised Classification H/α + Wishart (8 classes)

H/α/A + Wishart (16 classes)

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


X-Band PI-SAR ClassificationScattering Preserving Classification

Classification map – Original 4-look Classification map - speckle filtered (0.5)

81


L-Band PI-SAR ClassificationScattering Preserving Classification

Freeman/Durden Decomposition Classification map – Original data (5 - look)


Conclusion – Unsupervised Classification

PolSAR has great capability in terrain and land-use classification.For accurate classification, data correction are required:

CalibrationLook angle variationsOrientation angle variations – Azimuth slope

Incorporates interferometry (Pol-InSAR)

82


flight

N look

sea ice 1sea ice 2sea ice 3sea ice 4

water 1water 2water 3

land 1land 2land 3land 4

Colour code (5 null classes)

Sea Ice Classification

Labrador Sea (west coast of Newfoundland)

HH

HV

HH

VV

SIR-C/X

L-band Data


SURFACE PARAMETERS

Parameter inversion models:

I. Theoretical Models

II. Semi-/Empirical Extensions

III. Model Based Extensions

Modelling

and Inversion

Modelling and Inversion

83


VOLUMETRIC MOISTURE CONTENT

mv [vol. %]

Surface Parameters Description

ModelTopp et al. (1980)

Dielectric Constant e

"' εεεε jr −==

SURFACE ROUGHNESS

rms - height s [cm]

autocorrelation length l [cm]

Wavenumber k =2p/λks

X =4.00C =2.26 L =0.54 P =0.18

X =3, C =6, L =23, P =68Wavelength λ [cm]

klX =16.10C =9.03L =2.17P =0.74

Material Properties Geometric Properties

RAD

AR M

easu

rem

ents

Nat

ural

Sur

face


Models for the Estimation of Surface ParametersModeling and Inversion

EMPIRICALEXTENSIONS

THEORETICALMODELS

Geometrical-Optic 1963

Physical-Optic 1963

Oh et all. 1992

Dubois et all. 1995Integral Equation 1992

Shi et all. 1997

Ex-Bragg 1999

MODEL BASEDEXTENSIONS

SCATTERING DECOMPOSITION

APPROACHES

Eigen-DecompositionFreeman-Decomposition

Small Perturbation 1988

84


Small Perturbation Model

[ ] ( )( )

,00,

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

rP

rS

VVVH

HVHH

RR

SSSS

Sεθ

εθ

22

22

)sincos(

))sin1()(sin1(

θεθε

θεθε

−+

+−−=

rr

rrPR

θεθ

θεθ2

2

sincos

sincos

−+

−−=

r

rSR

Bragg Scattering Matrix:

Ideal Surface

p

s

VV

HH

RR

SS

= is independent of roughness

Exact solution of Maxwell equation for s reaching 0

ZRkjSZRkjS

PVV

SHH

⋅⋅=⋅⋅=

θθ

cos2cos2 Z = F.T.(E(x, y))

q = Incidence angle

k = 2π/λ

60 degree

25 degree


Small Perturbation Model (Bragg-Model)

Measured versus estimated volumetric moisture content mv [vol. %] using SPM

0

0.2

0.4

0.6

0.8

1

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0m v [vol %]

ks

elbe0-4elbe4-8weih0-4weih4-8

Validity range of the SPM for the ground measurements - surface roughness against

volumetric soil moisture

SPM

0

10

20

30

40

0 10 20 30 40measured m v [vol. %]

estim

ated

mv

[vol

. %]

Weiherbach 0-4 cmWeiherbach 4-8 cmElbe 0-4 cmElbe 4-8 cm

85


Models for the Estimation of Surface ParametersModeling and Inversion

EMPIRICALEXTENSIONS

THEORETICALMODELS

Geometrical-Optic 1963

Physical-Optic 1963

Oh et all. 1992

Dubois et all. 1995Integral Equation 1992

Shi et all. 1997

Ex-Bragg 1999

MODEL BASEDEXTENSIONS

SCATTERING DECOMPOSITION

APPROACHES

Eigen-DecompositionFreeman-Decomposition

Small Perturbation 1988


( )⎪⎩

⎪⎨⎧ ≤=

otherwise021

11ββββP

20 1

πβ ≤≤

Rotation SymmetricRoughness Term

Ideal Bragg Surface

Real Surface

zero cross-polarisation

and zerodepolarisation

non-zerocross-

polarisation

and non-zerodepolarisation

β

−β1

P(β)

+β1

β

k

SensorScattering Plane

AzimuthalOriented Surface

+ =

Polarimetric Surface Scattering Model ExtendedBragg Model (X-Bragg)

86


[ ] ))4(sinc1(00

0))4(sinc1( )2(sinc*0)2(sinc

13

1312

121

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−+=

βββ

β

CCC

CCT

23 2

1=C PS RR −( )( ) **2 PSPS RRRRC −+= 2

1 PS RRC +=2

0 1πβ ≤≤

I. Hajnsek, E. Pottier & S.R. Cloude, ‘Inversion of Surface Parameters in Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, submitted 2000.

[ ]( )( )

( )( )⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−+

+−+

== +

0000

02*

*2

PSPSPS

PSpSPS

PP RRRRRR

RRRRRR

kkTrrCoherency Matrix

for a Ideal Bragg Surface

Second Order Statistics - Coherency Matrix

Coherency Matrixfor a Real Surface


Prediction of the Ex-Bragg Model I

(HH+VV)(HH-VV) coherence versus b1 for different local incidence angles

Cross polarised power versus b1 for different local incidence angles

87


Decoupling Soil Moisture from Surface Roughness

2

2

11

3322

2 PS

PS

RR

RRT

TT−

−=

+

Function of ks Function of e‘ and AOI

ε‘ = 10-40AOI= 20°-

50°AOI= 35°

ε‘ = 10-40

)4(sin 13322

3322 β=+− c

TTTT


Scattering Entropy / Anisotropy / α-AngleCoherency Matrix Diagonalisation:

)()()(][ +++ ⋅+⋅+⋅= 3332221113 eeeeeeT rrrrrr λλλ

32

32

PPPPA

+−

=:

321

iiP

λλλλ++

=:

i3

3

1ii PPH log: ∑

=

=Scattering Entropy:

Scattering Anisotropy:

Totally Polarised ScattererTotally Unpolarised Scatterer

→=0H→=1H

1H0 ≤≤

2 Equal Secondary Scattering ProcessesOnly 1 Secondary Scattering Process

→=0A→=1A

1A0 ≤≤

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=


)cos(

iii

iii

i

i

iieγβαδβα

αr

Mean α-Angle:

332211 PPP αααα ++=

Appearance Probabilities:

),,( 321i =

88


Prediction of the Ex-Bragg Model II

Variation of Anisotropywith Roughness (Model Parameter ß1 )

Variation of Entropy/Alpha values with Dielectric Constant (45 degrees AOI)


Frequency:1.5to18.5 GHz10°

20°

30°

40°

50°

Anisotropy versus frequency plot forthe EMSL data

Entropy/alpha angle plot for the EMSL data

Experimental Data from the Joint Laboratory Center (Ispra)Collected in European Mircowave Signature Laboratory (EMSL)

quad-pol scattering matrix(HH,VV,HV,VH); s = 0.4 cm; surface correlation lenght l = 6; dielectric constant e‘ = 8; frequency range = 1.5-18.5

89


LHH Image Alpha AngleEntropy

Eigenvector DecompositionTest Site Elbe River - August 1997

N N N

0 1.5 km

N

Anisotropy


Inversion Procedure X-Bragg

X-Bragg ModelSLC Data


Entropy/Alpha


Entropy/Alpha

LUT-Comparison

Dielectric Constant

Universal Polynomial

INPUT DATA

Soil Moisture Content

90


Volumetric Moisture

N

N

0 500 m

Field 10

Field 13

Field 14

Field 16

Qualitative Presentation of the Estimated Surface Parameters

N

0 500 m

Field 10

Field 13

Field 14

Field 16

Surface Roughness


0

10

20

30

40

0 10 20 30 40measured m v [vol %]

estim

ated

mv [v

ol. %

]

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

Measured versus Estimated

Volumetric Moisture mv [%]

0-4 cm 4-8 cm corr.

Elbe RMSerror 8 3 0.7/0.8

Weih RMSerror 7 6 0.2/-

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1measured ks

estim

ated

ks

Elbe Weiherbach

ks corr.

Elbe RMSerror 0.14 0.6

Weih RMSerror 0.21 0.35

Surface Roughness ks

91


Main Problem

* The presence of vegetation cover limits drastically the performance of the algorithms

* Scattering decomposition techniques lead to an improved performance but do not solvethe problem

Outlook

Dual-Frequency Polarimetry (for example: L- and P-band)

Combination of Polarimetric and Interferometric Measurements

Combination of Mono- and Bi-Static Polarimetric Measurements

Main results for Quantitative - Surface Parameter Estimation

* The results of the investigation lead to the conclusion that moisture content and surface roughness of bare surfaces can be estimated with an accuracy of 10%, for

moisture content ranging from 0 up to 40 [vol. %] and roughness scales up to ks < 1.

Uncertainties during measuring the surface parameters leads to inaccurate measurements

which should be accounted.


References (Part I)Theory SAR-Polarimetry:

Boerner, W. M. et al., ‘Polarimetry in Radar Remote Sensing: Basic and Applied Concepts’, Chapter 5 in F. M. Henderson, and A.J. Lewis, (ed.), “Principles and Applications of Imaging Radar”, vol. 2 of Manual of Remote Sensing, (ed. R. A. Reyerson), Third Edition, John Willey & Sons, New York, 1998. Borgeaud, M., S. V. Nghiem, R. T. Shin & and J. A. Kong, ‘Theoretical Models for PolarimetricMicrowave Remote Sensing of Earth Terrain’, Journal of Electromagnetic Waves and Applications, vol. 3, no.1, pp. 61-81, 1989.Chen, H. C., ’Theory of Electromagnetic Waves: A Coordinate-Free Approach’, McGraw-Hill Book Company, New York, 1983. Cloude, S. R., ‘Group Theory and Polarisation Algebra’, OPTIK, vol.75, no. 1, pp. 26-36, 1986.Cloude, S. R., ‘Polarimetry: The Characterisation of Polarimetric Effects in EM Scattering’, PhD. Thesis, University of Birmingham, Faculty of Engineering, UK, October 1986Cloude, S. R. & E. Pottier, ’A Review of Target Decomposition Theorems in Radar Polarimetry’, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 2, pp. 498-518, 1996Cloude, S.R., ‘Symmetry, Zero Correlations and Target Decomposition Theorems’, Proceedings 4th Int. Workshop on Radar Polarimetry, PIERS, pp. 58-66, 1998.Collet, E., ‘Polarized Light: Fundamentals and Applications’, Marcel Dekker, Inc., New York, 1993.Graves, C. D., ’Radar Polarization Power Scattering Matrix’, Proceedings of the IRE, vol. 44, no. 5, pp. 248-252, 1956.Huynen, J. R., ‘Phenomenological Theory of Radar Targets’, Ph. D. thesis, University of Technology, Delft, The Netherlands, December 1970.Sinclair, G., ’The Transmission and Reception of Elliptically Polarized Waves’, Proceedings of the IRE, vol. 38, no. 2, pp. 148-151, 1950.Woodhouse, I., ’Introduction to Microwaves Remote Sensing’, CRC Taylor & Francis, p. 370, 2005.Van Zyl, J. J., ‘On the Importance of Polarization in Radar Scattering Problems’, Ph.D. thesis, California Institute of Technology, Pasadena, CA, December 1985.

92


Application (Classification / Surface Parameter Inversion)Cloude, S. R. & E. Pottier, ‘An Entropy Based Classification Scheme for Land Applications of Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, vol. 35, no.1, pp. 68-78, 1997.Hajnsek, I., Pottier, E. & Cloude, S.R., ‘Inversion of Surface Parameters from Polarimetric SAR’, IEEE Transactions on Geoscience and Remote Sensing, vol. 41, no. 4, pp. 727-745, 2003.Lee, J. S., M. R. Grunes, T. Ainsworth, D. Lu, D. L. Schuler, & S. R. Cloude, ‘Unsupervised Classification Scheme of Polarimetric SAR Images by Applying Target Decomposition Theorems and Complex WishardDistribution’, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 5, pp. 2249-2258, 1999.Lee, J. S., M. R. Grunes & G. De Grandi, ’Polarimetric SAR speckle filtering and its implication on classification’, IEEE Transactions on Geoscience and Remote Sensing, vol. 37, no. 5, pp.2363-2373, 1999.Nghiem, S. V., S. H. Yueh, R. Kwok, and F. K. Li, ‘Symmetry Properties in polarimetric Remote Sensing’, Radio Science, vol. 23, no. 4, pp. 713-720, 1988.Pottier, E., D. L. Schuler, J. S. Lee & T. L. Ainsworth, ‘Estimation of the Terrain Surface Azimuthal/Range Slopes Using Polarimetric Decomposition of Polsar Data’, Proceedings of IGARSS’99, Hamburg, Germany, 1999.Pottier, E., ‘Unsupervised Classification Scheme of POLSAR Images based on the Complex Wishard Distribution and the H/A/alpha Polarimetric Decomposition Theorem’, Proceedings 4th Int. Workshop on Radar Polarimetry, PIERS, pp. 535-547, 1998.Schuler, D. L., J.S. Lee & T. L. Ainsworth, ’Comparisation of Terrain Azimuthal Slope Effects in Geophysical Parameter Studies Using Polarimetric SAR Data’, Remote Sens. Environ, vol. 69, pp. 139-155, 1999. Ulaby, F. T. & Elachi, C., ’Radar Polarimetry for Geocience Applications’, Artech House, Inc., Norwood, MA, 1990.

References (Part II)

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