1

Imaging Polarimetric Interferometry: (POLInSAR) :

From SIR-C to Tandem-X

S. R. Cloude,

AEL Consultants, Scotland, UK E-mail : aelc@mac.com

Web :http://web.mac.com/aelc

Polarization in Remote Sensing Group: http://www.linkedin.com/

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Acknowledgement : All Terrasar/Tandem-X data provided courtesy of DLR under Research Contracts LAN 0638 and LAN 0943

1994 ……….. 2011

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Overview

1.  Introduction : Two missions and one story…

2.  The Motivation : why polarimetry with interferometry?

3.  Coherence Set Theory and Signal Processing Developments

4.  Products : Forest Height +…

5.  POLInSAR with Tandem-X : Can we do it?

6.  Conclusions and Session Overview…

Cloude S.R., Papathanassiou K.P.,“Polarimetric SAR Interferometry”, IEEE Transactions on Geoscience and Remote Sensing, Vol. GRS-36. No. 5, pp. 1551-1565, September 1998

First publication of POLInSAR results from this mission:

Shuttle Radar Heritage.. not just SRTM…

..To Tandem-X : A Space-borne single pass Polarimetric Interferometer

… launched June 21st 2010…

..two potential POLInSAR modes

•  Dual Polarization (inc. HH/VV)

•  Quad Polarization (only experimental)

2 satellites in close formation orbit..

250 -500m separation…

The Motivation…

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€

pi =λiλ∑

→ HN = − pi logN pi 0 ≤HN ≤1∑ 0 1

€

[J] = I1 00 1⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ H2 =1

€

[J] = I1 00 0⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ H2 = 0

Murphy’s Law : Can go wrong….will go wrong Cloude-Murphy : Can increase H…will increase H

N = 2 Wave Polarimetry …..but how about N = 3,4,5,6,7….??

Wave entropy

N = 3 POLSAR N = 4 Bistatic POLSAR/Compact POLInSAR N = 6 POLInSAR N = 8 Bistatic POLInSAR N = 9 Dual Baseline POLInSAR :

Low Entropy: The key to success in Remote Sensing

The entropy line

Microwave Scattering as an Entropy Source/Sink

€

[TRV ] = mv

0.5 0 00 0.25 00 0 0.25

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

⇒ H3 = 0.947POLSAR Forest

Scattering: An Entropy Source

How to lower the entropy of vegetation scatter?

..Mathematical solution is to zero fill €

€

TD[ ] =

0.5 0 0 00 0.25 0 00 0 0.25 0 0 0 0 0 0

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥

Entropy vs dimension D

…but how can we realise this solution?

€

Tv[ ] =mv

1+ f p

1 0 00 cos2θ sin2θ

0 −sin2θ cos2θ

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

1 τ 0τ * f pδ 00 0 f p (1−δ)

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ .1 0 00 cos2θ −sin2θ

0 sin2θ cos2θ

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Cloude 1999 Yamaguchi 2005 Neumann 2009 Arii 2010

..even for more recent volume models

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€

[T6] = mv

TRV eiφTRVe−iφTRV TRV

⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ p =

0.50.250.25000

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

⇒ H6 = 0.5803

POLInSAR : The perfect solution? Probing vegetation at low entropy

s1

s2

α

P z

y

€

⇒ kz =4πΔθλ sinθ

≈4πB⊥

λR0 sinθ=4πBcos θ −α( )

λR0 sinθ

€

φ = kzho

…not quite…coherence loss (Cloude-Murphy in action)

€

[T6] =T11 Ω12

Ω12*T T22

⎡

⎣ ⎢

⎤

⎦ ⎥ mv

TRV γeiφTRVγe−iφTRV TRV

⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ p =

0.5 − 2δ0.25 −δ0.25 −δ2δδ

δ

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

⇒ H6 > 0.5803

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Coherence Decomposition

€

˜ γ = γeiφ = ˜ γ v (γ procγ snrγ geom ˜ γ t ) 0 ≤ γ ≤1

€

f (z') = anPnn∑ (z')

an =2n +12

f (z')Pn (z')dz'−1

1

∫

€

f (z) = exp(−z −δ( )2

2χ 2)0

hv

Fourier-Legendre**

Gaussian-in-a-box*

*F. Garestier, P. Dubois-Fernandez and I. Champion, ”Forest height inversion using high resolution P-band Pol-InSAR data,” IEEE Trans. GRS, Vol. 46, No. 10, pp. 3544-3559, November 2008

**S. R. Cloude, ”Polarization coherence tomography,” Radio Sci., 41, RS4017, doi:10.1029/2005RS003436, September 2006

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Coherence Tomography: First Results

H/α image

Red=hh-vv Green=2hv Blue=hh+vv

Dihedral trihedral forest

Coherence Set Theory…

Equal Scattering Mechanisms (ESM) or not?

w1 w2

€

[T6] =T11 Ω12

Ω12*T T22

⎡

⎣ ⎢

⎤

⎦ ⎥

ESM⎯ → ⎯ ⎯ T11 = T22 ?€

d =T11 T22

12 (T11 +T22)

≈1?

€

γ c =1

1+ RtS

*T ⋅ t S

t S*T ⋅ ˆ t M

2 −1⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

≈1?

€

T11 = Tmaster ⇒ tMT22 = Tslave ⇒ t S

w1 = w2?

Baseline B

ML ratio test

Generalized Coherence test

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φ1

Constrained Coherence Region

€

[T ]−1[ΩH ]w = λw [ΩH ] =

12Ω12e

iφ1 +Ω12*Te−iφ1( )

[T ] =12T11 +T22( )

⎧

⎨ ⎪

⎩ ⎪

Max and min coherence for each φ1 are found from max/min eigenvalues of above.. By connecting the set of extreme coherences The shape of the boundary can be obtained

..to find the region inside of which the coherence variation with polarisation w is entirely contained

…(under the assumption w1 = w2) solve the following eigenvalue problem for all φ1

The size and shape of the coherence region/loci is important. ..It is often elliptical, with circular and linear as special cases.. LINKED TO SCATTERING MODELS..

Flynn T., Tabb M., Carande R., “Coherence Region Shape Estimation for Vegetation Parameter Estimation in POLINSAR”, Proceedings of IGARSS 2002, Toronto, Canada, pp V 2596-2598, 2002

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€

˜ γ iNTX = eiφ (zo )

fiNTX (z ')eikzzdz '

−hv

hv

∫

fiNTX (z ')dz '

−hv

hv

∫

2-Layer Coherence estimation

There are then five components to the coherence

X X Ignore these two by a)  using a dual TX system and b) no specular 3rd order scattering

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Linear Coherence Loci of 2-layer Random-Volume-Over-Ground (RVOG)

µmax and µmin determine the ‘visible’ line length

The mu-spectrum….

Surface only

Volume only

€

˜ γ (w) = eiφ (zo )( ˜ γ vo + F(w) 1− ˜ γ vo( ))

µmax

µmin

2. L Ferro-Famil,. M Neumann, Y Huang, “Multi-Baseline Statistical Techniques for the Characterization of Distributed Media”, Paper WE4.06.5, Proceedings of IGARSS 09, Cape Town, SA, July 2009

The Products…

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SIR-C / Test Site: Kudara,Russia Azimut

h

Range Pauli RGB Image

Temporal Baseline: 48 Hours

L-band

From SIR-C : Forest Height Estimation

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…and new products : Biomass from height @ L band

Biomass Estimation from Forest Vertical Structure: Potentials and Challenges for Multi‐Baseline Pol‐InSAR Techniques, Pardini, Matteo ; Kugler, Florian ; Lee, Seung‐Kuk ; Sauer, Stefan ; Torano Caicoya, Astor ; Papathanassiou Konstantinos,, Proc. ESA-POLInSAR 2011, Frascati, Italy, January 2011

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…improved by adding low frequency vertical structure information

Biomass Estimation from Forest Vertical Structure: Potentials and Challenges for Multi‐Baseline Pol‐InSAR Techniques, Pardini, Matteo ; Kugler, Florian ; Lee, Seung‐Kuk ; Sauer, Stefan ; Torano Caicoya, Astor ; Papathanassiou Konstantinos,, Proc. ESA-POLInSAR 2011, Frascati, January 2011

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And not just forestry… The theory scales with baseline/height ratio

for problems in agriculture

6 x6 maize plants (2m x 2m)

hv = 1.8m

1.5 - 9.5 GHz (10MHz steps)

θ = 44:0.25:45 degrees

φ= 0:5:360 degrees

Data courtesy of (EMSL), Ispra, Italy

Single,dual and triple baseline

S R Cloude, “Dual Baseline Coherence Tomography”, IEEE Geoscience and Remote Sensing Letters, Vol4, No. 1, January 2007, pp 127-131

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What are the opportunities and limitations for POLInSAR?

3 important issues:

•  Do we have significant X-Band forest penetration? •  Do we see a polarized ground at X-Band in dualpol mode (mu-spectrum)? •  Is the entropy low enough for forest height estimation?

(SNR as a major entropy source)

Tandem-X

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•  Central Kalimantan (540 000 ha) •  Vegetation: Tropical peat swamp forest types •  Topography: Almost perfectly flat (slopes < 0.1%) •  Biomass range: 50-400 ton/ha (high at edge and lower in centre). •  Height range: 5-25 m. •  Location centre: 114° 36’E, 2° 12’S

INDREX-II Campaign November 2004 onesian Radar EXperiment

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X -Band Tomography: Single-Pass-Single-POL Coherence

Antenna pattern

Use: - This VV coherence - Tree height from P-band data - Surface topography phase

..to generate vertical X-band profiles through the canopy…

..using Coherence Tomography

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X-Band Vertical Tomogram

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Low entropy source

High entropy diffuser

observer

Low entropy source observer Target

Decomposition Theory

..but POLInSAR also needs a good mu-spectrum: An Optical Analog

Terrasar-X Data : Vancouver 25/04/2010

High Entropy Image

Low Entropy Image

Alp

ha A

ngle

of

sour

ce

Amplitude ms(w)

© DLR 2010

A useful physical model: Checking the mu-spectrum..

POLSAR

RV

G Single or dihedral scattering

€

T2 =t11 t12t12* t22

⎡

⎣ ⎢

⎤

⎦ ⎥ = ms

cos2α cosα sinαeiδ

cosα sinαe− iδ sin2α

⎡

⎣ ⎢

⎤

⎦ ⎥ +mv

2 00 1⎡

⎣ ⎢

⎤

⎦ ⎥ + n

1 00 1⎡

⎣ ⎢

⎤

⎦ ⎥

POLInSAR

€

w =cosα

sinαeiδ⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ ˆ γ s =

w*TΩ12ww*TT11ww

*TT22w

w⊥ =−sinα

cosαeiδ⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒ ˆ γ v =

w⊥*TΩ12w⊥

w⊥*TT11w⊥w⊥

*TT22w⊥

€

w⊥*T w = 0

φ

φ = phase centre separation

RVOG

ALOS-PALSAR : Borneo, 10/05/2010 L-band satellite radar

Dual POL HH,VV

Total Scattering

Alpha color code

Dual POL HH,VV

Zero Entropy Scattering

ALOS-PALSAR : Borneo, 10/05/2010 L-band satellite radar

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Terrasar-X : Borneo, 16/04/2010 X-band Satellite Radar

Dual POL HH,VV

Total Scattering

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Dual POL HH,VV

Zero Entropy Scattering

Terrasar-X : Borneo, 16/04/2010 X-band Satellite Radar

Tandem-X : POLInSAR HH/VV Data sets Bistatic Mode

North Munich, Germany

12/04/2011

Kryckland, Sweden

21/02/2011

Mixed urban agriculture

and forestry

Boreal Forest

AOI=34o Perp Baseline =39m ambiguity height=134m kz =0.047

Tandem-X, North Munich, 12/04/2011

Total signal… ….zero entropy component

€

w⊥ w

Tandem-X, North Munich, 12/04/2011 POLInSAR Coherence Pair

Coherence of zero entropy component

φ

POLInSAR Phase difference φ

Tandem-X, North Munich, 12/04/2011 POLInSAR phase difference

..an idea of what to expect..

.for 20m high trees and kz = 0.05

..expect around 30 degrees phase difference

Δ

γ

Mean width

POLInSAR Mean Speckle Phase

Tandem-X, North Munich, 12/04/2011 Speckle model using mean coherence

River

Surface

Forest

X-band Coherence Regions

Conclusions and Session Summary

•  POLInSAR products depend on the variation of interferometric coherence with polarization - low entropy probing of random scatterers like forests

•  SIR-C was the first driver… - C and L bands quadpol with short repeat pass (days) and good SNR

•  Followed by maturation of coherence set theory and algorithms/models (RVOG). …validation using airborne quadpol sensors

- again with good SNR and short repeat times (minutes)

•  Satellite developments hindered by 2 issues ..lack of polarization diversity and/or long repeat times (e.g. 46 days ALOS –PALSAR)..

Now with Tandem-X we have a new generation: single-pass polarimetric interferometers in space… But…limited polarization (dual or compact) and limited SNR… Plus…we need better models for high frequency volume scattering…

High entropy diffuser +

distributed low entropy source

observer

X-band POLInSAR : a new model Vegetation as a distributed low-entropy source

Some important future issues:

- RVOG is invalid…smaller coherence region than expected…line fit will not give φ0 - Key to using coherence for vegetation products will then be good ground φ0 estimates - SNR as an important limiting entropy source for Tandem-X POLInSAR..