Polarimetric Calibration Using Distributed Odd-bounce TargetsPolarimetric Calibration Using

Distributed Odd-bounce Targets

Jiong CHEN 1, 3* Motoyuki SATO 2 Jian YANG 3

1. Graduate School of Environmental Studies, Tohoku University, Japan2. Center for Northeast Asian Studies, Tohoku University, Japan

3. Department of Electronic Engineering, Tsinghua University, China*E-mail: jiongc@cneas.tohoku.ac.jp

07/2011

HH HV

VH VV

S S

S S

HH HV

VH VV

Z Z

Z Z

After calibration

Retrieval of soil moisture

0

210 3

0

21 expHH

VV

ks

0

000.23 1 expVH

VV

ks

Estimation of biomass

Classification of terrainMonitoring of flood

Introduction

ALOS/PALSARY. Oh 1992 H. Yamada, et.al. 2001

2/13

Polarimetric Calibration

• Polarimetric SAR Model for Calibration

• Basic Assumptions

• Conventional Methods

41

3 22 1

11HH HV HH HV HH HV

VH VV VH VV VH VV

Z Z S S N N

Z Z S S F N NF

1. Reciprocity2.Statistical symmetryon distributed targets

3. Known Calibrators

HV VHS S * * 0HH VH VV VHS S S S 1 0

0 1TriS

Van Zyl Quegan Kimura

Assumption 1,2,3 Assumption 1,2 Assumption 1, Slight 2

3/13

Motivations

• The deployment of trihedral is inconvenient

– For low frequency system, the size should be relatively large

– To implement calibration ubiquitously

• The assumption is not always valid

– Only valid for statistically symmetric distributed targets

– Small value will cause large bias in the calibration results

* * 0HH VH VV VHS S S S

Develop a calibration method without the trihedral or the assumption * * 0HH VH VV VHS S S S

4/13

Basic Scheme and Assumptions

Conventional method : TrihedralConventional method : Trihedral

Proposed method : Use the statistic information of odd-

bounce targets

Proposed method : Use the statistic information of odd-

bounce targets

Robust estimator using odd-bounce targets

Robust estimator using odd-bounce targets

Assume cross-talk to be smallAssume cross-talk to be small

Advantage : 1. Standard trihedral calibrator is not needed 2. The assumption is not needed* * 0HH VH VV VHS S S S

Removal of non-reciprocal effect

Estimation of channel

imbalance

Estimation of cross-talk

Channel imbalance ratio

Channel imbalance product

5/13

Decomposition of Distortion Matrix

•

Channel ImbalanceChannel

ImbalanceNon-reciprocal

effectNon-reciprocal

effect Cross-talkCross-talk

1

1 2

2 1

1 2 1 1 1 1

1 0 1 'cos sin

0 ' ' 1sin cos

cos 'sin sin 'cos

' 'cos 'sin ' 'sin 'cos

R R RR I CF

F F F F

2

1 2

2 2 2 2

1 2 1 2

1 ' 1 0cos sin

' 1 0 'sin cos

cos 'sin ' 'cos 'sin

sin 'cos ' 'sin 'cos

T T TT C IF

F F

F F

6/13

Selection of Odd-bounce Targets

Statistical information of odd-bounce targets Trihedral

7/13

Typical odd-bounce targets

Statistical propertyAmplitude Phase

Flight direction

Optical image, captured from Google Earth

Removal of Channel Imbalance

•

Estimation of channel imbalance

Uncalibrated data

Removal of channel imbalance

Channel balanced data

Robust estimator for non-reciprocal effect

Non-reciporcaldistortion matrix

1 1

1 2

2 1

'

1 ' 1 'cos sin cos sin

' 1 ' 1sin cos sin cos

R T R R T T

HH HV

VH VV

Z I ZI C SC

S S

S S

8/13

Robust Estimator of Non-reciprocal Effect

• Odd-bounce targets : Good for the estimation of

• Distribution of on odd-bounce targets : Laplace

9/13

Similarity Parameters

2 2

1 2 1 2 1 22 2, /Hr S S k k k k

1, exp

2

xf x b

b b

1

ˆ arg minN

ii

x

The robust estimate

Fitting ResultLaplace distribution with

different parameters

Estimation of Cross-talk

•

10/13

1 2 4 3 1 2 1 2VH HV HH VVF Z F Z FF Z Z

4 1 21

3 2 3 42 1

11HH HH HH HV

VH VV VH VV

Z Z S S N N

Z Z S S F N NF

On Odd-bounce targets

2 1 2 1 1 2 1 2' ' ' '

VH HV HH VVF Z F Z FF Z Z

cos 1 sin Assuming

Assuming 1 2' '

Estimated Distortion Matrix

1 1

1 2 1 1 2 1

1 sin ' 1

' ' 'sin 'R

F F F F

42 2 2

3 21 2

11 ' ' 'sin

sin ' '

F FT

FF

Discussion on Results

• Calibration result

11/13

1.0000 0.0253 0.0038'

0.0180 0.0029 0.7145 0.0081

jR

j j

1.0000 0.0320 0.0068'

0.0320 0.0038 0.9638 0.3269

jT

j j

1.0000 0.0063 0.0071

0.0063 0.0080 0.7217 0.0237

jR

j j

1.0000 0.0024 0.0129

0.0115 0.0062 0.9572 0.3830

jT

j j

New distortion matrices

JAXA Standard distortion matrices

Co-polarized signature on trihedral

Uncalibrated JAXA standard calibrated result

New calibrated result Theoretical result

•

Removal of Faraday Rotation

Sendai 090604 Sendai 070414

Alaska 07072912/13

• A practical calibration scheme based on distributed odd-bounce targets is proposed

– The distortion matrix is decomposed firstly

– The statistical information of odd-bounce targets is used as alternative to trihedral

– A robust estimator based on odd-bounce targets is derived to estimate the non-reciprocal effect

– It can be used as a rough calibration method without the special deployment of trihedral calibrators, nor the un-correlation consumption

Conclusion

13/13