Calibration and Correction of Compact Polarimetric

SAR DataJun Hong1,3,4, Hong Tan2,3,4, Wen Hong1,3,4

1. National Key Laboratory of Microwave Imaging Technology, Beijing 100190, China;2. Key Laboratory of Technology in Geo-spatial Information Processing and Application

System，Chinese Academy of Sciences, Beijing 100190, China;3. Institute of Electronics，Chinese Academy of Sciences, Beijing 100190, China;

4. University of Chinese Academy of Sciences, Beijing 100039, China

23rd CEOS SAR Cal&Val Workshop

Concept

Compact polarimetric (CP) synthetic aperture radar (SAR)

Three typical modes Tran Rec1 Rec2

π/2

CTLR(Circular Transmit and

Linear Receive)R H V

DCP(Dual Circular Polarimetry)

R R L

π/4 45° H V

2

Advantages

Compared to a fully polarimetric (FP) system• Lower PRF• Wider swath• Lower data rate• Much lower energy consumption• lower cost and lower mass• Most importantly, reconstructed pseudo quad-

polarimetric information can be used in a similar way as the FP data

• Specially, the transmitted polarization is not affected by Faraday rotation in the CTLR and DCP modes

3

Current CP SAR systems

IndiaRISAT-1

2012

JapanALOS-2

(Experiment mode)2014

CanadaRCM

(Including 3 satellites)2018 as planed

4

Challenges

As a polarimetric SAR system, polarimetric distortions must be determined and corrected.• Very few measurements• Too many unknowns• Quite different from the calibration of the FP

SAR system

5

Previous work

1. System models• 2005, Souyris

– Use one cross talk to describe all distortions of the transmitting system

• 2008, Freeman– Take the Faraday rotation into account– Consider cross talks and channel imbalance of the

transmitted antenna instead of one distortion• 2014, Touzi

– Raise the question of nonideal transmitted polarized signal, such as an elliptical polarized signal is transmitted instead of an circular polarized one for the reason of a phase error between the horizontal and vertical antennas

6

Previous work

2. Calibration methods• A) Methods based on manmade calibrators• 2008, Freeman

– Three calibrators: Trihedral + 0°Dihedral + 45°Dihedral– Calibrated parameters: receiving distortions, Faraday

rotation angle• 2011, Jie Chen

– Calibrators: several different combination of active and passive calibrators

– Calibrated parameters: receiving distortions, Faraday rotation angle, and transmitting distortions

7

Previous work

2. Calibration methods• B) Methods based on natural distributed

targets• 2005, Souyris

– Raised the possibility of calibration with natural distributed targets

• 2009, Truong-Loï– Estimate the Faraday rotation angle using natural

distributed targets under certain conditions

8

Previous work

3. Correction methods• As pointed out by Freeman etc., it is not possible

to correct the transmission afterwards, since only one polarization is transmitted [1, 2].

[1] A. Freeman, P. Dubois-Fernandez, and M.-L. Truong-Loï, "Compact Polarimetry at longer wavelengths - calibration," in Proc. EUSAR, Friedrichshafen, Germany, 2008.[2] M.-L. Truong-Loï, P. Dubois-Fernandez, E. Pottier, A. Freeman, and J. C. Souyris, "Potentials of a compact polarimetric SAR system," in Proc. IEEE IGARSS, 2010, pp. 742-745.

9

Our focus

• 1. System model– Some distortions are not considered

• 2. Calibration methods– Methods based on manmade calibrators use at

least three calibrators and are costly– The question for calibration based on distributed

targets is ill-positioned• 3. Correction methods

– Transmitted distortions can not be corrected afterwards

10

1. System model

• Souyris

• Freeman

• Our model

2 1

1 1 2

1 1 1hh hvCTLR c

vh vv

S S n

S Sf nj j

dd

dé ùæ öé ù æ öæ ö æ ö

= + +ê úç ÷ ç ÷ç ÷ ç ÷ê ú -è ø è øë û è øè ø ë ûkur

2

1 1

3 1

3 2 2

1 cos sin

sin cos

1cos sin 1

sin cos

hh hvCTLR

vh vv

S S

S Sf

n

f nj

dd

dd

W W æ öé ù æ ö= ç ÷ç ÷ê ú - W Wè øë û è ø

W W é ù æ öæ ö æ ö× + ç ÷ç ÷ ç ÷ê ú- W W -è ø è ø è øë û

kur

2

1 1

3 1

4 2 2

1 cos sin

sin cos

1cos sin 1 0 1

sin cos 0

hh hvCTLR

vh vv

j

S S

S Sf

n

f ne jj

dd

dd

W W é ùé ù æ ö= ç ÷ ê úê ú - W Wè øë û ë û

W W é ù æ öæ ö é ù æ ö× + ç ÷ç ÷ ç ÷ê ú ê ú- W W -è ø ë û è øë û è ø

kur

Phase error

Cross talkin

transmitting

Transmitting distortions

11

2. Calibration method

To reduce the number of deployed calibrators, we propose a calibration method using distributed targets and one corner reflector [3].

[3] Hong Tan, Jun Hong. Calibration of Compact polarimetric SAR Images Using Distributed Targets and One Corner Reflector[J], IEEE Trans. Geosci. Remote Sens., 54(8): 4433-4444, 2016.

12

2. Calibration method

• Assuming– A homogeneous distributed target that respects

both the reflection symmetry and the rotation symmetry exists

• For– A reciprocal system

• With– The phase shift error small and negligible– The Faraday rotation angle already measured

externally (such as estimation from TEC models) 13

2. Calibration method

• We get

The following information is used to estimate the one channel imbalance and two cross talks• The second-order statistics of observations from

homogeneous distributed targets, i.e., the averaged covariance matrix

• The measurements from a corner reflector

2

1

1 1

2 2

1 cos sin

sin cos

1cos sin 1

sin cos

hh hvCTLR

vh vv

S S

S Sf

n

f nj

dd

dd

W W é ùé ù æ ö= ç ÷ ê úê ú - W Wè øë û ë û

W W é ù æ öæ ö æ ö× + ç ÷ç ÷ ç ÷ê ú- W W -è ø è øë û è ø

urk

14

2. Calibration method

A set of full polarimetric single-look complex L-band data over the Amazon rainforest from ALOS PALSAR is selected to simulate CP SAR measurements

15

2. Calibration method

Distortion parameters in simulation

16

2. Calibration method• SVD decomposition of Jacobian matrix• Three typical corner reflcetors are analyzed• Dihedral corner reflector at 0 deg is selected as the best in existance of

background noises, and is used in the following simulation

0 2 4 6 8 10-80

-60

-40

-20

0

20p/4 Mode

Eigenv alue number

Ene

rgy

(dB

)

Trihedral

Dihedral at 0

Dihedral at 45

0 2 4 6 8 10-80

-60

-40

-20

0

20DCP Mode

Eigenv alue number

Ene

rgy

(dB

)

0 2 4 6 8 10-80

-60

-40

-20

0

20CTLR Mode

Eigenv alue number

Ene

rgy

(dB

)

Largest value

17

2. Calibration method• Calibration results• Faraday rotation angle = 0 deg, SCR of corner reflector = 50 dB

-4 -2 0 2 4-0.05

-0.04

-0.03

-0.02

-0.01CTLR Mode

CI amplitude (dB)

CI

ampl

itude

err

or (

dB)

-20 -10 0 10 200.01

0.02

0.03

0.04

0.05

0.06

0.07CTLR Mode

CI phase (deg)

CI

phas

e er

ror

(deg

)

-35 -30 -25 -200

2

4

6

8

10

12CTLR Mode

CT amplitude (dB)

CT

am

plitu

de e

rror

(dB

)

|d

1|

|d2|

-200 -100 0 100 200-40

-20

0

20

40CTLR Mode

CT phase (deg)

CT

pha

se e

rror

(de

g)

arg(d1)

arg(d2)

( ) ( ) ( )1 2 1 2arg 20 , 20dB,arg arg 0f d d d d= = = - = =o o ( ) ( )1 2 1 23dB, 20dB,arg arg 0f d d d d= = = - = = o

( ) ( ) ( )1 23dB,arg 20 ,arg arg 0f f d d= = = =o o ( ) 1 23dB,arg 20 , 20dBf f d d= = = = -o18

2. Calibration method• Impacts of Faraday rotation angle on Calibration Accuracy• SCR of corner reflector = 50 dB

0 5 10 15 20-0.018

-0.016

-0.014

-0.012

-0.01CTLR Mode

FRA (deg)

CI

ampl

itude

err

or (

dB)

|f | ,DW = 0°

| f | ,DW = 0.5°

0 5 10 15 20-0.2

-0.15

-0.1

-0.05

0

0.05CTLR Mode

FRA (deg)

CI

phas

e er

ror

(deg

)

arg(f ),DW = 0°

arg(f ),DW = 0.5°

0 5 10 15 201

1.5

2

2.5

3

3.5CTLR Mode

FRA (deg)

CT

am

plitu

de e

rror

(dB

)

|d

1|,DW = 0°

|d2|,DW = 0°

|d1|,DW = 0.5°

|d2|,DW = 0.5°

0 5 10 15 2010

20

30

40

50

60CTLR Mode

FRA (deg)

CT

pha

se e

rror

(de

g)

arg(d

1),DW = 0°

arg(d2),DW = 0°

arg(d1),DW = 0.5°

arg(d2),DW = 0.5°

2. Calibration method

AVERAGE OF ABSOLUTE CHANGE IN ABSOLUTEESTIMATION ERRORS CAUSED BY THE EXISTENCE OF AN

FRA ERROR

Parameters π/4 DCP CTLR

(dB) 0.01 0.00 0.00

(deg) 0.06 0.01 0.01

(dB) 0.87 0.29 0.29

(deg) 1.96 2.85 2.85

(dB) 0.63 0.27 0.27

(deg) 2.13 1.66 1.66

f

( )arg f

1d

( )1arg d

2d

( )2arg d20

20 30 40 50 600

5

10

15

20

25

30CTLR Mode

SCR (dB)

CT

pha

se e

rror

(de

g)

arg(d1)

arg(d2)

20 30 40 50 601

2

3

4

5

6CTLR Mode

SCR (dB)

CT

am

plitu

de e

rror

(dB

)

|d

1|

|d2|

20 30 40 50 60-0.6

-0.4

-0.2

0

0.2CTLR Mode

SCR (dB)

CI

phas

e er

ror

(deg

)

20 30 40 50 60-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0CTLR Mode

SCR (dB)

CI

ampl

itude

err

or (

dB)

2. Calibration method• Impacts of Clutter and Noise of Coner Reflector on Calibration Accuracy• Faraday rotation angle = 0 deg

2. Calibration method• Dihedral corner reflector at 0 deg is recommended (if well

constructed)• The channel imbalance can be estimated with high

precision even in case of an average Faraday rotation angle estimation error of 0.5 deg or a SCR of the corner reflector as low as 20 dB

• As the cross talks are usually small values, they are more sensitive to noises, and larger errors are seen in their estimations

• To ensure that the calibration algorithm gives accurate estimations of the cross talks, the SCR of the corner reflector should be larger than 35 dB

• Among the three modes, the π/4 mode suffers from larger estimation errors than the other two modes

22

3. Correction method

• Our model can be rewritten as

• where

• can be defined as an equivalent transmit cross talk

( )2

1 1

1 cos sin cos sin 1 1

sin cos sin cos

CTLR RC LCc

hh hvc

hv vv

S S

S Sf j j

d

dd

d

W W= +

W W W W é ùé ùé ù æ ö æ ö æ ö æ ö= +ê úç ÷ ç ÷ ç ÷ ç ÷ê úê ú - W W - W W -è ø è ø è ø è øë û ë û ë û

ur ur urk RF SF J J

( ) ( )( ) ( )

2 3 4

2 3 4

1

1

j j

c j j

f e j e

f e j e

j j

j j

d dd

d d

- - +=

+ - -

As reported, impossible to be correctedCan be easily

corrected

23

3. Correction method

To remove the cross talk and the Faraday rotation effect in transmit, we propose a correction method [4].

[4] Hong Tan, Jun Hong. Correction of transmit crosstalk in reconstruction of quad-pol data from compact polarimetry data[J], IEEE Geosci. Remote Sens. Lett., 12(5): 1051-1055, 2015.

24

3. Correction method

• As

• We correct

'cos sin 1 1 1 1

sin cos c RC cj j j jd w d

W W é ù é ùæ ö æ ö æ ö æ ö æ ö+ = +ê ú ê úç ÷ ç ÷ ç ÷ ç ÷ ç ÷- W W - -è ø è ø è ø è ø è øë û ë û

' 2

jRC

jc c

e

e

w

d d

- W

W

=

=

'1 1hh hvCTLR c

hv vv

S S

S S j jd

é ùé ù æ ö æ ö= +ê úç ÷ ç ÷ê ú -è ø è øë û ë û

urk

25

3. Correction method

• It is true that the transmit cross talk can not be corrected to get the real scattering vector.

• But when reconstructing pseudo quad-polarimetric information in the form of covariance matrix instead of the scattering vector, it is possible.

26

3. Correction method

• An iterative method similar to Souyris’s [5] reconstruction method is derived

• With a similar assumption– Most natural distributed targets respect the

reflection symmetry

[5] J. C. Souyris, P. Imbo, R. Fjørtoft, et al. Compact polarimetry based on symmetry properties of geophysical media: The pi/4 mode[J], IEEE Trans. Geosci. Remote Sens. 2005, 43(3): 634-646.

27

3. Correction method

The covariance matrix

( ) ( )( ) ( )

( ) ( )( ) ( )

T* 11 12*12 22

*

1 2 1 2 1 2 1 2

1 2 1 2 1 2 1 2

CTLR CTLRCTLR

C C

C C

H a Pj j b a j j bX

P j j b V a j j b a

é ù= × = ê ú

ë û+ + - - -é ù é ù

= +ê ú ê ú- - - + +ë û ë û

ur urC k k

( ) ( )' ', c ca bd d= Â = Á2

hhH S= 2

vvV S=*

hh vvP S S= 2

hvX S=

28

3. Correction method

• Step 1: initical correction

( )

11 12

11 12**12 2212 22

*

11 12**12 22

1 2 1 2

1 21 2

CTLR

C Ca j bC C

C CC Caj b

d jdH jPX

jd djP V

é ùê ú+ +é ù ê ú= =ê ú ê úë û ê ú-+ê úë û

-é ùé ù= + ê úê ú-ë û ë û

C% %% % %

11 12 22

1 2 1 2 1 2, ,

1 2 1 2 1 2a j b a

d d da j b a

- - += = =

+ + -

29

3. Correction method

• Step 2: iterative algorithm to estimate X– Start with X=0

– Iterate until X converge

12(0)

11 22

jC

C Cr -

=%

% %

( )( )( )( )11 22 (0)

(0)

11 22 (0)

1

1

C CX

N d d

r

r

+ -=

+ + -

% %

( )( )12 ( ) 12

( 1)

11 ( ) 11 22 ( ) 22

ii

i i

jC X d

C X d C X dr +

- +=

- -

%% %

( )( )( )( )11 22 ( 1)

( 1)

11 22 ( 1)

1

1

i

i

i

C CX

N d d

r

r

+

+

+

+ -=

+ + -

% %

30

3. Correction method

Once X is estimated, the true covariance matrix can be get

*

11 12*12 22

1

1

1

1

ACCTLR

CTLR

H Pj jX

P j V j

d jd jX X

jd d j

-é ù é ù= +ê ú ê ú-ë û ë û

- -é ù é ù= - +ê ú ê ú

ë ûë û

C

C%

31

3. Correction method

Still, ALOS PALSAR data are used to simulate CP SAR data and to verify the validity of the

proposed method.

32

3. Correction method

-35 -30 -25 -20 -15 -10 -5-60

-40

-20

0

|dc| (dB)

Rel

ativ

e E

rror

in H

(%

)

-35 -30 -25 -20 -15 -10 -5

-20

0

20

40

|dc| (dB)

Rel

ativ

e E

rror

in V

(%

)

-35 -30 -25 -20 -15 -10 -5

-20

-10

0

|dc| (dB)

Rel

ativ

e E

rror

in X

(%

)

BC

AC

2

hhS

2

hvS

2

vvS

BC: before correction, AC: after correction

-35 -30 -25 -20 -15 -10 -5-0.1

-0.05

0

|dc| (dB)

Err

or in

| r|

-35 -30 -25 -20 -15 -10 -5-10

-5

0

5

10

15

|dc| (dB)

Err

or in

Pha

se( r

) (d

eg)

BC

AC

*

2 2

hh vv

hh vv

S S

S Sr º

33

3. Correction method

-200 -150 -100 -50 0 50 100 150 200-10

-5

0

5

10

15

Phase(dc) (deg)

Rela

tive E

rror

in H

(%

)

-200 -150 -100 -50 0 50 100 150 200-10

-5

0

5

10

15

Phase(dc) (deg)

Rela

tive E

rror

in V

(%

)

-200 -150 -100 -50 0 50 100 150 200-15

-10

-5

0

5

Phase(dc) (deg)

Rela

tive E

rror

in X

(%

)

BC

AC

BC: before correction, AC: after correction

-200 -150 -100 -50 0 50 100 150 200

-0.06

-0.04

-0.02

0

Phase(dc) (deg)

Err

or in

| r|

-200 -150 -100 -50 0 50 100 150 200

-10

0

10

20

Phase(dc) (deg)

Err

or in

Pha

se( r

) (d

eg)

BC

AC

2

hhS

2

vvS

2

hvS*

2 2

hh vv

hh vv

S S

S Sr º

34

3. Correction method

The proposed algorithm performs effectively and stably under certain

conditions for any transmit crosstalk amplitude no larger than -15dB.

35

Thanks!

Q & A

36