UAVSAR Polarimetric&Calibraon&

UAVSAR Polarimetric Calibra3on

Alexander Fore, Bruce Chapman, Brian Hawkins, ScoA Hensley, Cathleen Jones, Thierry Michel, Ronald Muellerschoen

Jet Propulsion Laboratory, California Ins3tute of Technology © 2013 California Ins3tute of Technology, Government Sponsorship acknowledged

Overview of Talk 1.  Summary of hardware events and calibra3on changes. 2.  SAR Performance over Time

–  Noise-‐Equivalent σ0 (NESZ). –  Resolu3on es3mated at corner reflectors.

3.  Radiometric and Phase Calibra3on –  Performed within UAVSAR processor: jurassicprok. –  Es3mated using point-‐targets and distributed targets. –  Periodically check / update using engineering flights.

4.  Cross-‐talk Calibra3on –  Runs as part of post-‐processing kit. –  Requires radiometric and phase calibra3on to be applied already. –  Es3mated using the data itself for each flight line.

5.  Temporal Stability of Calibra3on Parameters

Summary of Hardware Events / Calibra3on Changes

Start Date Event Effect

4/23/2009 Ka-‐band / L-‐band pod swap Changed L-‐band calibra3on

4/8/2011 L-‐band antenna switch New calibra3on; change in NESZ.

4/19/2011 Updated beam table Updated L-‐band calibra3on

6/14/2011 L-‐band calibra3on change* Updated calibra3on (~ 1dB change)

8/15/2012 Ka-‐band / L-‐band pod swap Changed L-‐band calibra3on

1/2/2013 Antenna re-‐installed in pod; accidental cable short.

Very noisy data due to cable short.

3/2/2013 Cable short repaired. Changed L-‐band calibra3on

* Retroac3vely applied to data star3ng in September 2012

SAR Performance

•  We have tracked the noise-‐equivalent σ0 over 3me and have found two regimes: – One for 3me period up to 2011-‐04-‐07 – Another for ajer 2011-‐04-‐07 – The difference is due to an antenna change.

•  The range and azimuth resolu3ons as es3mated by corner reflectors have been extremely stable over 3me.

NESZ Up to 2011-‐04-‐07

NESZ Ajer 2011-‐04-‐07

Range and Azimuth Resolu3on

Jan−08 Jan−09 Jan−10 Jan−11 Jan−12 Jan−13

2.4752.5

2.5252.55

2.5752.6

2.6252.65

2.6752.7

FWH

M [m

]

Mean, STD HH Range: 2.534, 0.040Mean, STD VV Range: 2.544, 0.041

HH FWHM RangeVV FWHM Range


0.925

0.95

0.975

FWH

M [m

]

Mean, STD HH Azimuth: 0.941, 0.051Mean, STD VV Azimuth: 0.941, 0.026

HH FWHM AzimuthVV FWHM Azimuth

Full Width at Half Max of Corner reflectors

Radiometric / Phase Calibra3on •  Antenna paAern correc3on performed within the processor. •  The radiometric and phase calibra3on is performed within the processor via pre-‐

computed parameters: –  Per-‐channel gain bias (HH,HV,VH,VV). (corner reflectors) –  HH-‐VV phase bias polynomial fit to incidence angle. (corner reflectors) –  HV-‐VH phase bias polynomial fit to incidence angle. (distributed targets)

•  Corner reflector array in dry lake bed in Rosamond, CA. –  23 corner reflectors (side length = 2.4 meters). –  Posi3on of CR measured very accurately with differen3al GPS.

Corner Reflector Calibra3on Es3ma3on

1.  For each imaged corner reflector (CR) we: –  Compute predicted normalized radar cross-‐sec3on (σ0) using analy3cal expression.

–  Compute observed σ0 via oversampling and integra3on for HH and VV channels.

–  Compute observed HH-‐VV phase at CR peak. 2.  Collect this data over typically 8 flight-‐lines

covering the range swath of UAVSAR. –  From these data we generate the radiometric and phase calibra3on parameters.

20 25 30 35 40 45 50 55 60 6548495051525354555657585960

Incidence Angle [deg]

Mea

s R

CS

[dB]

HHVV

20 25 30 35 40 45 50 55 60 6516171819202122232425262728


Mea

s/Pr

edic

ted

RC

S [d

B]

HH Mean: 20.87 VV Mean: 23.80

HH RMSE: 20.94 VV RMSE: 23.87

20 25 30 35 40 45 50 55 60 65−10

−4

2

8

14

20

26


HH−V

V Ph

ase

[deg

]

BIAS: 16.63 RMS: 17.52 20 25 30 35 40 45 50 55 60 65

1.1

1.15

1.2

1.25

1.3

1.35


Co−

Pol C

hann

el Im

bala

nce

BIAS: 0.185 RMS: 0.189

No Radiometric or Phase Calibra3on Applied

20 25 30 35 40 45 50 55 60 65282930313233343536


Mea

s R

CS

[dB]

HHVV

20 25 30 35 40 45 50 55 60 65−3

−2

−1

0

1

2

3


Mea

s/Pr

edic

ted

RC

S [d

B]

HH Mean: 0.02 VV Mean: −0.00

HH RMSE: 0.77 VV RMSE: 0.68

20 25 30 35 40 45 50 55 60 65−10

−4

2

8

14

20


HH−V

V Ph

ase

[deg

] BIAS: −0.11 RMS: 5.10

20 25 30 35 40 45 50 55 60 650.9

0.95

1

1.05

1.1

1.15


Co−

Pol C

hann

el Im

bala

nce

BIAS: −0.009 RMS: 0.033

With Radiometric and Phase Calibra3on Applied

04590135180

−45−15

1545

0

5

10

x 105

Phi

Co−Polarization Power; CR3; No Calibration

Theta04590135180

−45−15

1545

0

500

1000

Phi

Co−Polarization Power; CR3; With Calibration

Theta

04590135180

−45−15

1545

0

5

10

x 105

Phi

Co−Polarization Power; CR4; No Calibration

Theta04590135180

−45−15

1545

0

500

1000

Phi

Co−Polarization Power; CR4; With Calibration

Theta

Co-‐Polariza3on Signatures of Corner Reflectors

Cross-‐Talk Calibra3on •  We use a fully general distor3on model:

–  4 complex parameters that link polariza3ons (u,v,w,z) –  1 complex parameter for the HV/VH channel balance (α) –  1 complex parameter for the HH/VV channel balance (k) – assumed to be 1 via corner reflector analysis.

•  We use Ainsworth et al. method for cross-‐talk parameter es3ma3on. –  Data driven algorithm using local window to compute observed polarimetric covariance matrix (C).

–  Remove pixels with large hh-‐hv correla3on and very bright pixels.

–  Use a large window (~40,000 pixels) for computa3on of C. –  Rather CPU intensive, we use domain decomposi3on to perform parallel processing.

Fully general formula3on:

€

Ohh Ohv

Ovh Ovv

"

# $

%

& ' =Y

k wku 1"

# $

%

& ' Shh ShvSvh Svv

"

# $

%

& ' αk αkzv 1

"

# $

%

& ' +

Nhh Nhv

Nvh Nvv

"

# $

%

& '

€

Ohh

Ovh

Ohv

Ovv

"

#

$ $ $ $

%

&

' ' ' '

= D

ShhSvhShvSvv

"

#

$ $ $ $

%

&

' ' ' '

€

D :=

1 w α v / α vwu α uv / α vz wz α 1/ α wuz z α u / α 1

#

$

% % % %

&

'

( ( ( (

With k=1/√α; Y=1:

(*) T.L. Ainsworth, L. Ferro-‐Famil, and Jong-‐Sen Lee. Orienta3on angle preserving a posteriori polarimetric sar calibra3on. IEEE Transac3ons on Geoscience and Remote Sensing, 44(4):994–1003, April 2006.

Cross-‐Talk Calibra3on Algorithm

Assume radiometric and phase calibra3on:

Itera3ve parameter es3ma3on (*)

Cross-‐talk parameter es3mates: (u, v, w, z, α)

Construct observed polarimetric covariance matrix over window: Cij = < Oi Oj*>

E = D−1 =1

(uv−1)(vz−1)

1 −w −v vw−u / α 1/ α uv / α −v / α

−z α wz α α −w αuz −z −u 1

"

#

$$$$$

%

&

'''''

Calibra3on Matrix: Cross-‐Talk Removal

Cross-‐Talk Calibrated SLC HH, HV, VH, VV channels

SLC HH, HV, VH, VV channels (no cross-‐talk calibra3on)

0 1500 3000 4500 6000 7500 9000

0

0.1

0.2

0.3

0.4

abs(

alp

ha)

[dB

]

Range Pixel

0 1500 3000 4500 6000 7500 9000

0

10

20

30

arg

(alp

ha)

[deg]

Range Pixel

0 1500 3000 4500 6000 7500 9000

−40

−20

abs(

u)

[dB

]

Range Pixel

0 1500 3000 4500 6000 7500 9000

−40

−20

abs(

v) [dB

]Range Pixel

0 1500 3000 4500 6000 7500 9000

−40

−20

abs(

w)

[dB

]

Range Pixel

0 1500 3000 4500 6000 7500 9000

−40

−20

abs(

z) [dB

]

Range Pixel

Red: Es3mated cross-‐talk parameters as a func3on of range Black: Residual es3mated cross-‐talk parameters

•  u,v,w,z about -‐15 dB before cross-‐talk calibra3on. •  Ajer cross-‐talk calibra3on, residual cross-‐talk parameters are es3mated to be ~

-‐40 dB. •  Leaked power is propor3onal to cross-‐talk parameters squared.

Temporal Stability of Calibra3on Parameters

Here is a subset of all the Rosamond engineering flights taken up to end of 2012 -‐Each point represents an engineering flight over Rosamond. -‐Dashed lines represent change in calibra7on parameters. Here we show the mean observed / model ra3o in dB for each flight over the Rosamond CR array. On the next slide we show the RMS error in radiometeric calibra3on and phase calibra3on Note that other geophysical errors sources may be present (water, dirty CR, …etc).

Jan−08 Jan−09 Jan−10 Jan−11 Jan−12 Jan−13−1.5

−1

−0.5

0

0.5

1

Mea

n O

bs/M

odel

Rat

io [d

B]

Mean HH ratio [dB]: −0.272Mean VV ratio [dB]: −0.308

HHVV


0.1

0.2

0.3

RMSE

of O

bs/M

odel

Rat

io

Mean RMSE HH [dB]: 0.620Mean RMSE VV [dB]: 0.677

HHVV


2.5

5

7.5

10

Phas

e RM

S [d

eg]

Mean RMS HHVV Phase: 5.293

HH−VV Phase RMS


−0.05

−0.025

0

0.025

0.05

Co−P

ol Im

bal.

Mean f Bias: −0.002Mean f RMS: 0.028

BiasRMS

Jan−08 Jan−09 Jan−10 Jan−11 Jan−12 Jan−13−1.5

−1

−0.5

0

0.5

1

Mea

n O

bs/M

odel

Rat

io [d

B]

Mean HH ratio [dB]: −0.272Mean VV ratio [dB]: −0.308

HHVV


0.1

0.2

0.3

RMSE

of O

bs/M

odel

Rat

io

Mean RMSE HH [dB]: 0.620Mean RMSE VV [dB]: 0.677

HHVV


2.5

5

7.5

10

Phas

e RM

S [d

eg]

Mean RMS HHVV Phase: 5.293

HH−VV Phase RMS


−0.05

−0.025

0

0.025

0.05

Co−P

ol Im

bal.

Mean f Bias: −0.002Mean f RMS: 0.028

BiasRMS

Summary

•  Antenna change in spring 2011 caused: – Change in radiometric calibra3on. – Change in noise-‐equivalent sigma0.

•  UAVSAR has provided well calibrated data for more than 3 years.

Version September 25, 2012 submitted to Remote Sens. 17 of 26

A. Corner Reflector Model206

In Figure 8 we plot a diagram of a trihedral corner reflector. Consider a rectangular coordinate system207

in which the ortha-normal axes, (x, y, z), are oriented along each of the three short legs of the corner208

reflector with the origin where the three legs meet, and ˆP = Px

x + Py

y + Pz

z is the unit vector that209

points from origin of this coordinate system to the antenna phase center. Without loss of generality, we210

pick Px

Py

Pz

. Then the theoretical radar cross section for a trihedral corner reflector is given by211

[4]212

�cr

=

4⇡l4

�2

Px

+ Py

+ Pz

� 2

Px

+ Py

+ Pz

�2, (P

x

+ Py

� Pz

)

�cr

=

4⇡l4

�2

Px

Py

Px

+ Py

+ Pz

�2, (P

x

+ Py

Pz

) (15)

B. Computation of Observed Corner Reflector Response213

Using a database of surveyed corner reflector locations and the motion data, we are able to estimate the214

approximate position of each corner reflector within the single-look complex SAR data in range-azimuth215

coordinates. We extract a 64x64 chip of single-look complex (SLC) data centered on the peak pixel216

power, and oversample it by a factor of 8, then generate the oversampled CR response as the amplitude217

squared. In Figure 9 we plot an image of the oversampled HH CR response from a corner reflector on218

the Rosamond lake bed. In [6–8], two methods of computing the corner RCS are described: the “peak”219

method and the “integration” method. The “peak” method computes the corner RCS as the maximum220

of the oversampled corner reflector response times the range and azimuth resolutions. The “integration”221

method has been presented in different ways, however, they all involve summation of the oversampled222

corner reflector response over a larger region that contains all the side lobes and then subtraction of the223

estimated speckle power contained in the region. The speckle power is estimated using a region that224

does not contain the side lobes of the point target response.225

In this document, we compute the corner RCS as

�0 = �max

�

⇢

�

az

, (16)

where �max

is the maximum value of the oversampled CR response, �⇢

is the full-width at half maximum226

of the CR response in range, and �

az

is the same for the azimuth dimension. For a focused SAR image,227

these full-widths at half maximum are the range and azimuth resolutions (?? is this really true?).228

C. Estimation of Cross-Talk Parameters229

Range

Azi

muth

Oversampled HH RCS [dB]

64 128 192 256 320 384 448 512

64

128

192

256

320

384

448

512 −50

−40

−30

−20

−10

0

10

20

30

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