Review of HAARP Experiment and Assessment of Ionospheric ......Third ALOS PI Symposium Kona, Hawaii...

Third ALOS PI Symposium Kona, Hawaii

November 9-13, 2009

Review of HAARP Experiment and

Assessment of Ionospheric Effects

T. L. Ainsworth1, Y. Wang1, J.-S. Lee1,2

and K.-S. Chen2

1Naval Research Laboratory, Washington DC, USA2CSRSR, National Central University, TN (ROC)

2

Objectives

•

Determine ionospheric effects on PALSAR polarimetry

•

Develop ionosphere correction methods

–

Faraday rotation compensation

•

Assess required compensation tolerances

–

Based on desired polarimetric capabilities

•

Employ SAR to measure ionosphere properties

–

High resolution ionospheric measurements

3

TEC Effects on SAR

( )∫≈path

electron xdxnTEC

Sat

ellit

e A

ltitu

de ~

700k

m

Ionosphere F2 Layer Alt. ~300km

First-Order Effects on Pol. SAR:

•

Faraday Rotation ∝

TEC Value

•

Azimuth Shifts ∝

TEC Gradient

Total Electron Content,

θ

TEC Varies Diurnally and with Solar Sunspot Cycle

Ionosphere TEC Causes

•

Refraction, θ

•

Faraday Rotation

4

HAARP Experiment Concept

•

Generate artificial “TEC hole”

in ionosphere–

Use HAARP high power HF transmitter

•

Frequency: 3-10 MHz, Max Power: ~3.6 Mw

•

Synchronize with PALSAR quad-pol collect –

Image through artificially disturbed ionosphere

•

Compare with ionosphere electron density –

Ground based measurements

–

Tomographic

electron density information

High-frequency Active Auroral

Research Program

5

Observational Difficulties

•

Coordination of experimental conditions–

HAARP HF radar schedule

–

PALSAR quad-pol imagery collects

–

Naturally occurring phenomena•

Sufficient TEC levels

•

Solar activity affects the ionosphere–

Near the minimum of the 11 year solar cycle

•

Primary problems: –

Insufficient electron density

–

Limited observational opportunities

6

Opportunistic Observations

•

Naturally occurring ionospheric irregularity

•

Serendipity, or

•

Choose a good location –

Frequent ionosphere disturbances

•

Sufficient TEC variability

–

Frequent PALSAR quad-pol collects

–

Complementary, ground based dataset•

E.g. TEC / electron density mapping

8

Tomographic

Imaging Data

Ionosphere measurements taken at HAARP show spatial and day-to-day electron density variability

Quiet Day

31 March 2007; 0718 –

0736 UTC

59 62 65 68 71

Geomagnetic Latitude Nelec

[1011

e/m3]

Disturbed Day

1 April 2007; 0757 –

0814 UTC

59 62 65 68 71

Geomagnetic Latitude Nelec

[1011

e/m3]

High-frequency Active Auroral Research Program

9Faraday Rotation

Azimuth Profile of Faraday Rotation

Irregularity

Mean = 2.98127°

Polarimetric Faraday Effect

10

Observational Outlook

•

Better opportunities in the near-term–

Solar cycle is (should be) heading toward a maximum•

Increased free electron density –

increased TEC

•

Increased TEC variability

•

Opportunistic ionosphere observations –

Good solution at specific test sites•

Assuming routine quad-pol image collection

•

HAARP concept is feasible provided–

Well coordinated data collection plan•

PALSAR quad-pol imagery, HAARP HF radar, etc.

11

Faraday Compensation

How much does TEC affect SAR polarimetry?

•

Assess polarimetric effects on derived products

•

Treat Faraday rotations as a miscalibrations

•

Can one compensate dual-pol imagery?

uncompensated

12

Faraday Effects

•

Faraday rotation affects polarimetric calibration

–

Generates non-reciprocal SAR returns

–

Circular basis: Phase of RL·LR* correlation

•

Non-unique cross-talk / Faraday separation

–

Cross-talk induces non-reciprocal returns •

Affects RL·LR* correlations

–

PALSAR: cross-talk level not an issue

13

Faraday Rotation Estimation

⎥⎦

⎤⎢⎣

⎡ΩΩ−ΩΩ

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ΩΩ−ΩΩ

=⎥⎦

⎤⎢⎣

⎡cossinsincos

cossinsincos

vvhv

hvhh

vvvh

hvhh

SSSS

OOOO

•

Estimate

Faraday rotation, Ω, in the circular basis–

Well-defined –

based on second-order statistics–

Insensitive to target orientation angles –

Insensitive to scattering mechanisms in the scene

)]([21

vvhhvhhvRL OOjOOO ++−=

)]([21

vvhhhvvhLR OOjOOO ++−=

( )444

1 ππ≤Ω≤−−=Ω with*

LRRLOOArg

14

Faraday Rotation Matrix

where γ

= tan Ω, and Ω

is the Faraday rotation angle

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

−−

−−

∝

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

ΩΩΩΩΩ−Ω−

ΩΩ−ΩΩΩΩ−

ΩΩΩΩΩΩ

Ω−ΩΩΩΩ−Ω

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

VV

VH

HV

HH

VV

VH

HV

HH

VV

VH

HV

HH

S

S

S

S

S

S

S

S

O

O

O

O

1

1

1

1

cossincossincossin

sincoscossinsincos

sincossincossincos

sinsincossincoscos

2

2

2

2

22

22

22

22

γγγ

γγγ

γγγ

γγγ

⎥⎦

⎤⎢⎣

⎡ΩΩ−ΩΩ

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ΩΩ−ΩΩ

=⎥⎦

⎤⎢⎣

⎡cossinsincos

cossinsincos

vvhv

hvhh

vvvh

hvhh

SSSS

OOOO

15

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ΩΩ−Ω+Ω

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ΩΩ−Ω+Ω

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

VVVH

HVHH

VVVH

HVHH

VVVH

HVHH

VVVH

HVHH

tttt

SSSS

rrrr

OOOO

cossinsincos

cossinsincos

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

−−−−

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∝

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−

VV

VH

HV

HH

VV

VH

HV

HH

SSSS

k

k

zuuzvuvuwwzzvwwv

OOOO

11

11

11

11

2

2

2

2

11

1

γγγγγγγγγγγγ

αα

αα

Full Calibration Model

where γ

= tan Ω, and Ω


Faraday rotations

destroy diagonal dominance of the [X][G][F] calibration matrix. γ

is not necessarily a small parameter.

X-talk, [X] Gain, [G] Faraday, [F]

T.L. Ainsworth, L. Ferro-Famil & J.-S. Lee, TGRS, vol. 44, 2006, pp. 994-1003.

16

Faraday Rotations

( )[ ]

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

−−

−−

∝Ω

1

1

1

1

2

2

2

2

γγγ

γγγ

γγγ

γγγ

F

where γ

= tan Ω, and Ω


•

Faraday rotation and cross-talk matrices are similar

•

Faraday rotations affect cross-talk calibration−

Setting z = -u = -v = w and cross-talk generates “Faraday rotation”

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∝

11

11

zuuzvuvuwwzzvwwv

X

where u, v, w

and z

are the cross-talk coefficients

Cross-talk MatrixFaraday Rotation Matrix

17

Generic Error Metrics

•

Metrics should be simple

•

Similar metrics for point and distributed targets

–

Point targets metrics

•

Apply to scattering matrix formalism

–

Distributed target metrics

•

Apply to covariance / coherency matrices

18

Point Target Error Metric•

Define a point target metric to assess impacts of Faraday rotations and other polarization errors

( )Ω= FD( )( ) ( )

( )2

2

2

2

t

t

St

S SSID

Se

tt vecvec

maxvec

max−

=

Seek for the maximum normalized errors in the target space:

Evaluated as the induced norm:

( ) ( ) ( )( )

2

22

t

t4

S4 SSAID

AIDt vec

vecmax

−=−

Canonical targets display reciprocal scattering.Observations are not reciprocal due to Faraday rotations.

( )( ) ( )

( )2

2

2

2

t

t4

St

S SSAID

Se

tt vecvec

maxvec

max−

=⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

1000

02121

0

0001

4A

Faraday correction

19

Evaluation•

The defined metric is used to evaluate the compromised polarimetric accuracy due to Faraday rotation.–

Worst case situation: quad-pol and several dual-pol modes

( )Ω− 212 cos

20

Error Evaluation

•

Cross-pol coupling increases significantly with Faraday rotation and orientation angle rotations

•

Induced cross-talk is the similar for orientation and Faraday rotations

To maintain a -20 dB measurement accuracy, the Faraday rotation should be compensated better than 3 deg, which translates to a cross-talk of -25 dB.

21

Distributed Target Metric•

Polarization synthesis determines the maximum error for all allowed combinations of transmitted and received polarizations

•

Synthesis bias is obtained from a general eigen problem,

–

where A4

restricts error maximization to reciprocal scattering

( )( ) ( )

( )vvmaxvv

vvmax HHH

vAΣAvHH

HHH

tHH 44

144

44

44

ADDΣAAΣAADDΣA

tt

t

==

This error metric represents a worst case scenario.

[ ] basis V)(H, linear

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

∝

3001

0110

0110

1003

volumeC

22

Polarization SynthesisPredicted synthesis errors for typical natural targets.

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−−

977130097

130150140

097140976

57130

571452

30452

.e.e.

e..e.

e.e..

oo

oo

oo

.j.j

.j.j

.j.j

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−

721180182

180170360

182360865

8146164

8144133

61644133

.e.e.

e..e.

e.e..

oo

oo

oo

.j.j

.j.j

.j.j

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−

−

132070640

070841160

640160383

0102615

01027113

6157113

.e.e.

e..e.

e.e..

oo

oo

oo

.j.j

.j.j

.j.j

Sample covariance matrices drawn from PALSAR imagery

Urban Target

25

Freeman-Durden Model

Even though the cross-pol power does not change, the Freeman-

Durden volume scattering is reduced to keep the model positive semi-definite.

Overall, Freeman-Durden shows more yellow, i.e. less blue.

Freeman-Durden Display: Ω

= 0°


= 10°

Volume Scattering (dB)

Double Bounce (dB) Surface Scattering (dB)

Ω = 10°

26

Freeman-Durden ModelFreeman-Durden Display: Ω

= 0°


= 20°

Even though the cross-pol power does not change, the Freeman-

Durden volume scattering is reduced to keep the model positive semi-definite.

Overall, Freeman-Durden shows more yellow, i.e. less blue.

Volume Scattering (dB)

Double Bounce (dB) Surface Scattering (dB)

Ω = 20°

27

Conclusions

•

Quad-pol PALSAR data provides precise Faraday rotation estimates–

L-band quad-pol imagery can be polarimetrically calibrated in the presence of Faraday rotations

•

Faraday effects on PALSAR polarimetry –

Surface scattering shows greatest effect, i.e. |HH+VV|–

Quad-pol imagery •

Appears to tolerate up to ~10°

of uncompensated Faraday rotation–

Freeman-Durden classification comparison–

Standard distributed targets analysis

•

Quad-pol easily compensated for Faraday rotations

–

Dual-pol imagery•

Circular transmit modes display smallest Faraday effects •

Linear transmit dual-pol modes strongly effected –

Especially for surface and double bounce scattering –

Linear dual-pol modes require better Faraday compensation

28

Thank you

29

Orientation Angle

( )[ ]

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

ΓΓΓΓ−Γ−ΓΓ−Γ−Γ

ΓΓ−Γ−

∝

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−−−

−−

=

11

11

2

2

2

2

22

22

22

22

θθθθθθθθθθθθθθθθθθ

θθθθθθ

θ

cossincossincossinsincoscossinsincossincossincossincos

sinsincossincoscos

R

where Γ

= tan θ, and θ

is the orientation angle, a rotation about the line of sight.

Rotation, Faraday and Cross-talk matrices have similar forms

( )[ ]⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−

+=

θθ

θθ

θθ

θθθ

cossin

sincos

SS

SS

cossin

sincosS

VVVH

HVHH

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∝

11

11

zuuzvuvuwwzzvwwv

X( )[ ]

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

ΓΓΓ

Γ−Γ−Γ

Γ−Γ−Γ

ΓΓ−Γ−

∝

1

1

1

1

2

2

2

2

θR ( )[ ]

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

−−

−−

∝Ω

1

1

1

1

2

2

2

2

γγγ

γγγ

γγγ

γγγ

F

Rotation Faraday Cross-talk

Review of HAARP Experiment and Assessment of Ionospheric ......Third ALOS PI Symposium Kona, Hawaii...

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Transcript of Review of HAARP Experiment and Assessment of Ionospheric ......Third ALOS PI Symposium Kona, Hawaii...