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Motivation Cross-polarization Eect of IXR on SKA science Summary

SKA polarimetry specication
Do es the SKA really need to achieve its high p olarimetric purity (and sensitivity) sp ec?

Tobia Carozzi
Onsala Space Observatory Chalmers University, Sweden

AAVP workshop, Cambridge, 8 Dec 2010

Tobia Carozzi

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

SKA Polarimetry Brief
"Polarization purity
a.k.a
" is a key parameter in SKA sp ecication

cross-p olarization ratio (XPR), xp ol isolation, xp ol

discrimination, instrumental p ol, p ol leakage, cross-talk

, etc

Several SKA Key Science Projects need go o d p olarimetry

Table: SKA KSP polarization purity requirements

KSP
EoR Cosmic magnetism Pulsar timing These values are demanding!

raw PP [dB]
-30 -30 -40

institution-log SKA polarimetry

Tobia Carozzi


Motivation Cross-polarization Eect of IXR on SKA science Summary

Basic Problem of Polarimetry

The economics and technical challenges of polarimetry
Az=0
E l =0

315

Go o d p olarimetry is exp ensive Requires go o d channel isolation Low cross-p olarization over (almost) entire celestial hemisphere
225 270

22 45 67

45

90

135 180

Possible solution: improve p olarimetry in p ost-pro cessing

Calibration needs to done anyways
Is this p ossible and to what extent?

institution-log

Tobia Carozzi

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Raw Polarimetry Formulation
Basic (Jones) Measurement Equation for interferometer element is

where

V

is measured

V = Je voltages, e is Jones
1

vector and

J

is Jones

matrix. Consider the toy mo del of a go o d but leaky p olarimeter

Jtoy = G
and let the

d

d
1

|d |

1

raw

estimate of the Jones vector b e

^ eraw = V/G .
Then total relative error of the raw estimate is

^ RMS (e
where

raw

) < |d | + |V|/|V|

|V|/|V|

institution-log

is a function of

Aeff /T

sys .

Tobia Carozzi

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

XPR

The o-diagonal Jones matrix comp onents squared, i.e.

|d |2
is the

raw cross-polarization ratio

(or simply XPR)

XPR is a term in the relative error of raw p olarimetry

institution-log Tobia Carozzi SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Full Calibration Polarimetry

Can do b etter than raw calibration.

Full polarimetric calibration
1

is

^ e = J- V
This seems to give prefect solutions, rendering XPR meaningless. . . This is the conventional wisdow b ehind using the concept raw XPR for sp ecing p olarimetry.

institution-log Tobia Carozzi SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

IXR
But in reality we have noise Jones

J,

V

and an imprecise knowledge of

so there is still a nonvanishing tot. rel. err.

^ RMS(e)
where IXR is the

e

e

1

+... + IXR

2

J

J

+

V

V

,

intrinsic cross-polarization ratio
IXR =

dened as

gmax + gmin gmax - gmin

and

gmax , gmin

are max and min amplitude gains.

So the p olarimetric error dep ends on IXR also after calibration. IXR is newly dened parameter given in arXiv:0908.2330

Carozzi, Woan

institution-log

Tobia Carozzi

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Comparison of IXR and XPR
It can b e seen as an invariant XPR since any Jones matrix can b e written as

J = gU

IXR

1

IXR
1

V ,

U, V unitary

So for toy mo del, IXR=XPR But for general Jones matrix (

U, V = 1

) IXR

=XPR,

and then

raw XPR is only relevant to raw calibration, while IXR is relevant even after full calibration.
Therefore IXR is a b etter fundamental gure-of-merit for a p olarimeter than generic XPR.

institution-log SKA polarimetry

Tobia Carozzi


Motivation Cross-polarization Eect of IXR on SKA science Summary

What Should SKA Polarization Purity Be?

Dep ends on calibration & science:

If only raw calibration => IXR (or raw XPR) needs to be good If full calibration => IXR can be much less!
IXR useful in all cases

institution-log Tobia Carozzi SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Sensitivity Pulsars EoR Wideeld polarimetry

Polarimetric Antenna Sensitivity
Sensitivity can b e extended p olarimetrically

Aeff M = T T
where

M

is the eective Mueller matrix,

T

is the Stokes antenna

temp erature and telescop e

·

is a matrix/vector norm.

A related parameter is SNR of the Stokes estimate from the

S S

1

-

2

IXR

M T

S-

M

M

institution-log Tobia Carozzi SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Sensitivity Pulsars EoR Wideeld polarimetry

Polarization purity eects on Pulsar timing
Results of end-to-end Monte-Carlo simulations using dierent timing metho ds versus IXR

Metho d I:

Intensity timing
(raw)

Metho d I I:

Invariant interval
(raw)

Metho d I I I:

Matrix template matching (calibrated)

Figures by R. Paulin in

Karastergiou et al.
Tobia Carozzi

(to b e submitted 2010)

institution-log

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Sensitivity Pulsars EoR Wideeld polarimetry

EoR & polarization leakage in AA-lo
30 25

At low frequencies SKA is approximated by short dip oles in a plane. Its Jones matrix is
IXRM [dB]

20

15

10

5

J=

1

n
0

1

- mІ

-lm 1 - mІ

0

0

10

20

30

40 50 60 Angle off-axis [deg]

70

80

90

EoR contamination O-zenith, p olarized galactic

for which

IXRM =

1 1

+ nІ - nІ

foreground leaks into intensity.

Jeliў et al.
is 1

(2010)

Leaked p olarized to total p ower ratio

/IXRM

institution-log

Tobia Carozzi

SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Sensitivity Pulsars EoR Wideeld polarimetry

Dense AA Wideeld Polarimetry Issues
Dierences in E&H-plane versus D-plane
E-H planes

D-planes

This makes wideeld p olarimetry dicult and impacts on for instance Cosmic Magnetism... Suggested solution Polarization diversity by varying tile orientations

Ref. Carozzi, Maaskant (2010) Proceedings of Wide eld Science for SKA
Tobia Carozzi SKA polarimetry

institution-log


Motivation Cross-polarization Eect of IXR on SKA science Summary

Sensitivity Pulsars EoR Wideeld polarimetry

Dense AA Polarimetry Performance
Instantaneous FoV Beamforming

institution-log Tobia Carozzi SKA polarimetry


Motivation Cross-polarization Eect of IXR on SKA science Summary

Conclusions
SKA ought to have an IXR sp ec rather than raw XPR

Raw calibrated data requires good XPR Fully calibrated data requires moderate IXR
Polarization purity is imp ort for SKA science since it aects

nal data SNR (i.e. not just sensitivity) pulsar timing EoR contamination
SKA can fulll KSPs with lower IXR (or XPR) than in current sp ec!

institution-log Tobia Carozzi SKA polarimetry