Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.atnf.csiro.au/research/radio-school/2010/lectures/DMcC-pol_lecture.pdf Äàòà èçìåíåíèÿ: Thu Sep 30 08:37:50 2010 Äàòà èíäåêñèðîâàíèÿ: Mon Feb 14 00:27:18 2011 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

VLA @ 8.5 GHz B-vectors

Perley & Carilli (1996)

10 kpc

Polarimetry
Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September 2010

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Thursday, 30 September 2010


Electro-magnetic waves are polarized
E
S = c/4 (E â H)

H

·

S

E/M waves have direction, amplitude, frequency and polarization

Poynting vector S = c/4 (E â H)
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Outline of lecture
· · · · ·
Thursday, 30 September 2010

Polarization - what is it? How is it described Origins of polarized light How is it important to astrophysics How is it measured

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Polarized waves: linear

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Polarized waves: linear

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... at any angle


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or Circular - LCP, RCP
Right

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or Circular - LCP, RCP
Right

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or Circular - LCP, RCP
Right

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or Circular - LCP, RCP
Left Right

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IEEE Standard 211, 1969

IAU resolution, 1973

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Linear as sum of circulars

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Linear as sum of circulars

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Other combinations
· ·
The sum of two circular waves of unequal amplitude will have elliptical polarization. The sum of two orthogonal linears with phase difference 0 < < /2 will also have elliptical polarization.

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Polarization ellipse
y




Ex


Ey x

· · · · ·

tan = Ey / Ex tan 2 = tan 2 cos sin 2 = sin 2 sin is the position angle is the ellipticity

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Stokes description
· ·
Defined by George Stokes in 1852 Adopted for astronomy by Chandrasehkar (1949) in the solution of radiative transfer problems.

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Stokes parameters
· · · · · ·
For monochromatic waves I : total intensity Q : linear U : linear V : circular I2 = Q2 + U2 + V2

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Stokes parameters
· · · · · ·
For monochromatic waves I : total intensity Q : linear U : linear V : circular I2 = Q2 + U2 + V2

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Linear : Q and U
>0 <0 >0 <0

Q
(U = 0)
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U
(Q = 0)


Linear : Q and U
Q>0 Q<0 Q<0 U<0 Q<0 U>0
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U>0

U<0 U>0

Q>0


The PoincarÈ sphere

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The PoincarÈ sphere

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Partial polarization
·
Two monochromatic signals summed:
different frequencies different polarization ellipses

· ·

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Partial polarization
·
Two monochromatic signals summed:
different frequencies different polarization ellipses

· ·

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Pancharatnam's extension
V -U Q U -V
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S -Q

· · · ·

Radius represents I S = (Q,U,V) |S| I Unpolarized radiation (I - S) at centre .


Stokes parameters
· · · · · ·
For finite bandwidth radiation I : total intensity Q : linear U : linear V : circular I2 Q2 + U2 + V2

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Polarized light

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Polarized light
·
Loss of symmetry

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Polarized light
· ·
Loss of symmetry Polarized radiation

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Polarized light
· · ·
Loss of symmetry Polarized radiation Polarization-dependent propagation

· · ·

reflection scattering birefringence
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Scattering
· · ·
Light from the day time sky is sun light "Rayleigh scattered" by molecules in the atmosphere. Sky light is polarized, maximally at 90 degrees to the sun. The CMB is expected to be partially polarized because of Thompson scattering

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Birefringence
Birefringence occurs when light passes through anisotropic material whose refractive index differs for the two polarization modes.

Linear modes birefringent
Thursday, 30 September 2010

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Circular modes birefringent


Zeeman

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Synchrotron
+

a

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Synchrotron
+

a

-

a
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Synchrotron
+

a

a
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+

-

B


Faraday rotation

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Faraday rotation
Magnetised plasmas are birefringent: the two circular modes have refractive index dependent on the parallel component of the magnetic field, the electron density, and the wave frequency. The relative phase of the two modes changes along the propagation path, and so does the position angle of the resultant linearly polarized radiation. = RM
2

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Thursday, 30 September 2010


Faraday rotation
Magnetised plasmas are birefringent: the two circular modes have refractive index dependent on the parallel component of the magnetic field, the electron density, and the wave frequency. The relative phase of the two modes changes along the propagation path, and so does the position angle of the resultant linearly polarized radiation. = RM
2

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How is it measured?

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How is it measured?
Measures Ey

Measures Ex

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How is it measured?
Measures Ey

Measures Ex

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How is it measured?
Measures Ey

Measures Ex

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Imaging
· ·
I, Q, U and V are equivalent for aperture synthesis imaging, but for the possibility (certainty) of negative Q, U,V. We can define and measure visibilities for each of the Stokes quantities: for antennas p and q : Ex2 ExpExq , Ex Ey ExpEyq , etc

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Mars at 22GHz

credit: Myers/Perley, NRAO 27
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Mars at 22GHz
Q U

credit: Myers/Perley, NRAO 27
Thursday, 30 September 2010


Why is it so difficult?
· · ·
Depolarization leads to weak signals Conceptual difficulties - it is complicated Instrumental effects can be significant and difficult to separate from the signal

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Instrumental imperfections
· · ·
Leakage - a little Ex detected in y-feed, ... phase errors (in general, complex gain variations) polarization response varies within the beam

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Jones calculus
vx vy
Rec

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Jones calculus
vx vy
Rec

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Mueller calculus
Correlate
Rec

Measured visibilities

Rec

=

4 x 4 matrix

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References
· · · · · · ·
Radhakrishnan. Polarisation. URSI proceedings (1990) pp. 34 Hamaker et al. Understanding radio polarimetry. I. Mathematical foundations. Astronomy and Astrophysics Supplement (1996) vol. 117 pp. 137 Sault et al. Understanding radio polarimetry. II. Instrumental calibration of an interferometer array. Astronomy and Astrophysics Supplement (1996) vol. 117 pp. 149 Hamaker et al. Understanding radio polarimetry. III. Interpreting the IAU/ IEEE definitions of the Stokes parameters. Astronomy and Astrophysics Supplement (1996) vol. 117 pp. 161 Heiles et al. Mueller Matrix Parameters for Radio Telescopes and Their Observational Determination. The Publications of the Astronomical Society of the Pacific (2001) vol. 113 pp. 1274 Born and Wolf: `Principle of Optics', Chapters 1 and 10 Presentations from previous Synthesis Schools (Ohja, 2003; Perley 2006

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Polarisation a tutorial by V. Radhakrishnan
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