Polarimetry. Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September kpc. 8.5 GHz B-vectors Perley & Carilli (1996)

Transcription

1 8.5 GHz B-vectors Perley & Carilli (1996) 10 kpc Polarimetry Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September

2 Electro-magnetic waves are polarized E H S = c/4π (E H) S E/M waves have direction, amplitude, frequency and polarization Poynting vector S = c/4π (E H) 2

3 Outline of lecture Polarization - what is it? How is it described Origins of polarized light How is it important to astrophysics How is it measured 3

4 Polarized waves: linear 4

5 Polarized waves: linear 4

6 ... at any angle ψ ψ 5

7 or Circular - LCP, RCP Right 6

8 or Circular - LCP, RCP Right 6

9 or Circular - LCP, RCP Right 6

10 or Circular - LCP, RCP Left Right 6

11 IEEE Standard 211, 1969 IAU resolution,

12 Linear as sum of circulars 8

13 Linear as sum of circulars 8

14 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 < δ < π/2 will also have elliptical polarization. 9

15 Polarization ellipse y Ex tan α = Ey / Ex η ξ tan 2ψ = tan 2α cos δ χ α ψ Ey x sin 2 χ = sin 2α sin δ ψ is the position angle χ is the ellipticity 10

16 Stokes description Defined by George Stokes in 1852 Adopted for astronomy by Chandrasehkar (1949) in the solution of radiative transfer problems. 11

17 Stokes parameters For monochromatic waves I : total intensity Q : linear U : linear V : circular I2 = Q 2 + U 2 + V 2 12

18 Stokes parameters For monochromatic waves I : total intensity Q : linear U : linear V : circular I2 = Q 2 + U 2 + V 2 12

19 Linear: Q and U > 0 > 0 < 0 < 0 Q (U = 0) U (Q = 0) 13

20 Linear: Q and U Q > 0 U > 0 U < 0 Q < 0 Q < 0 Q > 0 U < 0 U > 0 Q < 0 U > 0 14

21 The Poincaré sphere 15

22 The Poincaré sphere 15

23 Partial polarization Two monochromatic signals summed: different frequencies different polarization ellipses 16

24 Partial polarization Two monochromatic signals summed: different frequencies different polarization ellipses 16

25 Pancharatnam s extension V S -U Q -Q U Radius represents I S = (Q,U,V) S I Unpolarized radiation (I - S) at centre. -V 17

26 Stokes parameters For finite bandwidth radiation I : total intensity Q : linear U : linear V : circular I 2 Q 2 + U 2 + V 2 18

27 Polarized light 19

28 Polarized light Loss of symmetry 19

29 Polarized light Loss of symmetry Polarized radiation 19

30 Polarized light Loss of symmetry Polarized radiation Polarization-dependent propagation reflection scattering birefringence 19

31 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 20

32 Birefringence Birefringence occurs when light passes through anisotropic material whose refractive index differs for the two polarization modes. Linear modes birefringent Circular modes birefringent 21

33 Zeeman 22

34 Synchrotron - + a 23

35 Synchrotron - + a - a 23

36 Synchrotron - + a - + B a 23

37 Faraday rotation 24

38 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 ψ of the resultant linearly polarized radiation. ψ = RM λ 2 24

39 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 ψ of the resultant linearly polarized radiation. ψ = RM λ 2 24

40 How is it measured? 25

41 How is it measured? Measures Ey Measures Ex 25

42 How is it measured? Measures Ey Measures Ex 25

43 How is it measured? Measures Ey Measures Ex 25

44 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 : E x2 E xp E xq, E x E y E xp E yq, etc 26

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

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

47 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 28

48 Instrumental imperfections Leakage - a little E x detected in y-feed,... phase errors (in general, complex gain variations) polarization response varies within the beam 29

49 Jones calculus v x v y Rec 30

50 Jones calculus v x v y Rec 30

51 Mueller calculus Measured visibilities Correlate Rec Rec = 4 x 4 matrix 31

52 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 Born and Wolf: Principle of Optics, Chapters 1 and 10 Presentations from previous Synthesis Schools (Ohja, 2003; Perley

53 Polarisation a tutorial by V. Radhakrishnan 33