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Polarimetry in Astronomy 2
Polarimetry: The Basics
)cos( tkExx zE
)cos( tkE yy zE
yx EEE
Light be described in terms of two components:
Taken from Hecht (1987) “Optics”
Polarimetry in Astronomy 3
Polarimetry: The Basics
Special cases:
= 0 or nlinearly polarised light
= /2 n and Ex=Ey circularly polarised light
Unpolarised light has a well-defined E which fluctuates rapidly, hence no net polarisation is measured.
In general light is elliptically polarised
Polarimetry in Astronomy 4
Introducing: - The Stokes Vectors
• Electromagnetic radiation can be described in terms of the Stokes Vectors; I, Q, U & V.
– I - total intensity– Q & U - describing linear polarisation– V - circular polarisation
• Polarisation PA:
• Degree of Polarisation:
– For linear polarisation V=0
Q
U1tan2
1
I
VUQ 2 22 P
Polarimetry in Astronomy 5
Why Stokes Vectors?
• Easy to describe polarisations:
• Additive - e.g.
light polarisedcircular right 100% 1,0,0,1
)(90at polarisedlinearly 100% )0,0,1,1(
45at polarisedlinearly 100% 0,1,0,1
)(0at polarisedlinearly 100% (1,1,0,0)
light ed)(unpolaris Natural 0,0,0,1
o
o
o
S
S
S
S
S
WestEast
SouthNorth
)0,0,0,2()0,0,1,1()0,0,1,1(
%705.22 )0,1,1,2()0,1,0,1()0,0,1,1(
)0,0,1,1()0,0,0,9()0,0,1,10(
21
021
SS
SS
S
P
Polarimetry in Astronomy 6
Sources of Polarised Emission • Synchrotron:
– dominant radiation mechanism in the optical - radio continua of the blazar class of AGN, also seen in SNR, pulsars
– emitted by charged particles, generally electrons accelerated by a magnetic field
– produces a high degree of linear polarisation (up to 45% in some blazars)
– polarisation position angle is aligned with the E vector perpendicular to the local magnetic field
Polarimetry in Astronomy 7
• Dichroic Absorption:
– also known as interstellar polarisation
– dichroic absorbers preferentially absorb radiation with one polarisation state and transmit the orthogonal state
– due to anisotropic dust grains aligning in the presence of a magnetic field
– radiation passing through such a cloud becomes polarised with an E vector parallel to the magnetic field
Polarimetry in Astronomy 8
• Scattering:– Light can be scattered by electrons or dust– High degrees of linear polarisation can result– Polarisation PA is perpendicular to the scattering plane– Degree of polarisation depends on the scattering angle,
– Circular polarisation can result from multiple scatters from dust
100%
0%
60%
N. Manset / CFHT Polarization of Light: Basics to Instruments 9
Part IV: Polarimeters
• Polaroid-type polarimeters
• Dual-beam polarimeters
N. Manset / CFHT Polarization of Light: Basics to Instruments 10
Polaroid-type polarimeterfor linear polarimetry (I)
• Use a linear polarizer (polaroid) to measure linear polarization ... [another cool applet] Location: http://www.colorado.edu/physics/2000/applets/lens.html
• Polarization percentage and position angle:
)II(
II
IIP
max
minmax
minmax
Part IV: Polarimeters, polaroid-type
N. Manset / CFHT Polarization of Light: Basics to Instruments 11
Polaroid-type polarimeterfor linear polarimetry (II)
• Advantage: very simple to make
• Disadvantage: half of the light is cut out
• Other disadvantages: non-simultaneous measurements, cross-talk...
• Move the polaroid to 2 positions, 0º and 45º (to measure Q, then U)
Part IV: Polarimeters, polaroid-type
N. Manset / CFHT Polarization of Light: Basics to Instruments 12
Polaroid-type polarimeterfor circular polarimetry
• Polaroids are not sensitive to circular polarization, so convert circular polarization to linear first, by using a quarter-wave plate
• Polarimeter now uses a quarter-wave plate and a polaroid
• Same disadvantages as before
Part IV: Polarimeters, polaroid-type
N. Manset / CFHT Polarization of Light: Basics to Instruments 13
Dual-beam polarimetersPrinciple
• Instead of cutting out one polarization and keeping the other one (polaroid), split the 2 polarization states and keep them both
• Use a Wollaston prism as an analyzer• Disadvantages: need 2 detectors (PMTs, APDs) or
an array; end up with 2 ‘pixels’ with different gain• Solution: rotate the Wollaston or keep it fixed and
use a half-wave plate to switch the 2 beams
Part IV: Polarimeters, dual-beam type
N. Manset / CFHT Polarization of Light: Basics to Instruments 14
Dual-beam polarimetersSwitching beams
Part IV: Polarimeters, dual-beam type
• Unpolarized light: two beams have identical intensities whatever the prism’s position if the 2 pixels have the same gain
• To compensate different gains, switch the 2 beams and average the 2 measurements
N. Manset / CFHT Polarization of Light: Basics to Instruments 15
Dual-beam polarimetersSwitching beams by rotating the prism
rotate by 180º
Part IV: Polarimeters, dual-beam type
N. Manset / CFHT Polarization of Light: Basics to Instruments 16
Dual-beam polarimetersSwitching beams using a ½ wave plate
Rotated by 45º
Part IV: Polarimeters, dual-beam type
N. Manset / CFHT Polarization of Light: Basics to Instruments 18
A real circular polarimeterSemel, Donati, Rees (1993)
Quarter-wave plate, rotated at -45º and +45º
Analyser: double calcite crystal
Part IV: Polarimeters, example of circular polarimeter
N. Manset / CFHT Polarization of Light: Basics to Instruments 19
A real circular polarimeterfree from gain (g) and atmospheric transmission () variation effects
• First measurement with quarter-wave plate at -45º, signal in the (r)ight and (l)eft beams:
• Second measurement with quarter-wave plate at +45º, signal in the (r)ight and (l)eft beams:
• Measurements of the signals:
rl SS 11 ,
rl SS 22 ,
)()(
)()(
22222222
11111111
VIgSVIgS
VIgSVIgSrrll
rrll
Part IV: Polarimeters, example of circular polarimeter
N. Manset / CFHT Polarization of Light: Basics to Instruments 20
A real circular polarimeterfree from gain and atmospheric transmission variation effects
• Build a ratio of measured signals which is free of gain and variable atmospheric transmission effects:
1for 2
1
2
11
4
1
2
2
1
1
21211221
2112
1
2
2
1
VI
V
I
VF
VVVIVIII
VIVI
S
S
S
SF
r
r
l
l
average of the 2 measurements
Part IV: Polarimeters, example of circular polarimeter
N. Manset / CFHT Polarization of Light: Basics to Instruments 21
Polarimeters - Summary• 2 types:
– polaroid-type: easy to make but ½ light is lost, and affected by variable atmospheric transmission
– dual-beam type: no light lost but affected by gain differences and variable transmission problems
• Linear polarimetry: – analyzer, rotatable– analyzer + half-wave plate
• Circular polarimetry:– analyzer + quarter-wave plate
2 positions minimum
1 position minimum
Part IV: Polarimeters, summary
Polarimetry in Astronomy 22
Polarimeter
To spectrograph or imager
To TV guider
Tilted slit/dekker
Arc lamp
/2 plate
Analyser
Calcite
/4 plate
Polarimetry in Astronomy 23
Summary
• Polarimetry provides information on where your photons originated– Have they been scattered?
– Have they been through dust?
– Have they (perhaps) come from a jet?
• Important for inclination dependent systems - eg AGN, YSO
• “Not as hard as it used to be” - easy data reduction
• But - very “photon hungry”
– so for a P~0.1% you need SNR ~1400 or 2E6 photons!
SNRP
2100