Polarimetry in Astronomy Or Do you know where your photons are coming from? Elizabeth Corbett AAO.

Polarimetry in AstronomyOr

Do you know where your photons are coming from?

Elizabeth CorbettAAO

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: 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


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


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


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


• 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


• 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


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

http://www.colorado.edu/physics/2000/applets/lens.html

http://www.colorado.edu/physics/2000/applets/lens.html


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)



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



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


Dual-beam polarimetersSwitching beams


• 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


Dual-beam polarimetersSwitching beams by rotating the prism

rotate by 180º



Dual-beam polarimetersSwitching beams using a ½ wave plate

Rotated by 45º



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


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



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



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


Polarimeter

To spectrograph or imager

To TV guider

Tilted slit/dekker

Arc lamp

/2 plate

Analyser

Calcite

/4 plate


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

Date post:	21-Dec-2015
Category:	Documents
Upload:	harold-stewart
View:	216 times
Download:	0 times

Polarimetry in Astronomy Or Do you know where your photons are coming from? Elizabeth Corbett AAO.

Documents