Polarimetry in astronomy
Experimental Astrophysics
December 8, 2014
Giorgos Leloudas
Based on lectures/slides by N. Patat, C. Keller, C. Wheeler
Outline
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General (and fun) facts about polarization
Polarization in astronomy
Mathematical background
Measuring polarization
– Dual-beam polarimeter
• Observations & relevant considerations
• (Very little on) spectropolarimetry
Some basics
• Light is a transverse wave
• In most cases we have random superposition
of many photons giving 0 net polarization
• No preferred direction
But in some cases …
• There is preferred direction. Light is polarized
• Trivia: an ideal polarizer lets 50% of the light
intensity through.
Polarization is common in nature
Examples
• What light is polarized in this picture ?
Blue sky ✔
Rainbow ✔
Clouds
✗
(not so much)
Everyday applications
Sunglasses
Photography
Visit polarization.com for more fun facts (octopus, bees, Vikings, etc)!
Experiment: sunglasses & LCD screen
Warning: do try this at home !
Sources of Polarization in the
Astrophysical context
•By electron scattering (Thomson. E.g. Solar Corona)
•By molecules scattering (Rayleigh. E.g. Earth’s atmosphere)
•By scattering small particles (Mie. E.g. Light Echoes)
•By resonant scattering (affects spectral lines only. E.g. SN)
•By dichroic absorption of aligned particles (IS polarization)
CIRCULAR
•Polarized emission in the presence
of magnetic fields (Zeeman effect)
Scattering produces linear polarization
perpendicular to the scattering plane
Examples - CMB
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BICEP2
B-mode polarization
Planck
Dust polarization
Planets
• Starlight is unpolarized but light reflected from
planets is very polarized
personally reminds me of:
First light from SPHERE imaging the dust ring around HR 4796A
Supernovae
• A powerful tool to study the asymmetries of
unresolved objects
Symmetric. Not polarized
Asymmetric. Polarized !
Do not expect spectacular numbers
• P = 0.4% for an ellipticity E = 0.9 (so 10% asymmetry)
Other examples
• AGNs
– Jets, magnetic fields,
sychnotron
• Scattering in Ly-a
blobs
• the Sun
– Zeeman effect
–…
Some typical values
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45 deg reflection off aluminum mirror: 5%
Clear blue sky: up to 75%
45 deg reflection off glass: 90%
LCD screen: 100%
Solar scattered polarization 1% to 0.001%
Exoplanet signal: 0.001%
The polarization Ellipse
• The tip of the electric vector draws an ellipse
in the plane perpendicular to the direction of
wave propagation
• Real electric field given by real part of Ē
• Intensity ~ E2
Let’s get quantitative
According to classical Wave Theory
λ
E0y
E0x
Φ2-Φ1
Maxwell Equations Solution:
(oh yes, they are linear)
Which can be rewritten as:
Which is equivalent to
From which one gets
Since
…after a bit of algebra one gets
i.e. an ellipse
Linear Polarization
Circular Polarization
Elliptical Polarization
With the following coordinate rotation
One can bring it to the canonical form:
a
b
where
RH
One can easily show that:
+ Right Handed – Left Handed
Which imply
Together with
These relations define all ellipsometric parameters and lead to the
Stokes Parameters.
The Stokes Parameters and
Stokes Vector
All Stokes parameters have the dimensions of intensity.
•Stokes parameters fully describe the polarization state of a
light beam, regardless of partial/total polarization;
• Stokes parameters describe the polarization state of the light
irrespective of its spectrum (monochromatic vs.
polychromatic);
•Stokes vectors are additive. The polarization status of a beam
resulting from the sum of two beams is described by the sum
of Stokes vectors. This is true only if there is no phase relation
between incoming beams. (Otherwise use Jones vectors).
I Intensity
U +45º preference
Q Horizontal preference
V Right Circ. preference
Back to the equations…
handedness
=I
Intensity
= U/Q
Azimuth
= V/I
Shape
Visualization
In general, and especially in the astrophysical context, light is only partially
polarized. In this case, the Stokes Parameters still give a correct representation of
the polarization state, but
So that one can introduce the polarization degree P as
Which can be separated into Linear and Circular:
In all real cases, Stokes Parameters are time averages on time ranges which are
much larger than the Electric field oscillation periods:
A totally unpolarized beam can be imagined as the superposition of two
perpendicular plane waves, with intensities and phases randomly changing on time
scales larger than the oscillation period.
Summing up
• Stokes Q:
– The difference between the amount of photons
whose electric field oscillates along the reference
direction and the direction perpendicular to it
• Stokes U:
– The difference between the amount of photons
whose electric field oscillates at 45 and 135 deg wrt
the reference direction
• Stokes V:
– right handed minus left handed circular polarization
Measuring Polarization
• This means measuring flux differences along
different electric field oscillation planes
• In principle one would be able to measure linear
polarization simply rotating a linear polarizer and
measuring the light intensity as a function of
rotation angle. In the presence of polarization
this would produce an intensity modulation, with
a period of 180º
• In practice we can do this for a limited number of
rotation angles
It can be shown that computing the I component of the S vector transformed
by a linear polarizer one obtains:
Or, in other words:
Therefore, fitting this law to the
observed f’s, one can immediately
get I, P and χ.
Why do we use dual-beam polarimeters
•Sky transparency and seeing variations hinder this method;
•This problem is reduced modulating the incoming beam with timescales faster
than the atmospheric fluctuations;
•This also implies that the detector has to be read out very fast. Typically the
detector is a photon-counter.
•All these things make this kind of instruments usable only when the photon
shot noise of the source+sky is much larger than the read-out noise.
•In most of the cases this means bright stars only.
Remarkable exceptions are polarimeters in space, where there are no transparency
fluctuations. For example WFPC2 on HST. But…
The magic Wollaston Prism
William Wollaston
The Wollaston Prims offers the possibility of measuring the intensity along two
perpendicular directions simultaneously.
The two beams are called Ordinary and Extraordinary and are separated by an angle
which is usually referred to as throw.
For astronomical polarimeters this is of the order of 10-20 arcsec.
This means that the image on the telescope focal plane is splitted in two identical images
(they differ for the polarization state), which are shifted by an amount equal to the throw.
This would generate a complete mess… unless one uses a mask, on the Focal plane, with
alternated opaque and transparent strips with a width equal to the throw.
This solves the problem of overposition between O and E images,but effectively covers
half of the field of view. Therefore, for panoramic polarimetry, two telescope pointings are
required to cover the whole field of view.
Of course, this is not a problem for single object studies (as in the case of Supernovae).
A mask is used to avoid overlap
An example from VLT-FORS1- M83 – V band
throw=22"
O
E
(The real galaxy)
To measure intensities along different planes, there are two possibilities. Either
you rotate the whole instrument(*) or…
You use a half-wave retarder.
VLT-FORS1 Half Wave Plate
(*) This would change the FOV, and requires mask/slit re-acquisition
Waveplate - from Wikipedia
• Constructed out of
birefringent material
• Refraction index
differs with light
orientation
• Can choose width to
control phase shift
of polarization
components of light
wave
A half-wave plate shifts the polarization
direction of linearly polarized light
Similarly, a quarter-wave plate converts
Linearly to circularly polarized light
(and vice versa)
Going back to the f’s
Need at least N = 2 retarder angles to solve for all unknowns. By introducing the
normalized flux differences F :
It can be shown that N = 4 and π/8 is the optimal
Choice. We thus obtain the following solution:
An example with a SN
θ=0
θ = π/8
θ = π/4
θ = 3π/8
Ordinary beam
Extraordinary beam
Error analysis and time budgets involved
• It turns out that
• To probe a polarization of 0.3% at the 3σ level
one needs a signal with SNR of 500 !
• To probe a 20mag target, FORS2 on a 8m
telescope just needs 1 sec for SNR = 28
• But for SNR = 500 one needs 350s ( x 4)!
• Spectropolarimetry even more timeconsuming
An extreme example
ESO-172
Boomerang Nebula
P~50% !
FORS1
A few words on spectropolarimetry
It is simply the same thing only that
we study the evolution of
polarization at different wavelengths
Examples from SNe
The Q-U plane