10-3 versus 10-5 polarimetry:
what are the differences?
or
Systematic approaches to deal with
systematic effects.
Frans Snik
Sterrewacht Leiden
Definitions
•
•
•
•
Polarimetric sensitivity
Polarimetric accuracy
Polarimetric efficiency
Polarimetric precision
Polarimetric sensitivity
The noise level in Q/I, U/I, V/I
above which a polarization signal can
be detected.
In astronomy: signals <1%
 polarimetric sensitivity:
10-3 – 10-5 (or better)
Polarimetric accuracy
Quantifies how well the measured
Stokes parameters match the real
ones, in the absence of noise.
r
r
Smeas  (X  X) Sin

Polarimetric accuracy
transmission 1
polarization rotation
polarization response
of photometry
I I Q I U I V I 


I Q Q Q U Q V Q

X
I U Q U U U V U 


I V Q V U V V V 
instrumental
polarization
Not
a Mueller
matrix, as it includes
related to
polarimetric efficiency
cross-talk
modulation and demodulation.
Polarimetric accuracy
 
 3
10

X 
103
 3
10
2
10
2
10
102
2
10
2
10
2
10
102
2
10
10 
2 
10 
102 
2 
10 
2
scale

zero level
>> 10-5 sensitivity level!
P  0.0010.01 P
Polarimetric efficiency
Describes how efficiently the Stokes
parameters Q, U, V are measured
by employing a certain
(de)modulation scheme.
 1/[susceptibility to noise in
demodulated Q/I, U/I, V/I]
del Toro Iniesta & Collados, Appl.Opt. 39 (2000)
Polarimetric precision
Doesn’t have any significance…
Temporal modulation
Advantages:
• All measurements with one optical/detector system.
Limitations:
• Susceptible to all variability in time:
– seeing
– drifts
Solution:
Go faster than the seeing: ~kHz.
• FLCs/PEM + fast/demodulating detector
Temporal modulation
Achievable sensitivity depends on:
• Seeing (and drifts);
• Modulation speed;
• Spatial intensity gradients of target;
• Differential aberrations/beam wobble.
Usually >>10-5
Spatial modulation
Advantages:
• All measurements at the same time.
– beam-splitter(s)/micropolarizers
Limitations:
• Susceptible to differential effects between the
beams.
– transmission differences
– differential aberrations
– limited flat-fielding accuracy
Never better than 10-3
Dual-beam polarimetry
“spatio-temporal modulation”
“beam exchange”
Best of both worlds:
Sufficient redundancy to cancel out degrading
differential effects (to first order).
– double difference
– double ratio
Can get down to 10-6
Increasing sensitivity
If
• All noise-like systematic effects have been eliminated;
• For each frame photon noise > read-out noise,
then:

 , ,
Q U V
I I I

N
1


N
N
total amount of
collected photo-electrons
= 1010 for 10-5 sensitivity!
• Adding up exposures;
• Binning pixels (in a clever way);
• Adding up spectral lines (in a clever way);
• Better instrument transmission and efficiency;
• Larger telescopes!
Increasing sensitivity
HARPSpol
±10-5
Kochukhov et al. (2011)
Snik et al. (2011)
Calibration
Create known polarized input:
• rotating polarizer
• rotating polarizer + rotating QWP
–misalignment and wrong retardance
can be retrieved with global leastsquares method
• standard stars
Calibration
• What does really limit calibration with
calibration optics?
• How to quantify calibration accuracy?
• How often does one need to calibrate?
• How to calibrate large-aperture telescopes?
• How stable are standard stars?
• How to efficiently combine with models/lab
measurements?
Systematic effects that (still) limit
polarimetric performance
•
•
•
•
Polarized fringes
Polarized ghosts
Higher-order effects of dual-beam method
Surprising interactions
– e.g.: coupling of instrumental polarization with bias drift
and detector non-linearity
• Polarized diffraction (segmented mirrors!)
• System-specific effects (e.g. ZIMPOL detector)
 Error budgeting approach