10-3 versus 10-5 polarimetry: what are the differences?

orSystematic approaches to deal with

systematic effects.

Frans SnikSterrewacht 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.

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rS meas = (X+ ΔX)⋅

r S in

Not a Mueller matrix, as it includes modulation and demodulation.

Polarimetric accuracy

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X =

I →I Q →I U →I V →I

I →Q Q →Q U →Q V →Q

I →U Q →U U →U V →U

I →V Q →V U →V V →V

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

transmission 1

instrumental polarization

cross-talk

polarization rotation

related topolarimetric efficiency

polarization responseof photometry

Polarimetric accuracy

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ΔX≤

− 10−2 10−2 10−2

10−3 10−2 10−2 10−2

10−3 10−2 10−2 10−2

10−3 10−2 10−2 10−2

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟

zero level>> 10-5 sensitivity level!

scale

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ΔP ≤ 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 sensitivityIf• All noise-like systematic effects have been eliminated;• For each frame photon noise > read-out noise,

then:

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σ QI ,U

I , VI( ) =

N

N=

1

N total amount of collected photo-electrons

• Adding up exposures;• Binning pixels (in a clever way);• Adding up spectral lines (in a clever way);• Better instrument transmission and efficiency;• Larger telescopes!

= 1010 for 10-5 sensitivity!

Increasing sensitivityHARPSpol

Kochukhov et al. (2011)Snik et al. (2011)

±10-5

Calibration

Create known polarized input:• rotating polarizer• rotating polarizer + rotating QWP

–misalignment and wrong retardance can be retrieved with global least-squares 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