1. 10 -3 versus 10 -5 polarimetry: what are the differences? or Systematic approaches to deal with systematic effects. Frans Snik Sterrewacht Leiden

2. Definitions Polarimetric sensitivity Polarimetric accuracy Polarimetric efficiency Polarimetric precision

3. 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)

4. Polarimetric accuracy Quantifies how well the measured Stokes parameters match the real ones, in the absence of noise.

5. Not a Mueller matrix, as it includes modulation and demodulation. Polarimetric accuracy transmission  1 instrumental polarization cross-talk polarization rotation related to polarimetric efficiency polarization response of photometry

6. Polarimetric accuracy zero level >> 10 -5 sensitivity level! scale

7. 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)

8. Polarimetric precision Doesn’t have any significance…

9. 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

10. Temporal modulation Achievable sensitivity depends on: Seeing (and drifts); Modulation speed; Spatial intensity gradients of target; Differential aberrations/beam wobble. Usually >>10 -5

11. 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

12. 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

13. Increasing sensitivity If All noise-like systematic effects have been eliminated; For each frame photon noise > read-out noise, then: 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! = 10 10 for 10 -5 sensitivity!

14. Increasing sensitivity HARPSpol Kochukhov et al. (2011) Snik et al. (2011) ±10 -5

15. 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

16. 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?

17. 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