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.
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
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: 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!
Increasing sensitivity HARPSpol 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