Image instabilities and polarization cross-talk

Abstract

We expand on our previous study of the impact of atmospheric seeing on polarization cross-talk, and show how the formalism that was developed in that work can be applied to treat the case of spatial modulators of polarization. Beside formally demonstrating how the problem of cross-talk is fully eliminated in such devices, we also gain insight on the meaning of polarimetric noise of temporal modulation schemes in the limit of very high modulation frequency. We also describe the problem of spectrograph instabilities, and how the spectral gradients that are naturally associated with a line spectrum feed into the problem of polarimetric errors induced by mechanical vibrations, thermal drifts, and pointing jitter. Finally, we show how this formalism can be used to estimate the contribution of polarization cross-talk to the errors on the elements of the 4$\times$4 Stokes response matrix, for the purpose of producing realistic error budgets for polarimetric instrumentation.

Figures (2)

• Figure 1: Polarization modulation errors induced by a "jitter" power spectrum $1/\nu^{1/2}$, in the presence of Stokes vector gradients in the incoming signal. In this example, the PSD of the jitter motion, $S(\nu)$, ranges between 0.01 Hz and 1 kHz, with a rms amplitude of 1 arcsec; the polarization modulator is a simple linear retarder with $150^\circ$ of retardance, continuously rotating over the modulation cycle consisting of 8 states; the integration time is $T=8$ s, with a camera duty cycle of 100%; finally, we assumed the optimal demodulation of the signals in a dual-beam polarimeter design. The normalized Stokes gradient vector is indicated in the plots, and is expressed in units of arcsec$^{-1}$. It describes a worst-case scenario for solar polarimetric observations, with an intensity contrast of 20% over the solar-granulation length scale, and assuming 10% linear polarization and 20% circular polarization. In this example, the linear polarization is assumed to be completely folded into Stokes $Q$, while Stokes $U$ is set to zero. Left: total modulation polarimetric errors; Right: polarization cross-talk errors only. The different curve styles indicate different Stokes parameters: $Q$ (dash), $U$ (dot-dash), $V$ (dash-triple-dot). The red curves in the left panel show the limit case of a spatial modulator (i.e., all 8 modulation states are acquired simultaneously; see Eq. (\ref{['eq:spat_error']})). We note the presence in both panels of Stokes-$U$ polarization cross-talk despite having assumed Stokes $U$ and its gradient in the signal to be zero. This explains the absence of a corresponding diagonal (spatial modulator) contribution in the left panel, and the fact that the Stokes-$U$ errors are exactly the same in the two panels, and completely due to polarization cross-talk from the non-zero Stokes parameters $Q$ and $V$.
• Figure 2: Top two rows: Example of spectrally resolved Stokes profiles of a narrow line (FWHM $\sim 6.3$ pm), observed with a resolving power of 200 000 (2-px critical-sampling), and assuming maximum linear polarization of 10% and circular polarization of 30%. The spectral gradients reported inside the panels are obtained through Eq. (\ref{['eq:del_beta_R']}), and must be used in Eq. (\ref{['eq:error']}) to estimate the corresponding polarimetric cross-talk errors. Bottom row: (left) modeled PSD of the image jitter at the detector in the spectral direction, delivering a target 1/8 px rms DW22; (right) polarization cross-talk errors induced by the same PSD, for a spectrograph configuration representing the observation of the synthetic Stokes profiles shown at the top, assuming a total integration time of 10 s and a 10-state modulation cycle.)