Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...

J. P. Leahy et al.: Planck pre-launch status: Expected LFI polarisation capabilityFig. 6. Plots of the components of the detector response Stokes vector W against frequency, as measured for the flight model amplifiers and OMTs.In each plot the solid line shows W I (i.e. the bandpass), scaled down by a factor of 10 for display purposes. On this scale W Q is essentiallyindistinguishable from W I and is not plotted. The cross-polar gains W U and W V are shown as dot-dashed and dotted lines, respectively. Scalingis arbitrary but self-consistent for all the curves for a given RCA. In particular the integrated CMB power for the two arms is identical, as it shouldbe for perfect calibration. Top left:LFI-19(largestη); Top right:LFI-21(typical);Bottomleft:LFI-26(largestδ); Bottom right: LFI-28(modelbandpass extension to low frequency shown as dash-triple-dotted line).We have derived the components of W(ν) fromthemeasuredOMT and model bandpass data for each RCA arm, excludingthe contribution of the optics, i.e. using J amp J OMT only.For J amp we used the bandpass estimates of Zonca et al. (2009),but with the OMT insertion loss divided out (since this is includedin J OMT ). Figure 6 plots example cases including theworst-performing OMTs.By integrating the components of W over frequency we canderive band-integrated values of η and δ, whicharelistedinTable 3. Wealsogivetheeffective ¯η and ¯δ for the differencesignal, ˜Q H ,assumingperfectcalibrationoftotalintensity.Theintegrals over the frequency band of Eq. (11)requireanassumedsource spectrum, and for the quoted figures we used the differentialCMB spectrum, η ∆T .As expected from the analysis in Sect. 4.1, thedominanteffectis rotation of the effective angle, i.e. finite ¯δ. Thefirst-orderprediction ¯δ ≈ (δ s +δ m )/2wasfoundtobeaccurateforallRCAs.There is a marked tendency for a significant position-angle rotationin the main arm, of order 1 ◦ ,whilethesidearmanglesaregenerally much closer to nominal. The overall angle for the horn¯δ, onlyexceedsourtargetaccuracyof0. ◦ 5, in two cases, LFI-19and LFI-26 (both shown in Fig. 6).LFI-19 follows the usual pattern of a large δ m with a smallerδ s in the opposite sense. On the other hand in LFI-26, δ s ≈ δ mwhich suggests that a physical misalignment of the OMT duringtesting could have been responsible.As a second-order effect, depolarisation is essentially negligiblewith all polefficiencies >99.8% and most >99.9%. Thedominant source of the small depolarisation we measured islinear-to-circular conversion, with variation of δ across the bandcontributing almost as much in some cases. Main-vs.-side misalignmentis 1 ◦ –2 ◦ for the 70 GHz OMTs, and smaller for theother bands; in all cases it a relatively minor source of depolarisation.When observing sources with non-CMB spectra, the bandintegrals will be slightly different. We evaluated this effect assumingpower law spectra with spectral index β = −3(appropriatefor synchrotron radiation) and β = 2(appropriateforthermalPage 11 of 26