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J. A. Tauber et al.: Planck pre-launch status: The optical systemto recover the beam shapes to sub-% accuracy in integratedpower.3. The determination of the angle of the principal plane of polarisationfor each detector. Two aspects must be consideredthat lead to different classes of systematic effects: relativeand absolute calibration. Relative calibration will bederived from Planck data alone by fitting cross-polarizationand polarizer angles in the map making equation. Any polarizedregion in the sky and in particular the high signalabout the Galactic plane will be used. Initial studies haveshown we can expect a precision around 1 ◦ for the polarizerorientations, and superior to 1% for cross-polarization leakage.More details about the method will be given in a forthcomingpaper.For absolute angle determination, the main calibrator is theCrab nebula (Tau A, NGC 1952), a supernova remnant ofintense, stable, and known polarization. Dedicated observationsat the IRAM 30 m telescope were conducted (Aumontet al. 2010) tomaptheCrab’spolarizationat86GHzwithhigh precision (∼0.3 ◦ orientation uncertainty, and ∼2% fractionalpolarisation uncertainty). Based on these maps and extrapolationof the synchrotron electromagnetic spectrum toPlanck frequencies (Macías-Pérez et al. 2010), it is possibleto construct an estimate of the signal measured by Planckif the detectors have their nominal orientation and crosspolarization.A maximum likelihood fit of the difference betweenthis estimate and the measured Planck signal providesthe true polarization properties of the detectors. Additionalinformation may be provided by other measurements of theCrab by SCUBA at 353 GHz and from observations of a fractionof the Galactic plane by BICEP at 100 and 150 GHz.An analysis of the accuracy achievable by the LFI channelsis made in Leahy et al. (2010).11. ConclusionsThe complexity of the Planck payload, and the low temperaturesachieved by the optical elements and detectors, have meantthat no end-to-end measurement of the optical response could bemade that fully represents the in-flight situation. The on-groundcharacterisation of the Planck optics was indeed based on multiplemeasurements of both qualification and flight models at feedhorn,reflector, and telescope level.Using a variety of analytical techniques, all the subsystemlevelmeasurements have been combined into a complete set ofestimated in-flight performances and associated uncertainties.The ground-based analyses have allowed us to conclude that:– The major characteristics of the main beams are within ourrequirements (Sect. 4).– The predicted uncertainty of the alignment is too large to usethe predicted beam shapes directly for calibration (Sect. 5).The shapes of the main beams will instead be measured inflightusing planets.– The reliability of the GRASP models of the beam shapes hasbeen verified to high accuracy (Sect. 6).– The range of potential misalignments is such that the inflightmeasurements can be used to correlate the GRASPbeam models to high accuracy (Sect. 7). The optimisedmodel can be used to extend the beam shape knowledgeto levels far below those directly measurable in-flight. Thisknowledge will be used to measure effects such as Galacticstraylight.– Anumberofpotentialsystematiceffects have been shownto be below significance level (straylight produced bySolar System sources, grating lobes, self-emission). Others(Galactic straylight, dust) have been modelled to assess theirpotential effects.It can be concluded that the ground activities have providedan adequate starting point for the in-flight optical calibrationactivities (outlined in Sect. 10), which will complement them.The current expectation is that with the combination of groundknowledge and flight measurements, Planck will be able toachieve its main requirements in terms of optical knowledge.Acknowledgements. The study, development, testing and data analysis of thecombined Planck optical system has been carried out under the leadership ofESA in close collaboration with industry (Thales Alenia Space (Cannes, France)and Ticra (Copenhagen), and the optical experts of the LFI, HFI and DK-PlanckConsortia. During the development, Thales Alenia Space was responsible for theoverall payload system, and in particular for the design, manufacture and test ofthe telescope support structure, the baffle andtheV-grooves.ESA,jointlywiththe Danish National Space Institute was responsible for the design and manufactureof the two reflectors. All of the cryogenic testing at reflector and telescopelevel was under the responsibility of ESA. J.T. wishes to emphasize especiallythe crucial, difficult, and very extensive modelling and data analysis ofthe system-level optics carried out by D. Dubruel, P. Nielsen, P. Martin, and R.Daddato, which have been crucial building blocks for our current understandingof the optical performance of Planck. Similarlyimportantefforts have been carriedout at instrument level and are described in Sandri et al. (2010) andMaffeiet al. (2010).Appendix A: Telescope definitionThe Planck telescope is defined by the relative location of thebest-fit ellipsoids defining the reflectors (see Table 4), and therelative location of the focal plane with respect to one of the reflectors(taken as the SR). Figure A.1 shows the relevant parametersfor the design configuration, and Table A.1 shows the correspondingvalues for the nominal alignment in-flight.Appendix B: Emissivity characterisationThe emissivity of the reflectors contributes directly to thebackground heat load on the detectors. However, at mm andsubmm wavelengths, the emissivity of a metallic surface dependsquite strongly on wavelength, temperature, and the characteristicsof the metal (purity, thickness). Thin film effects mayalso set in: the thickness of the coating of the Planck reflectorscorresponds to only a few skin depths. Measurements ofthis characteristic at low temperatures and short wavelengthsare rare as they are quite difficult and their accuracy is poorfor low emissivity levels. Nonetheless, some early measurementsof samples of the Herschel telescope confirm strong dependencewith temperature (Fischer et al. 2005). Although thecoating of the Herschel telescope is almost identical to thatof Planck, theunderlyingmaterialisdifferent (CFRP vs. sinteredsilicon carbide), and therefore specific measurements wereneeded. Reflection loss measurements were carried out using aresonator at the Applied Physics Institute in Nizhny-Novgorod(Parshin & Klooster 2008). Results are reproduced in Fig. B.1.Aconservativehypothesisthatreflectionlossisequivalenttotheemissivity of the clean reflectors would lead us to estimate thelatter as roughly 0.05%, 0.1%, 0.15%, and 0.2% at a temperatureof 120 K and frequencies of 50 GHz, 140 GHz, 340 GHz,and 500 GHz respectively. The emissivity must be lower at thein-flight temperatures of the reflectors (∼40 K), by as much asPage 19 of 22
A&A 520, A2 (2010)Fig. A.1. Dimensioning and relative positioning of the two reflectors with respect to the telescope coordinate system (see Fig. 3). O M1 and O M2are the vertices of the ellipsoidal surfaces of the PR and SR, respectively, and O RDP is the origin of the coordinate system defining the location ofthe focal plane. The corresponding (X, Y, Z)coordinatesystemsforeachreflector,focalplane,andtelescopearemarkedonthediagram.Thepointlabelled I is a fiducial point used to define the relative position of the SR andPR.Thegeometrydepictedherecorresponds to the design telescope;corresponding values for the in-flight nominal alignment are given in Table A.1.Table A.1. Planck telescope parameters.Notes. (a) See also Fig. A.1.Parameter a Design value Nominal in-flight valueAngle between Z M1 and Z M2 axis (deg) 10.1 10.0497Distance between O M1 and I (mm) 481.737 480.207Distance between I and O M2 (mm) 706.027 707.631Decentre of focal plane with respect to X M2 (mm) –108.42 –108.889Decentre of focal plane with respect to Z M2 (mm) –1026.83 –1024.184Angle of focal plane (X RDP )withrespecttonormal(deg) –21.27 –21.358Page 20 of 22
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