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A&A 520, A12 (2010)Fig. 9. Gaussian beam propagation between two horns, a) withoutlens,potentially a large fraction of the power can be lost; b) withalensthebeam is re-focused onto the second horn aperture.Fig. 11. Top left:HE11waveguideapertureelectricfield.Top right:horncorrugated waveguide with re-expansion for optimum matching withPSB in λ/4 cavity.Bottom: HFSSmodelofthePSBcouplingtohorn(Jones et al. 2003).Fig. 10. HFI 143 GHz channel horn coupling model with HFSS. a)Model reproducing the pixel shown in Fig. 1. b)Simulatedelectromagneticfield inside the structure.and experimental data) show that a maximum value of 90% canbe reached. This includes the losses through the lens.Modelling for the multi-mode channels has been more challenging.We did not find a unique lens that will couple all themodes in an optimal way. As confirmed through experimentalmeasurements, we have not been able to design a lens thatwill improve the coupling efficiency, because the gain for somemodes is counter-balanced by the losses through the lens forother modes. Since no solution was found on time, it has thenbeen decided not to use any lens for the multi-mode channels at545 and 857 GHz. It has to be noted that these channels will beused for high-frequency foreground removal and points sourceobservations for which sensitivity is less of an issue.Maximum efficiency will be strongly dependent on the accuracyachieved in the respective alignment of the optical components.Modelling of efficiency losses due to misalignment isalengthyprocedureevenwithsingle-modechannels.Itisevenmore complicated for few and multi-mode channels. We haveadopted an experimental approach in order to define these relativepositioning requirements. Experimental measurements havebeen performed on a 143 GHz detection assembly. Using ablackbody as a source and changing the spectral band of operation,we have been able to operate this detection assembly withvarious numbers of transmitted modes, thus in various regimesfrom single-mode to few- and then multi-mode operation.Measurements made on each configuration have shown thatamaximumtransversalmisalignmentof+/−0.3λ (x-y plane inFig. 9), where λ is the central frequency of operation, will allowthe horn coupling efficiency to be maintained within 95%of its maximum value when operated with only one or a fewmodes. A maximum misalignment of +/−0.4λ is possible whenoperated with several modes. Extrapolating these results for theworst cases of the 545 GHz detection assembly for few-modeoptics and 857 GHz detection assembly for multi-mode optics,we then found a maximum misalignment value of +/−150 micronsin the x-y plane of the horn apertures to maintain the horncoupling efficiency within 95% of its maximum value. Similarexperimental measurements have shown that the position tolerancebetween the components along the z axis (along thedetection assembly) is not as stringent. We found that a positiontolerance of +/−350 microns in the worst case scenario has tobe achieved for these optical components in order to stay within95% of the optical efficiency maximum value.Cooling down the instrument to the operating temperaturewill mainly affect the relative alignment of the three thermalstages (4 K, 1.6 K and 0.1 K) along the z axis of the detection assembly.Thermo-mechanical predictions of the whole instrumentensures that the position of these optical elements are knownwithin +/−350 microns.5.2. Detector horn coupling to bolometerThe bolometric detectors used in HFI (Holmes et al. 2008) arelocated in a λ/4 cavityattheexitofthedetectorhornwaveguide.For the spider-web bolometers (SWB − Bock et al. 1995;Yun et al. 2004), used for the unpolarised channels, crosspolarisationis not an issue and efficiency optimisation ofthe radiation coupling between the horn and the detector isthe main concern. Polarisation sensitivebolometers(PSB−Jones et al. 2003) areusedforthepolarisedchannels.PSBsaremade of two superposed linear grids orientated at 90 degrees respectivelyto each other, so that the incoming radiation is decomposedinto two orthogonal linear polarisation directions (designatedas detectors a and b). In this case, the EM field propertiesat the PSB had to be modelled carefully in order to minimise thecross-polarisation.Figure 11 shows the concept adopted to couple the radiationfrom the waveguide to the PSB. The white arrows insidethe waveguide (on the left of the figure) represent a polarisedelectric field of the HE 11 mode. We can see that these lines arecurved when reaching the edge of the waveguide. When this fieldwill be intercepted by the PSB, this curvature will create crosspolarisation.Limitation of this effect can be achieved by havinga PSB diameter slightly smaller that the waveguide diameter.A trade-off has thus to occur between PSB illumination (efficiency)and cross-polarisation. Again, we have used the softwareHFSS in order to optimise the design of the re-expansion of thehorn waveguide (such as Jones et al. 2003;andshowninFig.11Page 8 of 15
B. Maffei et al.: <strong>Planck</strong> pre-launch status: HFI beam expectations from the optical optimisation of the focal planeTable 3. HFSS simulation results for the horn-to-PSB coupling for the100 GHz polarised channel (Fig. 11).Frequency Cross-Pol Efficiency84 GHz 2.5% 98%100 GHz 3.3% 93%110 GHz 2.3% 99%Notes. Computations are for the edges and central frequencies of the100 GHz spectral band.bottom). An example of the results obtained for the 100 GHzhorn-to-PSB coupling is summarised in Table 3. Ofcoursebettervalues could be achieved if the design were optimised for asmall range of frequencies. This horn to detector coupling hadto be optimised for a 33% bandwidth in a similar manner tothe horn coupling discussed in the previous sub-section. Thesecross-polarisation and efficiency results are obtained assumingperfect components. We will see in the next section that thesevalues can be very sensitive to real hardware imperfections.No such detailed optimisation has been performed on themulti-mode channels. For the 545 and 857 GHz detector to horncoupling a simpler model has been used: we assumed that thecavity in which the detector is located behaves like a blackbody,thus, all modes are equally excited in power (Murphy et al.2010).6. FPU test results and analysisExtensive test and calibration campaigns have been performed atJPL/Caltech and Cardiff University at the component level, thenon each detection assembly and finally as an integrated instrumentat IAS. In this section we report on the relevant results andon the optical performances.6.1. Optical efficiencyThe optical efficiency is determined by measuring a known emissionfrom a source such as a blackbody (Sudiwala et al. 2000;Woodcraft et al. 2002). The detection assembly is operated inflight-like conditions, and the laboratory source radiates like theCMB (blackbody at T ∼ 3K).Theradiativepowerreceivedat the aperture of the front horn is calculated using Eq. (1).The effective detected power is calculated from previous calibrationof the detector. The overall optical efficiency is the ratiobetween detected and received powers. Because this measurementis performed on the overall detection assembly chain,the optical efficiency of each component of the chain cannot beexactly known from this measurement alone. Combinations ofmodelling and component level characterisation can give a betterpicture of the various contributions. Table 4 summarises thebest estimates of the optical efficiency for each component whenassumed to be perfect. We see that in the best case scenario, withsuch an optical configuration, the overall optical efficiency cannotbe larger than 56%. Some of these estimates are fairly robust.That is the case for the horn return loss which can be modelledand measured accurately as well as the filter stacks transmission(Ade et al. 2010). Other values cannot be known as accuratelydue to the non-ideality of the components. This is the case of theback and detector horns coupling efficiency, the detector horn tobolometer coupling efficiency and the detector efficiency. In thiscase the values given in Table 4 is the result of simulations onperfect components.Table 4. Break-down of the optical efficiencies of each component of adetection assembly.Component/coupling Av. Return Loss Av. In-band transm.Back-to-Back horn −19 dB 98.7%Filter stacks 75%Horn coupling (lens) 90%Detector Horn −19 dB 98.7%Coupling horn-detector 95%Detector efficiency 90%Total efficiency 56%Notes. Except for the filters stack transmission which has been measuredindependently, the other values are the theoretical maximumtransmission. The total gives the overall maximum optical efficiencyfor each channel assuming perfect components.Table 5. Optical efficiencies (in %) obtained from the various calibrationcampaigns (Catalano 2008).Polarised channels: 2 detectors per PSB (a and b)100-1 100-2 100-3 100-4 Av. σDet a 24.6 38.8 33.1 32.8Det b 32.8 39.8 28.7 26.7 32.2 4.1143-1 143-2 143-3 143-4 Av. σDet a 42.9 42.9 53.0 40.1Det b 38.5 44.1 46.7 37.4 43.2 3.55217-5 217-6 217-7 217-8 Av. σDet a 33.5 28.9 28.2 34.2Det b 33.8 31.3 26.2 34.6 31.3 2.7353-3 353-4 353-5 353-6 Av. σDet a 22.0 21.1 24.2 16.2Det b 25.9 22.6 23.1 15.6 21.3 2.8Total intensity channels143-5 143-6 143-7 143-8 Av. σ27.9 31.2 29.1 26.6 28.7 1.5217-1 217-2 217-3 217-4 Av. σ25.0 27.8 24.6 25.2 25.7 1.1353-1 353-2 353-7 353-8 Av. σ26.2 32.0 16.8 18.4 23.4 5.8545-1 545-2 545-3 545-4 Av. σ16.0 18.1 13.9 14.6 15.7 1.4857-1 857-2 857-3 857-4 Av. σ13.3 14.1 16.1 8.7 13.1 2.2Notes. Averages and standard deviations σ are calculated per channeltype (Polarised/total intensity − Frequency). These results represent thebest knowledge at present and caveats are explained in the correspondingsection.Table 5 summarises the measured optical efficiency of eachdetection assembly deduced from the calibration campaigns. Itis important to note that these measured values have been calculatedassuming top-hat like channel spectral transmissions withnominal bandwidth edges. Spectral measurements are still beingprocessed and a better analysis of the real optical efficiencieswill be performed and presented in a future post-launch dedicatedpaper. A preliminary analysis of these spectral data showsthat some of the bandwidths are actually narrower than the onespredicted. This will result in a lower power received by the detectorin comparison to the one assumed with Eq. (1) withatop-hat like bandwidth and nominal band edges. A more accurateanalysis should then lead to slightly better optical efficiencyvalues than the one presented in Table 5. Thediscrepanciesbetweenthe measured (Table 5) andideal(Table4) opticalefficienciesare probably due to hardware imperfections affectingPage 9 of 15
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A&A 520, E1 (2010)DOI: 10.1051/0004
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ABSTRACTThe European Space Agency
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