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

B. Maffei et al.: Planck pre-launch status: HFI beam expectations from the optical optimisation of the focal planeforeground signals will be observed. The remaining part of thehorn beam couples either to the sky via sidelobes or to tothe instrument through absorption ormultiplereflections.Thespillover can be defined as the overall radiative power that doesnot intercept the telescope reflectors, thus directly reaching thedetector antennas. This will result in an unwanted signal not directlyoriginating from the source of interest. It is therefore animportant parameter in assessing straylight control.The reduction of the spillover and the maximisation of thepower concentrated in the horn main beam is of great importance:not only the horn beam sidelobes have to be reduced, butthe main beam has to be as close to a Gaussian profile as possible,as a Gaussian beam does not change its shape or developsidelobes as it propagates (at least for single-mode case).In order to be consistent with the science requirements, thespillover has to be maintained to within one percent. A moredetailed requirement per band is given in Table 1. Anequivalentparameter defining the telescope illumination and the potentialstraylight contamination is called edge taper. Assuming aGaussian illumination of the secondary (M2) and primary (M1)mirrors by the horns, the edge taper defines the value of the illumination(in dB) at the edges of the mirrors. The further off-axisthe horn is with respect to the axis of the mirror, the less symmetricalthe edge taper value is for such a feedhorn position. Anaverage edge taper requirement corresponding to the spilloverrequirement is given in Table 1 for each spectral band.Thus, with a fixed telescope diameter, we need to make atrade-off between maximum resolution and spillover reduction.3.3. Optical efficiencyAssuming that we are observing the CMB radiation as a sourceand that the field of view of the detection assemblies is filled withthis radiation (extended source), the power absorbed by each detectorfrom the CMB source is:∫P = AΩɛ(ν)B (ν, T CMB ) dν (1)∆ν∆ν is the spectral bandwidth of the channel and B(ν, T CMB )isthebrightness distribution of the emission of the CMB according toPlanck’s law.The throughput, AΩ,isgivenbyn(λ) · λ 2 ,wheren(λ) = 1forasingle-modechannel(A being the effective aperture area of thefront horn, Ω the horn beam solid angle and λ the wavelength).In the case of the multi-mode channels n(λ) isadjustedtoproducethe required Ω to match the telescope aperture. This will beaddressed further in a future paper (2010).In this equation, ɛ(ν), the optical efficiency, is the only parameterremaining which can affect the amount of power receivedby the detector from the source. This will then directlyimpact the instrumental sensitivity.The optical efficiency takes into account several parametersassociated with the performance of each component forming thecold optics. It includes the detector efficiency η which is set bythe detector design and manufacture. One of the major tasks wasto optimise the optical efficiency in order to reach a requirementof ɛ = 0.25 when averaged over the spectral bandwidth and withagoalofɛ = 0.3.3.4. Focal surface curvatureThe chosen off-axis Gregorian telescope configuration is designedto accommodate the relatively large size of the focal planeFig. 2. Curvature of Planck focal surface from Thales study resultingfrom simulation of a perfect telescope. Each cross represents the theoreticallocation of the phase center of a front horn.formed by both instruments given the optical and mechanicalconstraints. The optimisation performed by Thales Alenia Spaceto reduce the averaged cross-polarisation (Dragone-Mitsugushicriteria) and minimise the straylight pickup as well as theaberration effects for each pixel resulted in an aplanatic configurationconsisting of two ellipsoidal reflectors giving a curvedfocal surface with an off-centre apex (Fargant et al. 2000). Thisshape has a pronounced slope across the focal plane and with differentorthogonal curvatures. This curved focal surface (Fig. 2)is computed assuming an ideal telescope. Each individual fronthorn has been designed such that its phase centre is located onthis theoretical focal surface (on each cross of Fig. 2) andorientedin such a way that its main beam aims at the centre of theprimary mirror.Additionally many of the single-mode detection assembliesare sensitive to polarisation (Table 7). The detectors (PSB, seeSect. 5.2) are oriented so that the telescope depolarisation effectis corrected.The real mirror surfaces, misalignments (within tolerances)and thermal effects will lead to perturbations in the focal surfaceshape, resulting in a de-focusing of the feedhorns (Tauber et al.2010a).3.5. Shadowing constraints on designBecause the focal surface is not planar, potential shadowingof one of the horn beam by an adjacent front horn could occur.This is a possibility not only between horns of the sameinstrument, but also between LFI and HFI. Studies on horn mutualcoupling and shadowing within Planck focal plane instrumentsby Thales (internal report) and then by the LFI team(D’Arcangelo et al. 2005) haveshownthatclearingeachhornbeam by +/−45 degrees respectively to its boresight axis isenough to make any shadowing effects on a given horn mainbeam pattern unnoticeable (within 1% error of the measurementsystem used).To meet the required overall sensitivity HFI needs to haveeight detection assemblies for each single-mode band dedicatedto CMB measurements (100, 143, 217 and 353 GHz). In orderto fit this number of assemblies within the focal plane, tworows of pixels for the first three spectral bands are needed. ThisPage 3 of 15