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Optical Characterization of the Keck Array Polarimeter at the South Pole Halpern, Mark Sep 24, 2012

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Optical Characterization of the Keck Array Polarimeter atthe South PoleA. G. Vieregga, P. A. R. Adeb, R. Aikinc, C. Bischoffa, J. J. Bockc,d, J. A. Bonettid,K. J. Bradforda, J. A. Brevikc, C. D. Dowellc,d, L. Dubande, J. P. Filippinic, S. Fliescherf,S. R. Golwalac, M. S. Gordona, M. Halperng, G. Hiltonh, V. V. Hristovc, K. Irwinh,S. Kernasovskiyi, J. M. Kovaca, C. L. Kuoi, E. Leitchj, M. Luekerc, T. Montroyk,C. B. Netterfieldl, H. T. Nguyenc,d, R. O?Brientc,d, R. W. Ogburn IVi, C. Prykef, J. E. Ruhlk,M. Runyanc, R. Schwarzf, C. Sheehyf,j, Z. Staniszewskic,d, R. Sudiwalab, G. Teplyc, J. Tolani,A. D. Turnerd, P. Wilsond, and C. L. WongaaHarvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138,USA;bDept. of Physics and Astronomy, University of Wales, Cardiff, CF24 3YB, Wales, UK;cCalifornia Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA;dJet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109, USA;eService des Basses Tempratures, DRFMC, CEA-Grenoble, 17 rue des Martyrs,38054 Grenoble Cedex 9, France;fSchool of Physics & Astronomy, University of Minnesota, 116 Church Street S.E.,Minneapolis, MN 55455, USA;gDepartment of Physics & Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver, BC V6T1Z1, Canada;hNIST Quantum Devices Group, 325 Broadway, Boulder, CO 80305, USA;iStanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA;jUniversity of Chicago, KICP, 933 E. 56th St., Chicago, IL 60637, USA;kPhysics Department, Case Western Reserve University, Cleveland, OH 44106, USA;lDepartment of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada;ABSTRACTThe Keck Array (Spud) is a set of microwave polarimeters that observes from the South Pole at degree angularscales in search of a signature of Inflation imprinted as B-mode polarization in the Cosmic Microwave Background(CMB). The first three Keck Array receivers were deployed during the 2010-2011 Austral summer, followed bytwo new receivers in the 2011-2012 summer season, completing the full five-receiver array. All five receivers arecurrently observing at 150 GHz. The Keck Array employs the field-proven Bicep/Bicep2 strategy of usingsmall, cold, on-axis refractive optics, providing excellent control of systematics while maintaining a large fieldof view. This design allows for full characterization of far-field optical performance using microwave sources onthe ground. We describe our efforts to characterize the main beam shape and beam shape mismatch betweenco-located orthogonally-polarized detector pairs, and discuss the implications of measured differential beamparameters on temperature to polarization leakage in CMB analysis.Keywords: Cosmic Microwave Background, polarization, Inflation, The Keck ArraySend correspondence to A. G. Vieregg, 60 Garden Street, MS 42, Cambridge, MA 02138 USA, E-mail:avieregg@cfa.harvard.eduMillimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VI, edited by Wayne S. Holland, Jonas Zmuidzinas, Proc. of SPIE Vol. 8452, 845226 ? 2012 SPIE ? CCC code: 0277-786X/12/$18 ? doi: 10.1117/12.926639Proc. of SPIE Vol. 8452  845226-1Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms1. INTRODUCTIONCosmological Inflation is a theory that describes the entire observable Universe as a microscopic volume that un-derwent violent, exponential expansion during the first fraction of a second. Inflation is supported by the flatnessand extreme uniformity of the Universe observed through measurements of the Cosmic Microwave Background(CMB).1,2 Measurements of the polarization of the CMB could prove to be an impressive tool for probing theepoch of Inflation. A generic prediction of Inflation is the production of a Cosmic Gravitational-Wave Back-ground, which in turn would imprint a faint but unique signature in the polarization of the CMB that has acurl component.3,4 This curl component of the polarization field is commonly called B-mode polarization, whilethe curl-free component, dominated by production due to density fluctuations at the time of last scattering, iscalled E-mode polarization. The strength of the B-mode polarization signature depends on the energy scale ofInflation, and would be detectable if Inflation occurred near the energy scale at which the fundamental forcesunify (? 1016 GeV).The Keck Array, also called Spud, is a set of five degree-scale microwave polarimeters that is currentlyobserving the CMB from the Martin A. Pomerantz Observatory at the South Pole in search of a B-modepolarization signature from Inflation.5 Each of the five receivers has 512 Transition Edge Sensor (TES) detectors,16 of which are dark, leaving 496 detectors that are coupled to planar arrays of slot antennas, for a total of2480 optical detectors in the entire instrument. Receivers utilize a compact, on-axis refracting telescope design.The first three Keck Array receivers were deployed during the 2010-2011 Austral summer and two newreceivers followed in the 2011-2012 deployment season. The first season of observation with the full five-receiverarray is currently underway, with all receivers observing at 150 GHz. The modular design of the Keck Arrayallows for future upgrades to include replacement of individual receivers to provide additional frequency coverageat 100 GHz and 220 GHz. The Keck Array leverages field-proven techniques employed for the Bicep andBicep2 telescopes, but with a vastly increased number of detectors, leading to increased sensitivity to the tinyInflationary B-mode signal. The current upper limit on the B-mode amplitude in the CMB is set by the KeckArray?s predecessor experiment, Bicep,6,7 and corresponds to r < 0.72 at 95% confidence level, where r is thetensor-to-scalar ratio. The Keck Array aims to reach a sensitivity corresponding to r = 0.01, where gravitationallensing of E-modes into B-modes should begin to be comparable in strength to the Inflationary signal.As sensitivity dramatically improves with each generation of experiments, control of systematics becomesincreasingly important. Precise characterization of the optical performance of Keck Array receivers is critical toreach these ambitious sensitivity goals. In the simplest mapmaking schemes, differential beam effects betweenco-located orthogonally-polarized pairs of detectors can lead to leakage of the CMB temperature signal into themuch smaller B-mode signal, potentially limiting the ability of the Keck Array to reach its design sensitivity ifthese systematics are not well understood.Characterizing the beam pattern of each of the 2480 Keck Array detectors in the far field presents a challengein both data acquisition and reduction. We describe here our effort to characterize the Keck Array opticalperformance through an extensive ground-based precision beam mapping campaign at the South Pole, anddiscuss our understanding of the cause of measured beam non-idealities and our strategy for mitigating the effectof measured differential beam components in CMB analysis.Four companion papers are also presented at this conference, focusing on the status of Bicep2 and the KeckArray (Ogburn et al.8), the sensitivity of the Keck Array (Kernasovskiy et al.9), the performance of the dual-polarization planar antenna array (O?Brient et al.10), and the thermal stability of Bicep2 (Kaufman et al.11).2. OPTICAL DESIGNEach Keck Array receiver is a compact, single-frequency, on-axis refractive telescope with an aperture of 26.4 cm,designed to maintain tight control of systematics. All optical elements are cold (4 K or 50 K) to maintain lowand stable optical loading on the focal plane. Figure 1 shows a schematic of the Bicep2/Keck Array opticalchain. An in-depth discussion of the design of Bicep2 optical elements can be found in Aikin et al.12The eyepiece and objective lenses are made of high-density polyethylene (HDPE) and are designed to provideeven illumination of the aperture, which is coincident with the objective lens. The illumination at the edge ofProc. of SPIE Vol. 8452  845226-2Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsAperture VacuumcloseoutNylon filterEyepiecelensObjective lens Teflon and nylon filtersMetal-mesh Low-pass edgefilterFocal planeFigure 1: A schematic of the Bicep2/Keck Array optical chain, from Aikin et al.12the aperture compared to the illumination at the center of the aperture is designed to be -12.4 dB for detectorsat the center of the focal plane. Both lenses as well as the telescope housing and aperture are cooled to 4 K.Two Teflon, two nylon, and one metal-mesh filter block IR radiation from reaching the focal plane. The twoTeflon filters and one nylon filter are located in front of the objective lens, and are held at 50 K. Another nylonfilter and the metal-mesh filter sit at 4 K between the objective and eyepiece lenses inside the telescope itself tofurther reduce loading. Teflon has excellent in-band transmission at cryogenic temperatures. While nylon hashigher in-band transmission loss, it has a steeper transmission rolloff, providing significant reduction of far-IRloading on the sub-Kelvin stages. The metal-mesh filter is a low pass filter with a cutoff at 250 GHz, providingadditional blocking of out-of-band power.Keck Array optical elements are anti-reflection coated with porous Teflon with an index of refraction matchedto the optical element and thickness matched to the observing frequency of each receiver, currently 150 GHz.Future upgrades to the array include receivers that observe at 100 and 220 GHz, which require different anti-reflection coatings but contain an otherwise identical optical system.The vacuum window has a 32 cm clear aperture, making design and construction of strong and durablevacuum windows a challenge. Keck Array vacuum windows are made of Zotefoam HD30, a nitrogen-expandedpolyethylene foam that was chosen for its high microwave transmission, its strength against deflection undervacuum, and its adhesion strength to epoxy used to bond the foam to an aluminum frame.To reduce sidelobe pickup, individual co-moving ground shields are installed in front of each receiver?s vacuumwindow. These forebaffles are coated on the inside with HR10 microwave absorber and a weatherproofing foam,providing good termination of sidelobes. The forebaffles intersect radiation at 9.5? off of the boresight axis fromthe edge of the vacuum window.The Bicep2 and Keck Array optical designs are identical except for a few small differences. The materialused for the vacuum window for Bicep2 is Zotefoam PPA30, but is Zotefoam HD30 for the Keck Array. Bicep2has a larger forebaffle than Keck Array receivers. The exact configuration of the IR blocking filters is differentbetween the two experiments; Bicep2 has one Teflon filter at 40 K, another at 100 K, and only has one nylonfilter (at 4 K).3. OPTICAL CHARACTERIZATION3.1 Near-Field Beam CharacterizationTo characterize aperture illumination, we measure the near-field beam pattern of each Keck Array detectorusing a chopped thermal source mounted on an x-y translation stage attached to the cryostat above the vacuumwindow, as close to the aperture stop of the telescope as possible. In practice, the source is about 30 cm aboveProc. of SPIE Vol. 8452  845226-3Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsthe aperture. Figure 2 shows the beam pattern of two example detectors in the near field. The left panel showsthe beam pattern of a detector near the center of the focal plane, which evenly illuminates the aperture. Theright panel shows the beam pattern of a detector near the edge of the focal plane that is significantly truncatedby the aperture because of non-ideal beam pointing at the focal plane (worst case). This type of truncationtranslates to some ellipticity in the beam pattern in the far field and only affects a small fraction of detectors.Near Field Map, Edge Detector[cm][cm]?15 ?10 ?5 0 5 10 15?15?10?505101500.51Near Field Map, Central Detector[cm][cm]?15 ?10 ?5 0 5 10 15?15?10?505101500.51Figure 2: Measurement of the near-field beam pattern for two example Keck Array channels, measured abovethe aperture stop at the vacuum window. Left: A detector near the center of the focal plane; Right: A detectornear the edge of the focal plane, showing significant truncation by the aperture (worst case).3.2 Polarization Angle and Polarization Efficiency CharacterizationWe must know the polarization angle, ?, and cross-polar response, , of each detector to correctly construct polar-ization maps of the sky. The polarization efficiency is calculated from the cross-polar response as (1 ? )/(1 + ).Bicep and Bicep2 measured these polarization parameters using a polarized broadband amplified microwavesource by rotating the telescope about its boresight while the source polarization remained fixed.7 For Bicep2,the polarization efficiency was measured to be < 1%, with leakage dominated by inductive crosstalk betweenfront-end SQUIDs in the readout system.12 This technique, however, would be tedious with the Keck Array be-cause as we rotate the drum that houses the receivers to rotate the receivers about their boresights, the physicallocation of each receiver also moves, making the data set much more difficult to take and analyze than it was forBicep and Bicep2.To measure the polarization angle and cross-polar response of each detector without having to rotate thedrum, we have developed a new rotating polarized broadband amplified microwave source (see Figure 3). Thesource emits radiation in the 140-160 GHz range, designed to cover the passband of the current Keck Arrayreceivers. A 50 ? load provides room-temperature thermal noise at the input of the first stage of amplification(80 dB). A series of frequency multipliers, amplifiers, and filters bring the output frequency to the desired range(140-160 GHz). Linearly polarized radiation is emitted by a 15 dB gain horn antenna, and is further polarizedby a free-standing wire grid, yielding cross-polar leakage of the source < 0.03%. Two variable attenuatorsin series allow for control of output power over a large dynamic range, making the source useful for far-fieldbeam mapping as well as sidelobe mapping with the source closer to the receiver. A microwave switch chopsthe source at ? 10 Hz. The entire source is mounted on a stepped rotating stage and has a total positionalrepeatability < 0.01?.We used the rotating polarized source to repeat a measurement of detector polarization angles and cross-polarresponse for Bicep2 in February 2012. An example of the polarization modulation vs. source angle for one pairof Bicep2 detectors is shown in Figure 3. The orthogonally-polarized detectors in the pair are 90? out of phase.We plan to make similar measurements with the Keck Array during the upcoming 2012-2013 summer season.Proc. of SPIE Vol. 8452  845226-4Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms?60 ?40 ?20 0 20 40 60 80 100 120 140 16000.10.20.30.40.50.60.70.80.91Source Angle (Degrees)Detector Response, NormalizedA DetectorB DetectorFigure 3: Left: The rotating polarized amplified thermal broadband noise source used for polarization charac-terization. Right: Polarization modulation vs. source angle of an example detector pair from Bicep2, measuredusing the rotating polarized source.3.3 Far-Field Beam Characterization3.3.1 Data Acquisition and ReductionMeasuring the beam pattern of each of the 2480 detectors of the Keck Array in the far field presents a challengeand requires an extensive beam mapping campaign at the South Pole. Figure 4 shows the setup used formeasuring the beam pattern in the far field. With all five receivers installed in the drum, we install a 1.2?1.8 maluminum honeycomb mirror, flat to 0.2 mm across the mirror, mounted on carbon-fiber rods. The mirrorassembly was designed to be installed with no overhead crane; the entire system weighs less than 150 kg. Themirror redirects the beams over the top of the ground shield and to a chopped thermal microwave source withan aperture of 20 cm mounted on a 10 m tall mast on the Dark Sector Laboratory, 211 m away. The thermalsource chops between a flat mirror directed to zenith (? 15 K) and ambient (? 260 K) at a tunable frequency,set to be 10 Hz.Figure 4: The setup for measuring far-field beam pattern of Keck Array detectors in situ at the South Pole.A chopped, broadband, microwave source broadcasts from a mast on the Dark Sector Laboratory (DSL), anda large aluminum honeycomb mirror is installed to redirect the beams of the Keck Array to the source. Left:The Keck Array in the foreground, with DSL in the background. Middle: The aluminum honeycomb mirror,installed on the Keck Array for beam measurements. Right: The microwave source mounted on a mast on theroof of DSL.Proc. of SPIE Vol. 8452  845226-5Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsThe size of the mirror allows us to map only three receivers at a time. By rotating the drum below themirror, we can move selected receivers into a position under the mirror for beam mapping. For each receiver, wetake data at five different drum angles so that we can check that a rotation of a receiver underneath the mirrordoes not affect the measurement. The five drum rotations used for each receiver are separated by 36?, for atotal drum rotation coverage of 144? for each receiver, the maximum we could achieve using any single mirrorposition.The data set discussed here consists of five measurements (one at each of five drum rotations) of each ofthe five Keck Array receivers, each with 496 optically-coupled detectors. This data set was taken in February2012, at the end of the most recent summer season. We filter the chop reference signal to match the filteringthat occurs in the readout system and then demodulate the timestream data. The reflection off the mirror andparallax effects are handled with a pointing model that describes the Keck Array mount system as well as themirror used for beam mapping.3.3.2 Beam ParametersFigure 5 displays measured beam maps for all detectors of a single polarization (denoted ?A? polarization) overthe entire array. We fit an elliptical Gaussian to the main beam for each detector, according toge?12 (~x?~r)??1(~x?~r) (1)where ~r is the location of the beam center, g is the amplitude, and ? is the covariance matrix. Ellipticityparameters, p and c, corresponding to amplitudes of the the ?plus? and ?cross? ellipticity orientations, aredefined below in Equation 2 as part of the covariance matrix.? =[?2(1 + p) c?2c?2 ?2(1 ? p)](2)Figure 6 shows an example map, the elliptical Gaussian fit, and the fractional residual after subtracting thefit. Average beam widths and ellipticities are shown in Table 1 for each receiver. The average beam width (?)over the array is 0.215 ? 0.007?. Figure 7 shows the measured far-field beam profile, averaged over all detectorsin one Keck Array receiver.Keck Array 2012 Receiver-Averaged Beam Parameter ValuesParameter Receiver 0 Receiver 1 Receiver 2 Receiver 3 Receiver 4Beam width (?, degrees) 0.214? 0.005 0.213? 0.006 0.213? 0.006 0.216? 0.008 0.218? 0.013Beam ellipticity1 0.010? 0.007 0.012? 0.006 0.012? 0.007 0.013? 0.010 0.013? 0.0101Beam ellipticity is defined as (?major ? ?minor)/(?major + ?minor), where ?major and ?minor are the eigenvalues of ?.Table 1: Receiver-averaged single beam parameters for all five Keck Array receivers with the standard deviationof these parameters across each receiver. The spread is dominated by real detector-to-detector scatter, notmeasurement uncertainty for individual detectors.3.3.3 Differential Beam ParametersThe beam pattern of a single detector can also be characterized as a set of perturbations on an idealized circularGaussian fit, with a nominal width (?n) equal to the receiver-averaged value and a nominal beam center equalto the calculated center for the pair of detectors from the initial elliptical Gaussian fit. We consider the firstsix perturbations, corresponding to the templates shown in Figure 8. These six templates correspond to relativeresponsivity, x-position offset, y-position offset, beam width, ellipticity in the ?plus? orientation, and ellipticityin the ?cross? orientation.We calculate the regression coefficient for each measured individual beam pattern against each templatemap. Differential beam parameters for a pair of co-located orthogonally-polarized detectors, which we denote?A? and ?B? detectors, are then the difference of the regression coefficients for each detector. Table 2 gives theProc. of SPIE Vol. 8452  845226-6Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms?A? Polarization MapsFigure 5: Measured beam maps of A polarization detectors for the entire array. The maps are arranged in alayout that represents the location and orientation of the five receivers in the drum, and does not represent thefield of view. In the far field, the five receivers have completely overlapping fields of view, and the beam centersare more closely spaced than shown here.correspondence between these differential beam parameters and the associated elliptical Gaussian fit parametersfor each beam map (Equations 1 and 2) in the limit of small perturbations.In this analysis, we extract differential beam parameters by calculating regression coefficients of individualdetector beam maps against each of the template maps and then differencing regression coefficients for eachdetector pair. This proves convenient when predicting and mitigating beam mismatch-induced polarization, asthe leakage scales linearly with these differential parameters. A full description of this parameterization and itsimplementation in analysis can be found in Aikin et al.13Proc. of SPIE Vol. 8452  845226-7Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms[Deg][Deg]Gaussian Fit?1 ?0.5 0 0.5 1?1?0.8?0.6?0.4?0.200.20.40.60.81 01[Deg][Deg]Measured Beam?1 ?0.5 0 0.5 1?1?0.8?0.6?0.4?0.200.20.40.60.81 01[Deg][Deg]Fractional Residual?1 ?0.5 0 0.5 1?1?0.8?0.6?0.4?0.200.20.40.60.81 ?0.1?0.08?0.06?0.04?0.0200.020.040.060.080.10.5 0.5Figure 6: Left: Example measured far-field beam pattern, linear scale. Middle: Gaussian fit to measured beampattern. Right: Fractional residual after subtracting the Gaussian fit in the middle panel. Note: Right-handpanel has a different color scale than the left two panels.0 0.5 1 1.5 2 2.5 3102030405060Degrees from Beam CenterdBiFar Field Beam ProleFigure 7: Radial profile of the Keck Array far-field beam pattern, averaged over one receiver. The profile showsthe first few sidelobes and nulls before the beam pattern falls to the noise floor of the measurement.We can calculate the regression coefficient for five of the templates shown in Figure 8 from beam maps, andextract differential beam parameters for each detector pair. The sixth coefficient, for the relative responsivity, isequivalent to differential gain which is calibrated frequently during CMB observations.Figure 9 shows an example of this decomposition for a representative detector pair. The first column showsthe normalized A beam map, the second column shows the normalized B beam map, and the third columnshows the difference between the normalized A and B maps. We construct a model, shown in the second row,by summing the position offset, beam width, and ellipticity components calculated via template regression foreach detector. The residual after subtracting the model is shown in the third row. The fourth column explicitlyshows the differential components (templates scaled by the regression coefficient) that are summed to give themodel for the normalized A-B difference map. The normalization explicitly sets the responsivity mismatch tozero.Histograms of all differential parameters for each detector pair in the Keck Array are shown in Figure 10 andreceiver-averaged values are shown in Table 3. Each measurement of each detector?s main beam must pass a setof criteria to be included in the final extraction of beam parameters, including a check that the beam center wasnot near the edge of the mirror and excluding measurements where the initial elliptical Gaussian fit failed. Notethat the relative amplitudes of the distinct differential parameters shown in the histograms and in Table 3 donot reflect the relative map amplitudes (templates scaled by the regression coefficient).This set of measurements of single normalized A-B difference residuals is noise-dominated (see Figure 9).Increased signal-to-noise beam map data would help improve the data quality. We will have the opportunityProc. of SPIE Vol. 8452  845226-8Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsFigure 8: Differential beam templates resulting in mismatch in (a) responsivity (b) x-position (c) y-position(d) beam width (e) ellipticity in plus (f) ellipticity in cross. In the limit of small differential parameters, adifferenced beam pattern constructed from the difference of two elliptical Gaussians can be represented as alinear combination of each of these templates. From Aikin et al.13Parameter DefinitionDifferential relative responsivity (?g) ?(gA/gn)/(gB/gn)Differential pointing in x (?rx) (~ra ? ~rb) ? x?/2?nDifferential pointing in y (?ry) (~ra ? ~rb) ? y?/2?nDifferential beam width (??) (?2A ? ?2B)/?2nDifferential ellipticity, plus orientation (?p) (pA ? pB)/2Differential ellipticity, cross orientation (?c) (cA ? cB)/2Table 2: The correspondence between differential beam parameters and the associated elliptical Gaussian fitparameters for each beam map in the limit of small perturbations. The two unitless parameters correspondingto differential ellipticity, p and c, are the ellipticity parameters defined in Equation 2. ?n is the receiver-averagedbeam width, ~ra and ~rb are the vector from the averaged detector-pair center to the A or B beam center, ?Aand ?B are the beam width for A and B, gA and gB are the responsivity for A and B, and gn is the nominalreceiver-averaged responsivity. This table is from Aikin et al.13to repeat this beam mapping campaign during the upcoming 2012-2013 deployment season, but with a highersignal level chopped thermal source and an amplified circularly polarized broadband noise source.4. MODELED DIFFERENTIAL BEAM EFFECTSThe largest of the clearly modeled differential beam effects is the pointing mismatch, indicating that the KeckArray has a pointing offset between orthogonally-polarized detector pairs that averages to 1.6?3.1% of the beamfull width at half maximum (FWHM) for different receivers. We have spent a great deal of effort characterizingthe mismatch and investigating its possible sources. A similar level of mismatch is observed in Bicep2,12 butwas not present in Bicep,7 which used horn antennas rather than planar antenna arrays. Bicep had a verysimilar optical design to Bicep2 and the Keck Array, using the same materials for lenses and filters.We have measured the pointing offset extensively in both the near field and the far field, in testbed locationsin North America as well as in situ at the South Pole. We have seen some evidence that the amplitude of thefar-field offset scales with the near-field offset. However, there appears to be a complex relationship between theoverall observed near-field mismatch and the overall far-field mismatch.Since deploying the Keck Array to the South Pole, we have made great progress in reducing the size of thenear-field mismatch arising at the focal plane. This effort is described in detail in O?Brient et al.,10 a companionpaper at this conference. Recent measurements have revealed that newly-produced replacement Keck ArrayProc. of SPIE Vol. 8452  845226-9Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsA PolData00.51B Pol00.51A/|A| ? B/|B|?0.100.1Differential Decomposition ComponentsBeam Width?0.0200.02Fit0 0 ?0.100.1Pointing?0.100.1ResidualDegrees?0.100.1Degrees-1 0 1 ?0.100.1Degrees?0.0200.02EllipticityDegrees-101 ?0.0200.020.510.51-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1-101-1 0 1Figure 9: Example plot of the linear basis fit parameter calculation for one pair of detectors. The first columnis the A beam pattern (normalized), the second column is the B beam pattern (normalized), the third columnis A-B; for these three columns, the first row is the measured map, the second row is the fit, and the third rowis the residual. The fourth column is the different decomposition components (the template multiplied by theregression coefficient).?0.1?0.05 0 0.05 0.1020406080Differential Beam Width?0.1?0.05 0 0.05 0.1050100Differential X Pointing?0.1?0.05 0 0.05 0.10204060Differential Y Pointing?0.1?0.05 0 0.05 0.1050100150200Differential Plus Ellipticity?0.1?0.05 0 0.05 0.1050100150200250Differential Cross EllipticityFigure 10: Histograms of differential beam parameters. Regression coefficients for each of the templates shown inFigure 8 are calculated individually for A and B detectors in a pair and are then differenced to extract differentialbeam parameters.detector tiles exhibit a near-field mismatch that is a factor of 10 smaller than in focal planes currently installedat the South Pole.Upcoming detailed measurements of the new reduced near-field mismatch focal planes in the far field willbe very informative. We expect a reduction of the far-field mismatch, but because of the apparent complexrelationship between the near and far-field effects, we do not necessarily expect a linear scaling between themeasured reduction of the near-field mismatch and the far-field mismatch.5. RESIDUAL DIFFERENTIAL BEAM EFFECTSTemperature to polarization leakage in CMB maps that arises from the linearly-modeled components of thedifferential beams described in the previous section can be mitigated in analysis. A discussion of the methods weProc. of SPIE Vol. 8452  845226-10Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsParameter Receiver 0 Receiver 1 Receiver 2 Receiver 3 Receiver 4Differential beam width (|??|) 0.014? 0.015 0.024? 0.024 0.025? 0.035 0.023? 0.020 0.031? 0.028Differential pointing (??r2x + ?r2y) 0.033? 0.018 0.037? 0.016 0.019? 0.014 0.031? 0.024 0.035? 0.024Differential ellipticity (??p2 + ?c2) 0.011? 0.007 0.013? 0.008 0.011? 0.012 0.013? 0.011 0.015? 0.015Table 3: Receiver-averaged differential beam parameters with the standard deviation of these parameters acrosseach receiver. Regression coefficients for each of the templates shown in Figure 8 are calculated individually forA and B detectors in a pair and are then differenced to extract differential beam parameters. Both real scatteramong detector pairs and measurement uncertainty for individual detector pairs contribute to the spread, butmeasurement uncertainty is subdominant, especially for the differential pointing parameterare implementing to reject these linear components in CMB mapmaking, which does not rely on measurementof their amplitude, can be found in Aikin et al.13 After this mitigation, temperature to polarization leakage dueto any unmodeled residual differential beam shape will remain.Figure 11 shows power vs. angular scale for an example measured beam pattern and for the differentialA-B residual after removing the extracted differential components. The A-B residual describes the higher-orderdifferential beam effects that remain after mitigation of leading-order effects. To reduce the noise floor of themeasurement of this residual, we have averaged over all five measurements of these detectors after accountingfor drum orientation rotation. Still, because of the limited signal-to-noise of these measurements, the residualpower shown here is only an upper limit on the actual residual differential power. We intend to improve thebeam map measurements next season to achieve higher signal-to-noise measurements by using brighter sources.At ` = 100, where our sensitivity to the Inflationary B-mode spectrum is best, the ratio between the un-modeled residual differential power that will remain after mitigation of leading-order effects in analysis and thepower in the main beam is at most at the 10?5 level for one typical pair of detectors only. This upper limitis already close to the raw rejection ratio needed to probe polarization to a level of r = 0.01. In actual CMBobservation, we also benefit enormously from averaging-down effects from observing the sky with many detectorsand at multiple drum angles. Full simulations of these effects are planned, and together with improved beammeasurements to constrain residual differential power to lower levels, the situation looks promising for controlof beam systematics to below the r = 0.01 level.6. CONCLUSIONSPushing deeper into the level of B-mode polarization to constrain r requires the dramatically increased sensitivitythat the Keck Array provides, but also requires tight control of systematics. Through a massive beam mappingcampaign, we have measured beam properties of each of the 2480 detectors in the Keck Array. We extractdifferential beam parameters using the same linear basis that will be employed for analysis mitigation of thesemodeled effects. The source of the dominant pointing mismatch is still under investigation. We believe thatthere is a complex relationship between the size and orientation of the near-field mismatch and that of the farfield.Measurements with new reduced near-field mismatch focal planes in the far field are upcoming. We expectthat the next generation of Keck Array focal planes will benefit from dramatically reduced far-field mismatch.For the current receivers, we have shown that noise-dominated upper limits placed on the unmodeled residualcomponent of the difference beam pattern already reach the 10?5 level at ` = 100 when including one pair ofdetectors only. We are optimistic that improved constraints on this residual, together with full simulations whichaccount for averaging-down effects from observing the sky with many detectors at multiple drum angles, willdemonstrate beam systematic control more than sufficient to reach r = 0.01.ACKNOWLEDGMENTSThe Keck Array is supported by the National Science Foundation, Grant No. ANT-1044978/ANT-1110087,and by the Keck Foundation. AGV gratefully acknowledges support from the National Science Foundation,Grant No. ANT-1103553. We are also grateful to Robert Schwarz for spending the winter at the South Pole inProc. of SPIE Vol. 8452  845226-11Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms0 50 100 150 200 250 300 350 400 450 50010?710?610?510?410?310?210?1100101lpowerbeamresidualratioFigure 11: Power vs. angular scale for a typical example beam pattern (blue) and the residual beam componentafter removing leading-order differential components (red). The maps are shown in Figure 9. The ratio of thetwo is shown in green.both 2011 and 2012 for this project, and to the South Pole Station logistics team. We thank our Bicep2, KeckArray, and Spider colleagues for useful discussions and shared expertise.REFERENCES[1] de Bernardis, P. et al., ?A flat Universe from high-resolution maps of the cosmic microwave backgroundradiation,? Nature 404, 955?959 (Apr. 2000).[2] Peiris, H. V. et al., ?First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: ImplicationsFor Inflation,? Astrophys.J.Suppl. 148, 213?231 (Sept. 2003).[3] Kamionkowski, M., Kosowsky, A., and Stebbins, A., ?A probe of primordial gravity waves and vorticity,?Phys. Rev. Lett. 78, 2058?2061 (Mar 1997).[4] Seljak, U. and Zaldarriaga, M., ?Signature of gravity waves in polarization of the microwave background,?Phys.Rev.Lett. 78, 2054?2057 (1997).[5] Sheehy, C. et al., ?The Keck Array: a pulse tube cooled CMB polarimeter,? in [Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series ], Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series 7741 (July 2010).[6] Chiang, H. C. et al., ?Measurement of Cosmic Microwave Background Polarization Power Spectra from TwoYears of BICEP Data,? Astrophys.J. 711, 1123?1140 (Mar. 2010).[7] Takahashi, Y. D. et al., ?Characterization of the BICEP Telescope for High-precision Cosmic MicrowaveBackground Polarimetry,? Astrophys.J. 711, 1141?1156 (Mar. 2010).[8] Ogburn, R. et al., ?BICEP2 and Keck Array operational overview and status of observations,? TheseProceedings (2012).[9] Kernasovskiy, S. et al., ?Optimization and sensitivity of The Keck Array,? These Proceedings (2012).[10] O?Brient, R. et al., ?Antenna coupled TES bolometers for BICEP2, The Keck Array, SPIDER, and Polar,?These Proceedings (2012).[11] Kaufman, J. P. et al., ?Thermal stability of the BICEP2 telescope,? These Proceedings (2012).Proc. of SPIE Vol. 8452  845226-12Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms[12] Aikin, R. W. et al., ?Optical performance of the BICEP2 telescope at the South Pole,? in [Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series ], Society of Photo-Optical InstrumentationEngineers (SPIE) Conference Series 7741 (July 2010).[13] Aikin, R. et al., ?Removing Instrumental Systematics Contamination from CMB Polarimetry Data,? InPreparation (2012).Proc. of SPIE Vol. 8452  845226-13Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms

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