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Primordial Inflation Polarization Explorer (PIPER) Halpern, Mark; Hinshaw, Gary F. Oct 5, 2012

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The Primordial Inflation Polarization Explorer (PIPER)Alan Koguta, Peter A. R. Adeb, Dominic Benforda, Charles L. Bennettc, David T. Chussa,Jessie L. Dotsond, Joseph R. Eimerc, Dale J. Fixsena, Mark Halperne, Gene Hiltonf, JamesHinderksa, Gary F. Hinshawe, Kent Irwinf, Christine Jhabvalag, Brad Johnsonh, Justin Lazearc, Luke Lowea, Timothy Millerg, Paul Mirela, S. Harvey Moseleya, Samelys Rodrigueza, ElmerSharpa, Johannes G. Staguhna, Carole E. Tuckerb, Amy Westona, and Edward J. WollackaaCode 665, NASA Goddard Space Flight Center, Greenbelt, MD USA 20771;bCardiff University, Cardiff, Wales CF103XQ, UK;cJohns Hopkins University, 3400 N. Charles St., Baltimore, MD USA 21218;dNASA Ames Research Center, Moffett Field, CA, USA 94035;eDept. of Physics & Astronomy, University of British Columbia, Vancouver, BC, Canada, V6T1Z1;fMailcode 817.03 National Institute for Standards and Technology, Boulder, CO USA 80305;gCode 553, NASA Goddard Space Flight Center, Greenbelt, MD USA 20771;hColumbia University, New York, NY USA 10027ABSTRACTThe Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne instrument to measure the gravitational-wave signature of primordial inflation through its distinctive imprint on the polarization of the cosmic microwavebackground. PIPER combines cold (1.5 K) optics, 5120 bolometric detectors, and rapid polarization modulationusing VPM grids to achieve both high sensitivity and excellent control of systematic errors. A series of flightsalternating between northern and southern hemisphere launch sites will produce maps in Stokes I, Q, U, andV parameters at frequencies 200, 270, 350, and 600 GHz (wavelengths 1500, 1100, 850, and 500 ?m) covering85% of the sky. The high sky coverage allows measurement of the primordial B-mode signal in the ?reionizationbump? at multipole moments ` < 10 where the primordial signal may best be distinguished from the cosmolog-ical lensing foreground. We describe the PIPER instrument and discuss the current status and expected sciencereturns from the mission.Keywords: polarimeter, cosmic microwave background, bolometer1. INTRODUCTIONA central principle in modern cosmology is the concept of inflation, which posits a period of exponential expansionin the early universe. The many e-foldings of the scale size during inflation force the geometry of space-timeto asymptotic flatness while dilating quantum fluctuations in the inflaton potential to the macroscopic scalesresponsible for seeding large-scale structure in the universe. Inflation provides a simple, elegant solution tomultiple problems in cosmology, but it relies on extrapolation of physics to energies more than 12 orders ofmagnitude beyond those accessible to particle accelerators.A critical test of inflation is its prediction of a background of gravitational waves. If inflation is responsible forthe observed temperature fluctuations, gravitational waves are expected to exist: just as quantum fluctuationsin the inflaton field generate a background of density perturbations, fluctuations in the space-time metric duringinflation generate a stochastic background of gravitational waves. In the simplest inflationary models, theamplitude of this background depends on the inflationary potentialV 1/4 = 1.06? 1016 GeV( r0.01)1/4(1)Send correspondence to: Alan.J.Kogut@nasa.gov; telephone 1 301 286 0853Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VI, edited by Wayne S. Holland, Jonas Zmuidzinas, Proc. of SPIE Vol. 8452, 84521J ? 2012 SPIE ? CCC code: 0277-786X/12/$18 ? doi: 10.1117/12.925204Proc. of SPIE Vol. 8452  84521J-1Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsEModes B ModesEven Parity Odd ParityI'I / \I / \ \'.\I / \ ' \ \.II'\\ //I\\\\\ I/ \ II I fl\\I \\\\ J,\\I\t I \\\\I\\\' '-' (\\-\II' \ I I\\\ I\\ I, I III / \\\ \\I \ I \/ \ I I I \ \ I \\ ' / I' // I\\ I\\//\\\'.'---\\\\f7I\I\\\ J/1\\ -\\/\\//I\r\I \\\II-:\' /\\I \\\' \ I \1\\' I',,I \\\!I'-'I/\'-i-'I/\\\ I' I I I 'i \ 'I / I / /I ' I I / I \ I I I \ \ I / ' / 'I '\ \ I Ii I I I I \ \ I //- '\ -\ j \ \ \ / / I \ / / / i / / \ I-15 -10 - 0 5 iu bPXOG8 Longitude (degrees)1510Figure 1. Simulated sky map showing CMB anisotropy (color) and polarization over a 30? ? 30? patch of sky. Thepolarization pattern can be decomposed into even-parity E-modes and odd-parity B-modes. Only gravitational waves canproduce a B-mode signal in the CMB on large angular scales.where r is the power ratio of gravitational waves to density fluctuations.Polarization of the cosmic microwave background (CMB) provides a direct test of inflationary physics. CMBpolarization results from Thomson scattering of CMB photons by free electrons. A quadrupolar anisotropy inthe radiation incident on each electron creates a net polarization in the scattered radiation. There are only twopossible sources for such a quadrupole: either an intrinsic temperature anisotropy or the differential redshiftcaused by a propagating gravitational wave. The two cases can be distinguished by their different spatialsignatures (Figure 1). Temperature perturbations are scalar quantities; their polarization signal must thereforebe curl-free. Gravitational waves, however, are tensor perturbations whose polarization includes both gradientand curl components. In analogy to electromagnetism, the scalar and curl components are often called ?E? and?B? modes. Only gravitational waves induce a curl component on large angular scales: detection of a B-modesignal in the CMB polarization field is recognized as a ?smoking gun? signature of inflation, testing physics atenergies inaccessible through any other means.1?8Figure 2 shows the CMB polarization as a function of angular scale. At the degree angular scales characteristicof the horizon at decoupling, the unpolarized temperature anisotropy is typically 80 ?K. These fluctuationsin turn generate E-mode polarization, which at amplitude ?3 ?K is only a few percent of the temperaturefluctuations. The B-mode amplitude from gravitational waves is unknown. Recent WMAP results suggest values0.01 < r < 0.1 for large-field inflation models, corresponding to Grand Unification energy scales or polarizationamplitudes in the range 30 to 100 nK.9 Signals at this amplitude could be detected by a dedicated polarimeter,providing a direct, model-independent measurement of the energy scale of inflation.Detecting the gravitational-wave signature will be difficult. As recognized in multiple reports,10?12 there arethree fundamental challenges:? Sensitivity The gravitational-wave signal is faint compared to the fundamental sensitivity limit imposedby photon arrival statistics. Even noiseless detectors suffer from this photon-counting limit; the onlysolution is to collect more photons.? Foregrounds The gravitational-wave signal is faint compared to the polarized Galactic synchrotron anddust foregrounds. Separating CMB from foreground emission based on their different frequency spectrarequires multiple frequency channels.Proc. of SPIE Vol. 8452  84521J-2Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsFigure 2. Angular power spectra for unpolarized, E-mode, and B-mode polarization in the cosmic microwave background.Filled points and error bars show the PIPER sensitivity to the B-mode power spectrum with amplitude r = 0.02. PIPERhas the sensitivity and sky coverage required to detect the primordial signal within the ?reionization bump? at largeangular scales where it may best be distinguished from the competing lensing signal.? Systematic Errors The gravitational-wave signal is faint compared to both the unpolarized CMBanisotropy and the dominant E-mode polarization. Accurate measurement of the B-mode polarizationrequires strict control of instrumental effects that could alias these brighter signals into a false B-modedetection.Satisfying the simultaneous requirements of sensitivity, foreground discrimination, and immunity to systematicerrors presents a technological challenge. Cosmological foregrounds present an additional operational challenge.Gravitational lensing by the matter distribution between the surface of last scattering at z ? 1090 and theobserver today produces a shear field, shifting a fraction of the dominant E-mode polarization into a B-modelensing signal (dotted line in Figure 2). This lensing foreground dominates the inflationary signal on smallangular scales. On intermediate scales of a few degrees, the lensing foreground has a similar power spectrum asthe primordial signal and (for primordial amplitude near the expected value r ? 0.02) a comparable amplitude.Distinguishing the primordial signal form the lensing foreground requires mapping the polarization over asignificant fraction of the sky. Inflation produces a stochastic background of gravitational waves, which sourceCMB polarization via Thomson scattering. Multiple scatterings, however, erase information from any previousscattering. The B-mode power spectrum is thus modulated by the ionization history of the universe, with twoprominent peaks corresponding to changes in the ionization fraction of the early universe. The last scattering atrecombination (redshift z ? 1090) as the universe shifts from an ionized to a neutral medium produces a B-modepeak at angular scales of a few degrees. Re-ionization of the universe at redshift z ? 10 scatters a fraction of theCMB photons to produce a second B-mode peak on large angular scales. This ?reionization bump? at angularscales ? > 30? is an important discriminant for the primordial signal, allowing clean separation of the primordialsignal from the lensing foreground.This paper describes an instrument designed to characterize primordial inflation through its distinctive sig-nature in the polarization of the cosmic microwave background. The Primordial Inflation Polarization ExplorerProc. of SPIE Vol. 8452  84521J-3Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsVariabLe-DeLayPoLarizationModuLatorsCoLdOpticsDetectorArrays3500 LiterBucket DewarSLow spin(10 mm period) BeamsTo SkyFigure 3. PIPER payload showing the twin telescopes mounted inside an open 3500 liter liquid helium dewar. Variable-delay polarization modulators provide simultaneous sensitivity to both linear and circular polarization. Four 32 ? 40arrays of transition-edge superconducting bolometers operating at 100 mK provide instrumental polarization sensitivityof NEQ ? 2 ?K s1/2.(PIPER) combines 5120 superconducting detectors with rapid polarization modulation to measure both linearand circular polarization. A series of high-altitude balloon flights maps 85% of the sky in each of 4 frequencybands. PIPER has the sensitivity, frequency coverage, and control of systematic errors needed to detect theprimordial signal, while the high sky coverage provides the angular response needed to unambiguously separatethe cosmic signal from the lensing foreground. A series of eight flights provides sensitivity r < 0.007 at 95%confidence.2. INSTRUMENT DESCRIPTIONThe Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne instrument to measure the distinctivesignature of primordial inflation in the linear polarization of the cosmic microwave background. Figure 3 showsthe PIPER instrument. It consists of two co-aligned telescopes cooled to 1.5 K and mounted within a large liquidhelium bucket dewar. A variable-delay polarization modulator (VPM) on each telescope injects a phase delaybetween incident orthogonal linear polarizations, which are then re-combined and re-imaged onto a focal planecontaining 5120 superconducting bolometers cooled to 100 mK.2.1 OpticsPIPER uses fully cryogenic optics, with all optical surfaces maintained at 1.5 K or colder within a 3500 literliquid helium bucket dewar. Boiloff helium gas maintains a cold barrier between the optics and the ambientatmosphere; there are no windows or other emissive elements between the telescope and the sky.The fully cryogenic design provides two important advantages. The first is sensitivity. With no warm elementsin the optical path, instrumental emission and associated photon noise are reduced to negligible levels. PIPERProc. of SPIE Vol. 8452  84521J-4Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsVPMPrimaryMirror FoldingFlatSecondaryMirror Lyot StopPressureWindow LensesFocalPlanesAnalyzerGridReimagingOpticsFigure 4. Ray trace analysis for a single PIPER telescope showing the VPM, reflective fore-optics, and reimaging opticswithin the detector cryostat. The cryogenic optics allow sufficient design flexibility to combine high performance withina compact footprint, producing Strehl ratio > 0.97 across the full 4.?7 ? 6? field of view on the sky.operates within a few percent of the photon noise limit imposed by the atmosphere at balloon altitudes. Thegain in sensitivity is significant: PIPER is a factor of three more sensitive than a comparable instrument withambient-temperature (250 K) optics. The improved sensitivity in turn provides an order-of-magnitude decreasein integration time, allowing PIPER to reach noise levels in a single overnight flight that would otherwise requirea week or more of integration from a long-duration Antarctic flight. Overnight observations are highly desirable:freed from restrictions on pointing too close to the Sun, PIPER can observe nearly 2pi steradians in a single flightto measure the B-mode signal across the ?reionization bump.?The second principal advantage of cryogenic optics is flexibility for the optical design. With no noise penaltyfor additional reflecting surfaces, the optical path can be optimized for throughput and beam quality. Figure 4shows the optical design. Light from the sky enters a windowless liquid helium bucket dewar and reflects from avariable-delay polarization modulator (?2.2), which creates a phase delay between orthogonal linear polarizationstates incident on the telescope. Reflective fore-optics consisting of a primary mirror, folding flat, and secondarymirror transfer the light to reimaging optics within the detector cryostat.The near-Gregorian fore-optics on each telescope reimage the primary pupil (at the VPM) to the secondarypupil within the detector cryostat. A Lyot stop at the secondary pupil controls illumination on the VPM. Ananti-reflection coated silicon lens then slows the beam before it passes through a analyzer grid which splits therecombined beam into two orthogonal linear components. Each polarization passes through a final lens thatconverts the beam to f/1.6 before illuminating one of two identical total-power detector arrays.PIPER achieves excellent optical performance in a compact configuration. Strehl ratios vary from 0.99 to0.97 across each 32 ? 40 pixel detector array. Despite the off-axis fore-optics, the beams on the sky are highlysymmetric across the full 4.?7? 6? field of view on the sky.132.2 Polarization ModulationVariable-delay polarization modulators impose a fast (3 Hz) modulation on the polarized component of theincident light to allow efficient detection of faint polarized signals in the presence of much brighter unpolarizedemission.14?16 Figure 5 shows the design. Each VPM consists of a regular grid of 41 ?m diameter wires spaced112 ?m apart in front of a flat reflective plate. Incident light polarized parallel to the wires reflects fromthe grid. The perpendicular component is transmitted through the grid to the reflective backshort and backProc. of SPIE Vol. 8452  84521J-5Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsOutput Signal Input SignalRotary FlexuresCounterweightMirror Wire GridWarmDrive 'MotorDriveShaft -RotaryFlexuresWireGridFra meMirrorFigure 5. (Left) Schematic of VPM operation. The VPM uses a wire grid positioned in front of and parallel to a moving flatmirror. The phase delay between orthogonal linear polarizations is controlled by modulating the grid?mirror separation.(Right) CAD model of the VPM. A warm motor and cam connect to the cryogenic section to move the mirror. A rotaryflexure maintains parallelism between the mirror and grid. (Right) VPM assembly prior to wire grid installation. Theentire structure is made from stainless steel to minimize displacement or distortion from differential thermal contractionduring cryogenic operation.through the grid again, where it recombines with the parallel component. The additional distance traveled bythe perpendicular component creates a phase delay between the components in the recombined beam. In thelimit that the wavelength is large compared to the wire geometry, the phase delay may be written? =4piz?cos ? (2)where z is the separation between the grid and the backshort, ? is the observing wavelength, and ? is the angle ofincidence?. The recombined beams pass through a second analyzer grid with wires oriented at 45? with respect tothe VPM grid. The reflected and transmitted components are orthogonal linear combinations of the polarizationstates defined by the VPM grid. Defining a coordinate system such that Stokes U is parallel to the VPM wires,the power incident on the detector arrays following the analyzer grid may be writtenPR = 1/2 [I +Q cos?? V sin?]PT = 1/2 [I ?Q cos?+ V sin?] , (3)where PR and PT refer to the reflected and transmitted legs, respectively.17 As the VPM backshort sweeps backand forth, the power incident on each detector consists of a dc term (Stokes I) plus modulated terms proportionalto the linear (Q) and circular (V) polarization.Each telescope has a VPM as the first element in the optical path to modulate the sky signal prior to injectionof any elliptical polarization from the reflective optics. Each VPM modulates Stokes Q in a coordinate systemdefined by the orientation of the wires in the reflective grid. The two telescopes orient the VPM grid wires at45? to each other so that one VPM is sensitive to Stokes Q and the other to Stokes U in a coordinate systemfixed on the sky. Parallactic rotation of the sky relative to the instrument allows cross-calibration of the twotelescopes.The sensitivity to each polarization state depends on the VPM mirror stroke. A sinusoidal mirror strokeminimizes transient acceleration while providing sensitivity to both linear and circular polarization. We strokethe mirror through linear translation ?z ? 0.3? to sample both the ?Q and +Q peaks of the detector response(Eq. 3). The resulting modulation provides effective sensitivity of 0.75 for linear polarization and 0.62 for circularpolarization relative to an ideal (square-wave) stroke.?This equation sometimes appears in the literature with the cos ? factor incorrectly placed in the denominator. Thistreatment is correct.Proc. of SPIE Vol. 8452  84521J-6Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms32 x 40 pixel detector arraySingle pixelAbsorber and BolometerTESN\2OQitrnSupport GridFigure 6. Detector arrays. (Left) Fabricated 32 ? 40 prototype array with absorbing grid. (Center) Schematic showingbackshort-under-grid architecture for a single pixel. (Right) Photomicrograph showing transition-edge superconductingbolometer and the supporting legs.2.3 DetectorsThe phase-delayed, re-combined beams from the VPM and optical system within each telescope are split by ananalyzer grid and imaged onto total-power detector arrays. PIPER uses four identical 32? 40 pixel arrays (onein each linear polarization for each of two telescopes) for a total of 5120 detectors within the instrument.Figure 6 shows the PIPER detector array. PIPER uses transition-edge superconducting (TES) bolometersformed from a Mo:Au bilayer with normal-state resistance 20 m?. Interdigitated normal metal stripes suppressnoise.18 The bolometers are located on a square silicon membrane 1.4 ?m thick mounted in planar array usingthe Backshort-Under-Grid (BUG) architecture19 with pixel pitch 1135 ?m. A reflective backshort behind eachpixel increases the electric field intensity near the membrane to increase detector absorption. The fixed backshortdistance is chosen to maximize absorption in the lowest three PIPER bands containing appreciable CMB signalwhile reducing absorption in the highest frequency band to prevent saturation from the bright dust signal.The BUG architecture allows efficient coupling to the sky. The sky is imaged directly onto the detector array;there are no feed horns or similar coupling structures. A deposited bismuth layer on the suspended membranesprovides impedance matching to free space. Electrical patches deposited on the grid walls carry signals fromthe bolometers to the back surface of the array; there are no reflective traces on the sky side of the array. Thedetector array mates directly to a NIST two-dimensional time-domain multiplexer chip using indium bump-bondtechnology.20 The detectors are read out using the University of British Columbia Multi-Channel Electronics(MCE).213. SYSTEMATIC ERRORSMeasurement of a small linear polarization in the presence of much brighter unpolarized sources requires carefulcontrol of systematic error. The PIPER design avoids several potential effects entirely while reducing others tonegligible levels.3.1 T ?? BThe mixing of unpolarized flux into a false polarized signal, commonly referred to as ?instrumental polarization,?is especially important to control given that the unpolarized flux is likely to be a factor of 108 larger than theB-mode signal. Scattering, off-axis reflections, and transmission through dielectrics can all induce polarizationon an initially unpolarized signal. PIPER?s VPMs are placed at the front of the optical system so that thepolarization modulation is encoded on the CMB before any of these effects can occur within the instrument.Proc. of SPIE Vol. 8452  84521J-7Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsFigure 7. (LEFT) Simulated sky maps for I, Q, and U are shown with co-polar and cross-polar beams superposed. Thecross-polar level assumed is -25 dB. Angular rotation of the cross-polar response relative to the linearly polarized skysignal produces a systematic error signal mixing Stokes Q and U . (RIGHT) Time-ordered signals for a half-wave plateand VPM modulation. The upper panels show the simulated signals with (dashed) and without (solid) the cross-polarresponse, while the bottom panels show the difference between the two cases.The symmetric instrument design mitigates any residual effects resulting from imperfections in the VPM. EachVPM feeds two detector arrays which sense orthogonal linear combinations of the Stokes Q and V parameters(Eq. 3). Sky signals have opposite signs in the two arrays, while instrumental effects (differential emissivity, etc)produce the same sign in both arrays.Fully cryogenic operation further mitigates instrumental polarization. Radiation scattered or diffracted fromthe VPM or other optical surfaces terminates within an absorbing cavity inside the bucket dewar. Superfluidliquid helium forces the cavity to be isothermal to mK precision, eliminating temperature gradients within the1.5 K instrument stage. Gradients can exist within the 100 mK stage, but surfaces at this temperature havenegligible mm-wave emission.3.2 ?T ?? BInstrument asymmetry can alias unpolarized temperature fluctuations on the sky into a false polarization signal.Front-end VPM modulation mitigates this effect by injecting a time-dependent phase delay between orthogonalpolarizations without altering the beam shape on the sky. The 3 Hz modulation is rapid compared to the scanmotion of the beam across the sky: PIPER does not rely on pixel-to-pixel comparisons for determination of thesky polarization.3.3 E ?? BB-mode polarization is faint compared to the dominant E-mode signal. Instrumental mixing of Stokes Q andU produces a similar mixing of E and B, potentially masking the primordial B-mode signal behind a brightersystematic error. PIPER takes advantage of the difference between astrophysical linear and circular polarizationto eliminate this source of error. The VPM modulates the instrument response between linear polarization(Stokes Q) and circular polarization (Stokes V ). The sky at millimeter wavelengths contains multiple sources oflinear polarization but no significant circular polarization: the Stokes V signal from the sky should be negligible.Instrumental effects (e.g. a cross-polar beam response) combine with the VPM modulation to map linearlypolarized sky signals into a false V signal. However, with no sky V signal to serve as a source, there is nocorresponding mapping of sky V into a false Q signal and hence no mixing of Q and U .Figure 7 illustrates the VPM advantage. Typical beam patterns yield cross-polar response at the -25 dBlevel. Rotation of the cross-polar beam pattern with respect to the sky (either from physical rotation of theinstrument or rotation of the polarization basis by a half-wave plate) mixes Stokes Q and U to yield an errorsignal indistinguishable from true sky polarization. The VPM, in contrast, rotates between linear and circularProc. of SPIE Vol. 8452  84521J-8Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsFigure 8. PIPER sensitivity and sky coverage. The map shows the polarized dust intensity at wavelength 500 microns.assuming a constant 3% dust fractional polarization. Contours show signal-to-noise ratio 3, 10, 30, 100, and 1000 withineach beam spot on the sky. Overnight flights from Ft Sumner, NM and Alice Springs, Australia combine to observe thediffuse polarized emission at high signal to noise ratio over 85% of the sky.polarization. Since the sky contains no significant circular polarization, the error signal is negligible (see, e.g.,Ref [22] Appendix A for a discussion of VPM cross-polar response).4. FLIGHT OPERATIONSPIPER operates as a conventional balloon payload launched from mid-latitude sites. The focal plane images a4.?7? 6? field of view on the sky pointed 50? from vertical. During the day the payload scans in azimuth to mapselected regions of the sky in the anti-solar direction, providing deep integrations over small regions of the sky.During the night the payload spins about a vertical axis once every 10 minutes to rapidly map large areas of thesky. A single overnight flight observes more than 50% of the sky. We anticipate a series of flights alternatingbetween northern and southern hemisphere sites to maximize sky coverage (Figure 8).PIPER will map the sky in both linear and circular polarization (Eq. 3). At millimeter wavelengths, the skyis expected to have negligible circular polarization. Maps of the circular polarization thus provide an independentrealization of the noise as well as a test for systematic errors.The high sky coverage allows PIPER to measure the expected rise in B-mode power at ` < 10 (the ?reioniza-tion bump?) where the primordial signal may best be distinguished from the lensing foreground. 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