UBC Faculty Research and Publications

Primordial Inflation Explorer (PIXIE) Mission. Halpern, Mark 2010

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


52383-Halpern_SPIE_7731_77311S.pdf [ 16.75MB ]
JSON: 52383-1.0107584.json
JSON-LD: 52383-1.0107584-ld.json
RDF/XML (Pretty): 52383-1.0107584-rdf.xml
RDF/JSON: 52383-1.0107584-rdf.json
Turtle: 52383-1.0107584-turtle.txt
N-Triples: 52383-1.0107584-rdf-ntriples.txt
Original Record: 52383-1.0107584-source.json
Full Text

Full Text

The Primordial Inflation Explorer (PIXIE) Mission  Alan J. Kogut*a, David T. Chussa, Jessie L. Dotsonb, Dale J. Fixsena, Mark Halpernc, Gary F. Hinshawa, Stephan M. Meyerd, S. Harvey Moseleya, Michael D. Seiffertd, David N. Spergelf, Edward J. Wollacka aCode 665, NASA Goddard Space Flight Center, Greenbelt, MD, USA 20771; bNASA Ames Research Center, Moffett Field, CA, USA 94035; cDept. of Physics & Astronomy, University of British Columbia, Vancouver, BC, Canada, V6T 1Z1;   dDept of Astronomy & Astrophysics, University of Chicago, Chicago, IL, USA;   eJet Propulsion Laboratory, MS 169-506, Pasadena, CA, USA 91109;   fDept of Astrophysical Sciences, Princeton University, Princeton, NJ, USA 08544 ABSTRACT The Primordial Inflation Explorer (PIXIE) is an Explorer-class mission to map the absolute intensity and linear polarization of the cosmic microwave background and diffuse astrophysical foregrounds over the full sky from frequencies 30 GHz to 6 THz (1 cm to 50 μm wavelength). PIXIE uses a polarizing Michelson interferometer with 2.7 K optics to measure the difference spectrum between two orthogonal linear polarizations from two co-aligned beams. Either input can view either the sky or a temperature-controlled absolute reference blackbody calibrator. The multi- moded optics and high etendu provide sensitivity comparable to kilo-pixel focal plane arrays, but with greatly expanded frequency coverage while using only 4 detectors total. PIXIE builds on the highly successful COBE/FIRAS design by adding large-area polarization-sensitive detectors whose fully symmetric optics are maintained in thermal equilibrium with the CMB. The highly symmetric nulled design provides redundant rejection of major sources of systematic uncertainty. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r << 10-3.   PIXIE will also return a rich data set constraining physical processes ranging from Big Bang cosmology, reionization, and large-scale structure to the local interstellar medium. Keywords: cosmic microwave background, polarization, FTS, bolometer  1. INTRODUCTION A central principle in modern cosmology is the concept of inflation, which posits a period of exponential expansion in the early universe shortly after the Big Bang. The many e-foldings of the scale size during inflation force the geometry of space-time to asymptotic flatness while dilating quantum fluctuations in the inflaton potential to the macroscopic scales responsible for seeding large-scale structure in the universe. Inflation provides a simple, elegant solution to multiple problems in cosmology, but it relies on extrapolation of physics to energies more than 12 orders of magnitude beyond those accessible to particle accelerators. Measurement of the linear polarization of the cosmic microwave background (CMB) provides a direct test of inflationary physics. CMB polarization results from Thomson scattering of CMB photons by free electrons. Scattering of an isotropic radiation field produces no net polarization, but a quadrupole moment in the incident radiation yields a polarized signal. The required quadrupole can result from either temperature anisotropy in the radiation field itself, or the differential redshift as gravity waves propagate through an isotropic medium. Temperature or density perturbations are scalar quantities; their polarization signal must therefore be curl-free. Gravity waves, however, are tensor perturbations whose polarization includes both gradient and curl components. In analogy to electromagnetism, the scalar and curl components are often called ``E'' and ``B'' modes. Only gravity waves induce a curl component: detection of a B-mode signal in the CMB polarization field is recognized as a ``smoking gun'' signature of inflation, testing physics at energies inaccessible through any other means1,2,3.  *Alan.J.Kogut@nasa.gov; phone 1 301-286-0853 Space Telescopes and Instrumentation 2010: Optical, Infrared, and Millimeter Wave, edited by Jacobus M. Oschmann Jr., Mark C. Clampin, Howard A. MacEwen, Proc. of SPIE Vol. 7731, 77311S · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.857080 Proc. of SPIE Vol. 7731  77311S-1 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms Figure 1.  Angular power spectra for unpolarized (TT), E-mode (EE), and B-mode (BB) polarization.  The blue band shows the predicted range for the inflationary signal. The PIXIE un-binned sensitivity (dashed red line) matches the confusion noise from gravitational lensing of the primordial E-mode signal. PIXIE can measure even the minimum predicted B-mode power spectrum at high statistical confidence (red points and error bars). Figure 1 shows the predicted angular power spectra of the E- and B-mode polarization. The simplest inflationary models predict an observable B-mode signal, with amplitude in the range 30--100 nK thermodynamic temperature (blue band). Detection of this signal would have profound consequences.  The amplitude r of the gravity-wave signal depends directly upon the energy scale of inflation,   (1) where r is conventionally expressed as the ratio of the tensor to scalar power.  A positive detection would not only establish inflation as a physical reality, but would provide a model-independent determination of the relevant energy scale to test physics at energies near Grand Unification.  Characterization of the B-mode power spectrum would additionally probe the trans-Planckian physics between the beginning and end of the inflationary epoch, providing direct observational input to the ultraviolet completion of quantum field theory and gravity4. Detecting the inflationary signal is difficult.  As recognized in a series of reports5,6,  there are three fundamental challenges: sensitivity, foregrounds, and systematic errors. • Sensitivity: The inflationary signal is faint compared to the fundamental sensitivity limit imposed by photon statistics. Even noiseless detectors suffer from this photon-counting limit; the only solution is to collect more photons. Conventional designs accomplish this using large (kilo-pixel) detector arrays, adversely impacting both mission complexity and cost. • Foregrounds: A second challenge for CMB polarimetry is separating the CMB signal from Galactic foregrounds. Foreground emission within the Galaxy is polarized and is brighter than the dominant E-mode polarization even at the foreground minimum near 60 GHz (Figure 2).  Detecting the much fainter B-mode signal requires foreground cleaning effective at the few percent level, which in turn requires multiple frequency channels to measure the amplitude, polarization vector, and frequency dependence of each foreground component. V 1/ 4 = 1.06 ×1016 GeV r 0.01 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1/ 4 Proc. of SPIE Vol. 7731  77311S-2 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms • Systematic Errors: The gravity-wave signal is less than 1% of E-mode polarization, which in turn is only a few percent of the unpolarized temperature fluctuations on the sky. Even a small admixture of power from either unpolarized sources or the dominant E-mode polarization into a spurious B-mode pattern could overwhelm the primordial signal. The mission design must rigorously control stray light and the instrumental separation of polarized from unpolarized signals in order to confidently detect primordial polarization. Satisfying the simultaneous requirements of sensitivity, foreground discrimination, and immunity to systematic errors presents a technological challenge.  Most instrument designs currently fielded combine focal-plane arrays containing hundreds to thousands of detectors arranged in a modest number (typically 3 to 6) of frequency channels.  In this paper, we describe an instrument capable of measuring the CMB and diffuse foregrounds with background-limited sensitivity in over 500 frequency channels using only 4 detectors.  The resulting reduction in complexity and cost make the instrument an attractive candidate for a future Explorer mission. 2. INSTRUMENT DESCRIPTION  The Primordial Inflation Explorer (PIXIE) is a mission concept designed to detect the polarization signal from an inflationary epoch while remaining within the constraints of NASA's Explorer program. It consists of a polarizing Michelson interferometer which interferes two optical inputs to measure the fringe pattern as a function of the optical phase delay. It uses only 4 semiconductor bolometers to measure both the frequency spectrum and polarization state of the sky to nK precision at wavelengths 1 cm to 50 μm. Observing from low Earth orbit, it can achieve B-mode sensitivity r«10-3 while also providing important new results ranging from the ionization history of the early universe to the spectrum and anisotropy of the far-infrared background to the chemical and energy balance of the interstellar medium. Figure 2.  Polarized emission from Galactic synchrotron (green) and dust (blue) is brighter than CMB polarization (grey) at all wavelengths.  PIXIE observes over 500 spectral bands from 1 cm to 50 μm wavelength to separate CMB from foreground emission. Proc. of SPIE Vol. 7731  77311S-3 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms Figure 3. the Fouri An unpol instrumen  Figure 3 interferomete beams using which move another set concentrator field incident     for the two expressions a constant term the difference   Schematic sho er transform of t arized blackbod t spin modulate shows a schem r. Polarizing another grid o s to inject an of grids. As feeds measure  from the sky. detectors shar pply for the t  (not modulat  spectrum bet wing the instrum he frequency sp y calibrator can s the polarizatio atic of the in wire grids sep riented 45º w optical phase the dihedral  the resulting  The power at ing the left-sid wo detectors ed by the mirr ween the   pola PLx = 12 PLy = 12 x̂ ent concept (le ectrum of the S  be inserted to n to map the ful strument optic arate the two ith respect to t delay. The ph mirrors move fringe pattern the detectors a e feed, where sharing the rig or movement) rization from (ELx 2∫ + ERy2 ) (ELy 2∫ + ERx2 ) ft) and optical tokes Q linear p fill either beam l IQU Stokes pa al design. Lig orthogonal lin he first grid, a ase-delayed b , a pair of p from the mixe s a function of  L and R den ht-side feed).  plus a modul one beam and + (ELx2 − ERy2 ) + (ELy2 − ERx2 ) layout (right). olarization diffe to provide abso rameters on the ht from 2 ind ear polarizati nd then route eams are then olarization-se d beams. Let  the mirror op ote the left a   We can exp ated term prop the   polarizat cos(zω /c) dω cos(zω /c) dω ŷ The fringe patte rence between t lute spectral inf  sky. ependent beam ons from each  them to a dih  re-combined nsitive bolom  tical position z nd right beam ress the detec ortional to th ion from the ot rn at the detecto he two input bea ormation, while s enters a M  input beam, edral mirror a and re-mixed eters in each   represent the  may be writte s on the sky ted fringe patt e Fourier trans her beam. r is ms.  the ichelson mix the ssembly through of two  electric n (2) (similar ern as a form of Proc. of SPIE Vol. 7731  77311S-4 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms PIXIE op beam, the rig repeatedly in  in coordinate and sky coor perform a Fo  for the   dete and Sν denote the full frequ for each pixe temperature the sky the i (Eq. 4).  Int calibration sc each mode. Figure 4 spacecraft sp Sun or the E open to the s remain in the adiabatic dem unobstructed  Figure 4. shields to separates matrix. ˆ x erates in a nu ht beam, or to terchange    an s           fixed dinate system urier transform ctor in the left s the synthesi ency spectrum l in the sky. distribution on nstrument nul erleaving obse ale to linear p shows a pos in axis, which arth.  An exter ky.  The calib rmal equilibriu agnetization  view to deep   Possible confi  block radiation  Stokes I, Q, an ˆ x ˆ ′ x , ˆ ′ y[ ] lled configura  leave both b d    on the dete with respect to s.  Since the m  of the fringe  feed, where zed frequency  of the I, Q, a When the cali  the sky (inclu ls all unpolari rvations with olarization, w sible configur is maintained nal  blackbody rator, beam-fo m with the sk refrigerator. space while av guration for the  from the Sun o d U parameter ˆ y  r E = S I tion.  An unpo eams open to ctors.  The sk  the instrumen irror stroke a pattern each m  spectrum in b nd U paramete brator blocks ding the mono zed emission  and without hile providing ation for the perpendicular  calibrator mo rming optics, y.  Each semic The observat oiding emissio  PIXIE observa r Earth.  It obse s independently Ex cosγ + Ey( υ Lx = 1 4 Iυ L − IυR[ = Ex2 + Ey2, Q = larized blackb the sky.  The y signal then b t, where γ is t t 1 Hz is fast irror stroke to  ins ν set by the rs, referenced either beam, t pole) as well so that the fri the calibrator  a valuable cr PIXIE observ to the Sun line ves to cover e  beam splitters onductor bolo ory operates n from the Su tory.  The instru rves from a pola  within each pi sinγ)ˆ ′ x + Ey( + Qυ cos(2γ) Ex 2 − Ey2, and ody calibrator spacecraft spin ecomes he spacecraft r compared to  obtain the dif                    ar  mirror throw  to an absolute he fringe patte as the linear p nge pattern re  allows straig oss-check of t atory.  The t  and nearly an ither beam an , and interfero meter is coole from a polar n or Earth. ment is mainta r sun-synchrono xel to provide cosγ − Ex sinγ + Uυ sin(2γ)] U = 2Ex Ey  can be move s at 4 RPM a otation angle the 4 RPM sp ference spectra e the Stokes p and sampling.  calibration st rn encodes in olarization.  W sponds only t htforward tra he polarization wo parallel b ti-nadir to min d can be stowe meter are ma d to base temp sun-synchrono ined at 2.7 K an us orbit.  The r a nearly diagon )ˆ ′ y d to fill either bout the beam relating the ins acecraft spin,  olarization par   PIXIE thus m andard, indep formation on hen both bea o the sky pola nsfer of the  solutions obt eams point al imize signals d to leave bot intained at 2.7 erature 0.1 K us orbit to a d is surrounded apid spin efficie al pixel covaria  the left  axis to (3) trument we may (4) ameters easures endently both the ms view rization absolute ained in ong the from the h beams 25 K to using an llow an  by ntly nce Proc. of SPIE Vol. 7731  77311S-5 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms The PIXIE in error rejectio of power in t to B-mode p gravity wave detector arra more photons  where x=hν/ absorptivity, through the o single-mode wavelength. PIXIE has 4 the frequency spectral bins, covers the ra Galactic fore The freq moves, we o Figure throug and sp instrum strument desi n necessary to he tensor and s olarization am  signal using ys results from , not necessar kT, ν is the o T is the phys ptics.  The li optics, the ete  For multi-mo detectors each  range 30--60  compared to ~ nge 30 GHz t grounds. uency bins in btain Ns detec  5.  Simulation h 2 complete in ace-reversal sy ental signals. 3. SENSI gn meets the s  detect the infl calar modes, r plitude 30—1  kilo-pixel arr  the need to ily more detec bserving frequ ical temperatu ght-gathering ndu and wave ded optics, how  with etendu 4 0 GHz where 1500 single-m o 6 THz (1 cm  the synthesiz tor samples o NEPph 2 showing the ob terferograms wh mmetries in th TIVITY AN imultaneous d ationary signa  = T/S. The si 00 nK7,8,9. Cur ays of transit overcome pho tors. The spec ency, A is th re of the sour ability of an i length are rel ever, the bea  cm2 sr.  The  the CMB is b ode detectors  to 50 μm) t ed spectra are ver an optical oton = 4AΩc 2 (kT h served fringe p ile observing an e time-ordered D SYSTEM esign goals of l.  The gravity mplest inflatio rent state-of-t ion-edge supe ton noise stat tral density of e detector are ce, ε is the s nstrument is s ated as AΩ=λ m size is fixed spectrometer p rightest, PIXI  in ~6 bins for o provide hig  set by the m  path length ± )5 3 αεf x 4 ex −∫ attern on a sing  unpolarized CM data, allowing ATIC ER  sensitivity, fo  wave signal i nary models p he-art instrum rconducting b istics. Strictly photon noise i a, Ω is the de ource emissivi pecified by its 2 so that the b  and the numb roduces spectr E observes ov  comparable C h signal-to-no irror throw an Δz. The Four 1 1+ αεf ex −1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ d le detector as th B signal. Sky  straightforward RORS reground sepa s generally cha redict 0.01 < r ents10,11,12 sear olometers.  T  speaking, how s given by13 tector solid an ty, and f is th  etendu AΩ. eam size scal er of modes N a with bin wid er 44,000 ind MB polarimet ise polarizatio d detector sam ier transform x e mirror sweep signals must ob  identification ration, and sy racterized by  < 0.16, corres ch for the infl he push to k ever, the nee gle, α is the e power trans For diffraction es with the ob  scales as N = th 15 GHz.  O ependent mod ers.  The full s n maps of all pling.  As th of the sample s back and fort ey multiple time and removal o stematic the ratio ponding ationary ilo-pixel d is for (5) detector mission -limited serving  AΩ/λ2. ver just es in 40 pectrum relevant e mirror d fringe h - f Proc. of SPIE Vol. 7731  77311S-6 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms pattern returns frequencies n × c/(2Δz) where n=0,1,2, ... Ns/2.  With Ns = 1024 and ΔL = 1 cm, we obtain 512 bins of width 15 GHz each.  The corresponding physical movement x = z / [4 cos(α) cos(δ/2)] = 2.6 mm accounts for the folded optics as well as the off-axis optical path (α=15°) and beam divergence (δ=7°). A full cycle of the mirror from one endpoint to the other and back thus contains 2 complete interferograms (Figure 5). A Fourier transform uniformly sampled from -1 to +1 has sharp edges at ±1, leading to ringing in the frequency domain.  In addition, the CMB only produces fringes near zero path length -- observations at longer optical path, necessary to provide sufficiently narrow frequency bins, have almost no CMB signal and thus contribute little to the CMB sensitivity.  We minimize ringing and maximize sensitivity by varying the mirror stroke to apodize the Fourier transform.  A commonly used apodization is (1-z2)2.  PIXIE observes any given location on the sky for at least 13 consecutive orbits.  Each orbit uses a different mirror stroke length, ranging from a shortest stroke Δz=3.3 mm (physical movement ±0.9 mm) to a longest stroke 10 mm (physical movement ±2.6 mm).  Figure 8 shows the resulting apodization.  By spending relatively more time near zero delay, we apodize the Fourier transform to retain narrow frequency bins while simultaneously increasing the sensitivity to CMB signals by 37% compared to uniform sampling. The PIXIE observing strategy provides immunity to 1/f noise or other instrumental drifts.  A single interferogram takes data as the mirror moves from one endpoint through the null to the other endpoint.  Not only does this provide null tests against systematic errors, but the spatial symmetry about zero path length forces the sky signal entirely into the real part of the Fourier transform.  The imaginary part corresponds to the anti-symmetric component of the sampled data and will consist only of instrument noise and systematic errors.  This provides a powerful check on systematics while yielding a clean measurement of the instrument noise (including any 1/f component) fully coincident with the noise in the final sky spectra.  In addition, the Fourier transform operates on short stretches of data, ranging from 330 ms to 1 second (depending on the mirror apodization stroke).  Each interferogram is independent, so 1/f noise or drifts on time scales much longer than 1 second will appear as a constant slope or a low-order polynomial in any given fringe pattern. Such artifacts affect only the lowest few frequency bins of the Fourier transform and do not project onto either the CMB or foreground spectra. 3.1 Amplitude Modulation The spacecraft spin provides additional protection against systematic errors.  The fringe pattern shown in Figure 5 corresponds to an unpolarized CMB signal.  The 4 RPM rotation introduces an additional modulation for polarized emission from the sky.  Figure 7 shows the resulting fringe pattern.  Unlike simple polarization-sensitive bolometers, Figure 6.  Apodization of the optical phase delay created by scanning the mirror through different path lengths on different orbits.  The actual apodization (solid line) closely approximates the optimum (dashed line) and suppresses ringing while yielding a 37% increase in sensitivity to the CMB compared to uniform sampling. Proc. of SPIE Vol. 7731  77311S-7 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms where instrum modulation o locked sine w The amp Consider, for optical fringe electronics). or spacecraft to additive s correspondin transform th coordinates computed sp the CMB pol interferogram projection on 3.2 Sum an PIXIE's optical syste polarization aliasing of p ellipticity.  P and a redund beam elliptic [14]. Compar Figure an amp at a sin ent rotation p f the entire fr ave, efficientl litude-modula  instance, an  pattern of a t  Even if the sy  spin, its overl ystematic erro g to either the e simulated da and associated ectra Qν (Eq 4 arization.  Sin ), the power to CMB polar d Difference S symmetric des ms. The rotat signal (at twi ower from a l IXIE has 4 po ant pair behind ity: requiring ing data betw 7. Simulated fri litude modulatio gle frequency. roduces a sin inge pattern. y suppressing ted interferen additive signa rue sky signal stematic error ap with the am r signals by s  orbit period, ta from each  spin angle γ ) to a differen ce the sinusoid in the Fourie ization is smal pectra ign reduces se ion of a non-c ce the spin fr ocal temperatu larization-sen  a second feed the systematic een bolometer nge patterns fro n (dotted envel usoidal respon  The resulting any spin-synch ce fringes are l of the form and Vs(t) = sin  signal occurs plitude-modul imulating the spin period, ha mirror stroke , and solve fo tial Planck spe al error signal r-transformed l, with rejectio nsitivity to oth ircular (ellipt equency) whe re quadrupole sitive bolomet .  If we consid  error signal t s significantly m a single detec ope) on the enti se to polarized  modulated fr ronous drifts.  a powerful g Vdet = Vo(t) + (ωt +φ)  is a  at a particular ated CMB frin  PIXIE time-o lf the spin per  (Eq. 2) to ob r the Stokes ctrum to quan  lacks power o spectra is co n better than - er potential s ical) beam ac rever the un-p  moment to a ers: one pair i er the output o remain belo relaxes the dep tor observing p re fringe pattern  sky signals, inge pattern i  uard against  Vs(t), where sine-wave syst ly important f ge pattern is s rdered data w iod, or the mi tain sky spec I, Q, and U tify the projec n short time s ncentrated in 65 dB. ystematic erro ross an un-po olarized sky false polariza n orthogonal l of a single det w a few nK re endence on b olarized CMB. , efficiently sup PIXIE's rotatio s readily distin broad classes Vo(t) is the de ematic error ( requency relat mall.  We qua ith the period rror stroke per tra, tag each s parameters.  W tion of system cales (short sp the first few rs.  Consider t larized sky w contains a loc tion signal gro inear polariza ector, we find quires the bea eam ellipticity The instrument pressing spurio n produces am guished from of systematic tector output f e.g. from the b ed to the mirro ntify the susce  of the additi iod.  We then pectrum with e then comp atic error sign atial frequenci frequency bin he effects of n ill produce a al saddle poin ws rapidly wi tions behind o significant cou m ellipticity e .  The two det  rotation impose us signals locke plitude  a spin-  effects. rom the ack-end r stroke ptibility ve term  Fourier the sky are the als onto es in the s.  The on-ideal spurious t.  The th beam ne feed, pling to <3×10-4 ectors in s d Proc. of SPIE Vol. 7731  77311S-8 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms each feed share the full optical chain to the sky, differing only in polarization orientation.  Their sum and difference spectra (Eq. 4) may be written as   (6)   where δG/G is the fractional calibration error between the two detectors.  The sum is dominated by the unpolarized spectrum, while the difference has contributions from both the polarized sky spectra and a term proportional to the gain error times the unpolarized spectrum.  We may then recover the sky spectra I, Q, and U using the following algorithm. We generate the detector sum spectra and bin them by sky position to find the unpolarized spectrum Isum in each pixel, ignoring the second-order term δG/G (Q+U). We then generate the detector difference spectra and use the sky position and rotation angle to solve for the polarization spectra Q and U plus an unpolarized correction term Idiff. The final sky solution uses I = Isum + Idiff to recover the unpolarized gain mismatch term. The use of sum and difference spectra greatly reduces the ΔT → B coupling. This translates into relaxed requirements for instrument beam ellipticity e.  Simulations show that for calibration error as large as 1%, achieving systematic errors below 3 nK only requires beam ellipticity e<0.06.  In practice, the calibration error will be much smaller, reducing beam artifacts to negligible levels. 3.3 Symmetry and Null Tests Null tests are an important demonstration that systematic errors are small compared to the instrument noise.  PIXIE's highly symmetric design provides a large number of such tests.  A few of the more important null tests include: • Interferograms from a single detector should remain unchanged as the mirror moves forward or backward. Any difference traces errors in the detector response function. • Interferograms on the same detector taken 1/4 spin apart should have polarized signal opposite in sign.  Any difference indicates a residual instrumental polarization. • Interferograms on the same detector taken 1/2 spin apart should be identical.  Any difference indicates cross-polar leakage. • Interferograms on the left detector should be identical to those from the right detector 1/4 spin later.  Any difference indicates cross-polar leakage or detector calibration error between the two sides of the instrument. • Interferograms taken with the calibrator over one aperture should be opposite to interferograms taken with the calibrator over the other aperture.  Any difference indicates asymmetries in the instrument optical path. • Spectra from a given pixel should be identical when the pixel is revisited.  Re-visits occur on all time scales from a single orbit for pixels near the celestial poles to 6 months for pixels near the celestial equator. In addition, the interferograms are symmetric about zero phase delay so that the sky signal contributes only to the real part of the synthesized spectra.  The imaginary part consists of an independent realization of the instrument noise (plus any systematics), obtained simultaneously with the noise realization in the sky signal.  All null tests in the list above thus use the imaginary part of the synthesized spectra to characterize the statistical properties of the noise in that test -- PIXIE does not rely on difference tests to determine the noise properties.  4. FOREGROUNDS AND FREQUENCY SPECTRA  Four foreground components are relevant for CMB polarization.15,16  Synchrotron emission results from cosmic ray electrons accelerated in Galactic magnetic fields; the amplitude (in intensity units) scales as Ssynch ~ ναs  where the spectral index αs ≈ -1 is spatially variable and steepens with increasing frequency.  Polarized dust emission results from Sυ sum = 1 2 Iν L − IνR + δGG Qν cos(2γ) + Uν sin(2γ)( ) ⎡ ⎣ ⎢ ⎤ ⎦⎥ Sν diff = 1 2 Qν cos(2γ) + Uν sin(2γ) + δGG Iν L − IνR( )⎡ ⎣ ⎢ ⎤ ⎦ ⎥ Proc. of SPIE Vol. 7731  77311S-9 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms grains aligned in the same magnetic field and scales as Sdust ~ ναd Bν(Tdust) where αd ≈ 2 and Bν is a blackbody at temperature Tdust. Free-free emission from electron-ion collisions in the warm interstellar medium is largely unpolarized, but may acquire a small polarized component in scattering from ubiquituous dust grains.  In addition, electric dipole emission from a population of small, rapidly spinning dust grains dominates Galactic emission at wavelengths near 1 cm.17,18  Although the intrinsic polarization from such emission is predicted to be less than a few percent19, it complicates foreground cleaning through confusion with the synchrotron component of diffuse continuum radio emission. These emission mechanisms are smooth functions of frequency so that multi-frequency observations can be combined to model and remove foreground contamination.  The required number of frequency channels depends on the number of fitted parameters.  The most optimistic technique fixes the spectral dependence and fits only the CMB, synchrotron, and dust amplitudes, requiring a minimum of 3 frequency channels.  Fitting additional parameters (synchrotron spectral index, synchrotron spectral curvature, free-free or spinning dust contribution, dust color temperature, dust spectral index, dust alignment) requires additional frequency channels. PIXIE samples the observed fringe pattern at 1024 spatial frequencies to synthesize frequency spectra in 512 bins spaced 15 GHz apart.  A low-pass filter on the front-end optics blocks zodiacal light, but no other passband filters are required. The broad spectral coverage and clean optical path provide an ideal data set to constrain models of foreground emission. The number of frequency channels is much larger than any plausible number of foreground parameters, allowing straightforward statistical assessment of the utility of adding additional foreground parameters.  Foregrounds are observed through the same optics and using the same calibration as the CMB, automatically including frequency bands where the foregrounds dominate the sky as well as bands where the CMB is more prominent.  The large number of frequency bands provides a minimum "noise penalty" for linear combinations of frequency channels used to reject foreground emission.  Assuming (for illustration) a simple model with power-law synchrotron and dust foregrounds (αs and αd independent of either sky position or frequency), the noise in a foreground-cleaned PIXIE map is only 8% worse than the ideal case of noise weighting with no foregrounds. The broad frequency range of the PIXIE data provides rich ancillary science in addition to the primary goal of inflationary science. Thomson scattering of CMB photons from free electrons at the epoch of reionization sources E-mode polarization on large angular scales. The same scattering necessarily distorts the unpolarized CMB away from a blackbody.  PIXIE will observe both the E-mode polarization and unpolarized spectral distortion.  The combination can be used to fix not only the optical depth, but also the gas temperature, and hence provide information on the ionization mechanism at redshift z ~ 10.  PIXIE data in the far-infrared will characterize the monopole, dipole, and higher-order power spectrum of the far-IR background to test the matter distribution at redshift z ~ 3.  PIXIE will measure line emission from the interstellar medium, including the prominent CII (158 μm), NII (205 μm), and OI (63 μm) lines as well as the CO series.  5. DETECTOR IMPLEMENTATION  PIXIE requires detectors with large absorbing area (etendu 4 cm2 sr) capable of detecting a single linear polarization (cross polar response 1% or smaller).  The longest mirror stroke samples the detector 1024 times per 1 second stroke, so the detector time constant should be of order 1 ms.  To minimize lost time from cosmic-ray hits, the absorbing area for photons should be large compared to the geometric cross section.  Finally, ultra-broad-band detection at the photon limit requires device (phonon) NEP < 10-16 W Hz-1/2. The PIXIE detectors require absorber area a factor of ten larger than the detectors flown on the BOOMERANG suborbital instrument or ESA's Planck satellite.20,21 Existing polarization-sensitive bolometer designs can not simply be scaled to meet the PIXIE requirements.  As the detector linear scale becomes larger than a wavelength, thermalization of the active absorber area becomes problematic. This problem is especially acute for multi-moded optics where significant spatial gradients in optical power can occur across the absorber. As the instrument beam scans across the sky, these gradients will shift across the absorber. The response of the thermistor will be a complex sum of the thermal response along individual strands, with power absorbed far from the thermistor delayed in time with respect to power absorbed Proc. of SPIE Vol. 7731  77311S-10 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms nearby. The time-ordered signal from the thermistor will then include a contribution from sources other than the interferometer fringes (Eq. 2), aliasing power from bright unpolarized sources into the much fainter polarization. We have developed a large-area polarization-sensitive bolometer for multi-moded optical systems such as PIXIE. Figure 8 shows a schematic of the PIXIE detector. It consists of a set of thin, parallel strands of doped crystalline silicon, micro-machined from an ion-implanted layer and suspended from an un-doped crystalline silicon frame. PIXIE will operate from 1 cm to 50 μm wavelength; the wire pitch is thus set at 30 μm. Un-doped cross beams spaced every 300 μm provide additional mechanical support without adding significantly to the geometric cross section; the geometric filling fraction is only 11%.  We deviate from the PSB design in two significant ways. The entire device, including the absorbing strands and thermal link to the bath, is made from crystalline silicon to increase the thermal conductance and decrease the absorber time constant. To stabilize the thermal response of the entire detector, we add two thick (0.5 μm) gold bars along the edges where the absorbing strings connect to the frame. The gold bars dominate the heat capacity of the detector to allow thermalization of the contribution from individual wires. A set of 4 ion-implanted silicon thermistors are thermally anchored to the gold bars to monitor the temperature. The time constant of the device is set by the thermal conductance G of a series of silicon legs linking the absorber/bar composite to the silicon frame, which also serve to mechanically support and stiffen the absorbing structure. The detector is physically large, with detector area 12.7 x 12.7 mm. Despite the large area, the time constant for heat transport across the absorbing strands is short (τ=0.6±0.1 ms), validating the choice of crystalline silicon for the detector substrate.  REFERENCES [1] Kamionkowski, M., Kosowsky, A., and Stebbins, A., "Statistics of cosmic microwave background polarization," PRD, 55, 7368 (1997). [2] Seljak, U, and Zaldarriaga, M., "Signature of Gravity Waves in the Polarization of the Microwave Background", PRL, 78, 2054 (1997). [3] Hu, W., and White, M.J., "A CMB polarization primer," New Astronomy, 2, 323 (1997). [4] Lyth, D.H., "What Would We Learn By Detecting a Gravitational Wave Signal in the Cosmic Microwave Background", PRL, 78, 1861 (1997). [5] Bock, J., et al., "Task Force on Cosmic Microwave Background Research", arXiv:astro-ph/0604101v1 (2006). [6] Dodelson, S., et al., "the Origin of the Universe as Revealed Through the Polarization of the Cosmic Microwave Background", Astro2010 White Paper 67, arXiv:0902.3796 (2009). Figure 8. Schematic of PIXIE polarization-sensitive bolometer.  Thin wires of doped crystalline silicon absorb a single linear polarization.  Gold bars depositied over the ends of the wires thermalize the device.  The measured time constant is 0.6 ms.   Four ion-implanted thermistors provide temperature readout. The inset at left shows the absorbing strands and thermalizing bar on the fabricated device Proc. of SPIE Vol. 7731  77311S-11 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms [7] Spergel, D.N., et al., "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters," ApJS, 148, 175 (2007). [8] Linde, A.D., "Current Understanding of Inflation," New Astronomy Reviews, 49, 35 (2005). [9] Lyth, D.H., and Riotto, A., "Particle Physics Models of Inflation and the Cosmological Density Perturbation," Phys. Rep., 314, 1 (1999). [10] Montroy, T.E., et al., " SPIDER: a new balloon-borne experiment to measure CMB polarization on large angular scales," Proc SPIE, 6267, 6267R (2006). [11] Oxley, P., et al., "The EBEX Experiment",  Proc SPIE, 5543, 320 (2004). [12] Chuss, D., et al. "Primordial Inflation Polarization Explorer". Proc. SPIE, 7741 (2010) [13] Mather, J.C., "Bolometer noise: nonequilibrium theory," Applied Optics, 21, 1125 (1982). [14] Shimon, M., "CMB polarization systematics due to beam asymmetry: Impact on inflationary science", PRD, 77, 083003 (2008). [15] Page, L, et al., "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis", ApJS, 170, 335 (2007). [16] Gold, B, et al., "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission", ApJS, 180, 265 (2009). [17] Kogut, A., et al., "ARCADE 2 Observations of Galactic Radio Emission", ApJ, submitted, arXiv:0901.0562 (2009). [18] Gold, B., et al., "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission", ApJS, in press (2010). [19] Lazarian, A., and Draine, B. T., "Resonance Paramagnetic Relaxation and Alignment of Small Grains", ApJL, 536, 15 (2000). [20] Jones, W.C., et al, "Instrumental and analytic methods for bolometric polarimetry," A&A, 470, 771 (2007). [21] Holmes, W.A., et al., "Initial Test Results on Bolometers for the Planck High Frequency Instrument," Applied Optics, 47, 5996 (2008).  Figure 9: Polarization-sensitive bolometer during thermal testing. Proc. of SPIE Vol. 7731  77311S-12 Downloaded from SPIE Digital Library on 13 Sep 2011 to Terms of Use:  http://spiedl.org/terms


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items