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Optimization and sensitivity of the Keck Array Amiri, Mandana; Burger, Bryce; Davis, Greg; Halpern, Mark; Hasselfield, Matthew; Wiebe, Donald V. Sep 27, 2012

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Optimization and sensitivity of the Keck ArrayS. Kernasovskiy,a,b P. A. R. Ade,c R.W. Aikin,d M. Amiri,e S. Benton,f C. Bischoff,g J.J.Bock,d,h J. A. Bonetti,h J. A. Brevik,d B. Burger,e G. Davis,e C.D. Dowell,d,h L. Duband,i J.P. Filippini,d S. Fliescher,j S.R. Golwala,d M. Halpern,e M. Hasselfield,e G. Hiltion,k V.V.Hristov,d K. Irwin,k J. M. Kovac,g C. L. Kuo,a,b E. Leitch,l M. Lueker,d,h C.B. Netterfield,f H.T. Nguyen,d,h R. O?Brient,d,h R. W. Ogburn IV,a,b C. L. Pryke,j C. Reintsema,k J.E. Ruhl,mM.C. Runyan,d R. Schwarz,j C. D. Sheehy,j Z. Staniszewski,d,h R. Sudiwala,c G. Teply,d J. E.Tolan,a,b A. D. Turner,h A. Vieregg,g D. V. Wiebe,e P. Wilson,h C. L. WonggaStanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA;bKavli Institute for Particle Astrophysics and Cosmology (KIPAC), Sand Hill Road 2575,Menlo Park, CA 94025, USA;cDept. of Physics and Astronomy, University of Wales, Cardiff, CF24 3YB, Wales, UK;dCalifornia Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 USA;eDepartment of Physics and Astronomy, University of British Columbia, 6224 AgriculturalRoad, Vancouver, BC V6T1Z1, Canada;fDepartment of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada;gHarvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138;hJet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109, USA;iService des Basses Tempratures, DRFMC, CEA-Grenoble, 17 rue des Martyrs, 38054Grenoble Cedex 9, France;jSchool of Physics and Astronomy, University of Minnesota, 116 Church StreetS.E.,Minneapolis, MN 55455;kNIST Quantum Devices Group, 325 Broadway, Boulder, CO 80305, USA;lUniversity of Chicago, KICP, 933 E. 56th St., Chicago, IL 60637 USA;mPhysics Department, Case Western Reserve University, Cleveland, OH 44106 USA;ABSTRACTThe Keck Array (SPUD) began observing the cosmic microwave background?s polarization in the winter of 2011at the South Pole. The Keck Array follows the success of the predecessor experiments Bicep and Bicep2,1using five on-axis refracting telescopes. These have a combined imaging array of 2500 antenna-coupled TESbolometers read with a SQUID-based time domain multiplexing system. We will discuss the detector noise andthe optimization of the readout. The achieved sensitivity of the Keck Array is 11.5 ?KCMB?s in the 2012configuration.Keywords: Cosmic Microwave Background, polarization, inflation, Keck Array, Bicep2, TES, detector noise1. INTRODUCTIONInflation, the theory that the universe experienced exponential expansion in its first fraction of a second, wasoriginally introduced as a way to solve the horizon problem?why the universe was nearly homogenous andgeometrically flat.2 Since then, it predicted many phenomena since confirmed by observation: gaussianity, scale-invariance, and adiabaticity.3,4 It also is predicted to have produced a gravitational wave background. Thetensor perturbations generated would leave a signature in the curl component of the polarization (B-mode) ofthe Cosmic Microwave Background radiation (CMB).5,6 The curl-free component of the polarization (E-mode) isSend correspondence to S. Kernasovskiy,E-mail: sstokes@stanford.eduMillimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VI, edited by Wayne S. Holland, Jonas Zmuidzinas, Proc. of SPIE Vol. 8452, 84521B ? 2012 SPIE ? CCC code: 0277-786X/12/$18 ? doi: 10.1117/12.926934Proc. of SPIE Vol. 8452  84521B-1Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsdominated by the scalar, mass density perturbations. The ratio of the tensor to scalar perturbations (r) dependson the energy scale of inflation.The DASI experiment was the first to detect the polarization of the CMB,7 detecting the E-mode polarization.The E-mode polarization power spectrum is determined by the same physics as the temperature power spectrumand thus provided a good test of the CMB paradigm. The B-mode polarization signal is much smaller than theE-mode, and the current upper limits on r < 0.21 (95% CL) actually come from WMAP and SPT8 using thetemperature information. BICEP provides the best upper limit from the B-mode power spectrum at r < 0.72(95% CL).1The Keck Array (aka SPUD) is a ground based polarimeter currently observing the CMB. The Keck Array isthe latest of the Bicep/Bicep2 family of experiments. All three experiments use similar optical designs, Bicep2uses a focal plane with the same detectors as the Keck Array, and the Keck Array transitioned to a closed-cycleHe cooler and increased the number of receivers. These experiments were designed specifically with the goal ofmeasuring the imprint of gravitational waves from inflation on the polarization of the CMB. Measuring such asignature will require a lot of sensitivity in large angular scale (` ? 100) polarization. Our strategy is to integratedeeply on a 800 deg2 patch of sky with a 0.5 deg FWHM beam.This paper is focused on the Keck Array and its sensitivity. Several companion papers presented at thisconference focus on the current status of Bicep2 and the Keck Array (Ogburn et al.9), the Keck Array opticalperformance (Vieregg et al.10), the performance of the dual planar antennas (O?Brient et al.11), and the thermalstability performance of Bicep2 (Kaufman et al.12).2. INSTRUMENTThe Keck Array consists of a set of five telescopes, each of which is very similar in design to Bicep2.13?15 Eachtelescope consists of a 26.4 cm aperture, refractive optics focusing light onto a focal plane of 256 dual-polarizationdetector pairs. Currently, all five telescopes are observing at 150 GHz. In the future, we have the ability to switchthe optics and detectors of individual telescopes to either a frequency of 100 GHz or 220 GHz. This modulardesign allows for tight systematic control, including a complete shielding from the ground, stable temperatureof the optics and loading on the focal plane, and end-to-end optical measurements.The receiver and all of the optics, are cooled to 4K using a closed-cycle He pulse tube system. This is themain difference in design between the Keck Array and Bicep2, which uses liquid helium. The focal plane iscooled to 270 mK using a 3He/4He 3-stage sorption fridge.The first 3 receivers were deployed to the South Pole in the Martin A Pomerantz Observatory (MAPO) forthe 2011 season, using the 3-axis mount originally built for the DASI experiment. The remaining 2 receivingwere installed and observations with the full 5 receivers commenced in 2012.2.1 DetectorsThe detectors, developed at JPL for joint use in Bicep2, SPIDER and the Keck Array experiments, consistsof phased array antennas feeding into Ti transition-edge sensor (TES) bolometers,16,17 described in detail inO?Brient et al.11 These detectors are lithographically patterned, making it easier to produce many detectors at atime. Each camera element consists of two phased antenna arrays, with orthogonal polarization direction. Eachsignal is then bandpass filtered and terminated into a Ti TES suspended in a SiN membrane. A single 4? Si tilecontains 64 detector pairs and a focal plane unit has 4 tiles. In each focal plane, 16 detectors are left dark. Darkdetectors consist of the complete TES island structure, but are not connected to their corresponding antennas.The detectors in the Keck Array are the result of extensive fabrication and testing. The earliest of thecurrently used detectors were made in the summer of 2010, and the latest in late 2011. The thermal connectionbetween the TES and the bath can be modeled using load curves by sweeping the detector bias and reading theoutput current with the focal plane held at different temperatures. For small temperature changes ?T aroundthe transition temperature Tc, the load power to the bath Pbath is approximated by Equation 1.Pbath = K(T?+1 ? T ?+1bath ) ? Pbath0 +Gc?T (1)Proc. of SPIE Vol. 8452  84521B-2Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsThe Keck Array detectors have thermal conductivities Gc of 40 ? 90 pW/K, Tc of 470 ? 530 mK and thermalconductance exponent ? of 2.5. The Gc and Tc were designed to minimize the detector noise, while leavinga margin of safety to ensure the detectors are not saturated during observations. Under standard observingconditions at the South Pole, the focal planes are cooled to 270 mK, and the Joule power PJ is 5-10 pW intransition. The optical loading (P ), measured by comparing the saturation power of the dark detectors to thelight detectors is 2? 4 pW. The detector parameters are summarized in Table 1.Receiver Rx0 Rx1 Rx2 Rx3 Rx4Gc(pW/K) 80 50 80 40 60Tc(mK) 530 500 530 470 500PJ(pW ) 7.7 6.7 7.4 4.9 7.2Table 1: Summary of detector parameters for the Keck Array receivers. There is significant variation withinreceivers by detector tile, but the values are averaged here for conciseness.The optical efficiencies of the detectors are measured in the lab as part of the standard testing regimen. Themeasurements are taken by placing a beam-filling, microwave-absorbing cone over the vacuum window of thereceiver at room temperature (? 295K) and at liquid nitrogen temperature (? 74K at the South Pole). Theoptical efficiency ? is defined as the fraction of power that the bolometer measures compared to total light powerinput.P = ?? ?2?1h?exp(h?/kT )? 1d? (2)where P is the measured power with the bolometer, and ?1 and ?2 are the band defining frequencies. At150 GHz, both of these temperatures are well in the Rayleigh-Jeans limit (h?  kT ). Equation 2 reduces to?P = ?kB???? ?T , where??? is the fractional spectral bandwidth (0.22), ? is the band center frequency (145GHz), and ?T is the difference in temperature of the loads. From these measurements, the median opticalefficiency ? is ? 30%.2.2 ReadoutWe apply a voltage bias to the TESs and read out the current from the detectors using time-division multi-plexed superconducting quantum interference devices (SQUID).18 These were developed at NIST and are usedin numerous other CMB/submillimeter experiments. This multiplexing system consists of 3 stages of SQUIDs.Each detector is inductively coupled to a first stage SQUID (SQ1). A set of 33 SQ1s are inductively-coupledinto a summing coil leading to a single second-stage SQUID (SQ2). They are multiplexed by simply turning theSQ1 biases on and off. When its bias is turned off, the SQ1 is superconducting and does not contribute to thesumming coil. The output of the SQ2 then leads to a high gain SQUID series array (SSA) before exiting thecryostat. The SQ1s and SQ2s are placed on the focal plane unit along with the detectors at 270 mK. The SSAsare cooled to 4K. This readout system is also described by Ogburn et al.9,15The electronics for the SQUID multiplexers (Multichannel Electronics or MCE) were developed at UBC.19These electronics control the current bias and flux feedback (to center the SQUID V (?) modulation curve) forevery SQUID. They also bias the TESs, with only 1 common bias line used per 32 TESs. The detectors sharinga single bias line are all drawn from the same detector tile and have similar enough properties that this isacceptable.3. OBSERVATIONSThe Keck Array observes the CMB in a patch of 800 deg2 in the southern hemisphere known as the ?SouthernHole?. This patch of sky has very low dust and synchrotron foreground emissions. It overlaps with the observingregions of several other experiments located in the southern hemisphere including BICEP/Bicep2 and SPTPol.150 GHz is near the minimum of expected astronomical foreground contaminations for this patch.Proc. of SPIE Vol. 8452  84521B-3Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms10?1 100 101100101102103104HzpA?Hz  medianFigure 1: Polarization pair differenced noise spectrum for all of the pairs in one receiver. Most of the 1/f noiseinduced by the atmosphere is common mode and is removed by differencing the pairs. The red line indicates`=100 when scanning at 1.6 deg/s in azimuth.The observing strategy is to scan in azimuth while stepping in elevation. Every 2 days, the entire telescope,ground shielding baffles, optics and detectors are rotated about the boresight. We observe at 4 different boresightrotations: 2 sets of 180? rotations offset 45? from each other, completing the Stokes Q and U maps. The 180?rotation takes advantage of the small size of the Keck Array to suppress systematics. In every 48 hour cycle,the Keck Array observes 4?9 hours on the CMB patch, 1?6 hours on the galactic plane, and spends 6 hours oncryogen servicing.3.1 CalibrationsDuring the Austral summer we perform instrument calibrations. A source is placed a distance of 200m awayfrom the Keck Array and is observed using a large, 45 deg, flat mirror to produce maps of the detector beams.The beams have a median FWHM of 0.5deg. The optical characteristics of the Keck Array will be more fullydescribed by Vieregg et al. in these proceedings.During observations, calibration measurements are routinely taken. Every hour, the Keck Array does a 1deg elevation nod on the sky (elnod) in order to calibrate the relative gain between each polarization pair ofdetectors. The TES biases are also swept to measure the operating resistance and the saturation power. Every10 hours, we do a larger dip on the sky and a full load curve.4. DETECTOR NOISEWe measure the noise of the detectors in several ways. In normal data taking mode, we multiplex, filter, anddownsample the timestream to 20 Hz. The targeted range of CMB modes is ` ? 30 ? 300, with a peak fromprimordial gravitational B-modes expected at ` ? 80. In combination with a scan velocity of 1.6 deg/s inazimuth, the B-mode signal will appear at frequencies between 0.1 and 1 Hz in the recorded timestreams. Thussaving the data at 20 Hz is more than sufficient to retain the information on the targeted ` range. This ` range isalso sufficiently high to avoid 1/f induced by variations of the atmosphere into the polarization pair-differenceddata. Figure 1 shows the noise spectrum in pair-differenced observational data.We are able to record data from single detectors at higher sampling frequencies by avoiding the multiplexingstep in the readout described in Section 2.2. An example of single detector noise spectra, taken at 400kHz, asit is biased through transition is in Figure 2. We have taken such noise spectra from every detector as they arebiased through transition to characterize their noise properties.In the 2010 SPIE proceedings, Brevik et al.20 presented a detailed model of the noise of Bicep2 detectors.Since the detectors of Bicep2 and the Keck Array follow the same design, they have a similar noise profile. TheProc. of SPIE Vol. 8452  84521B-4Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms102 103 104 105100101102103104HzpA/?HzNoise through transition  0.100.240.330.420.520.630.750.870.97R/Rnorm102 103 104 105100101102103104HzpA/?HzNoise through transition  0.050.090.140.270.340.420.510.610.710.830.950.99R/RnormFigure 2: High frequency noise spectra for a single detector plotted for different fractional TES resistancesR/Rnormal. The detectors are normal conducting at high biases (black) and superconducting at low biases(yellow). The bolded noise spectra are at the biases used during standard observations. The detector on theleft is a detector with substantial excess noise, which shows up as increased noise between 102 and 104 Hz. Thedetector on the right is typical of those with less excess noise at low biases.noise spectrum is composed of photon noise, phonon noise, Johnson noise, amplifier noise, and an excess noisewhich seems to peak broadly at 1kHz. Figure 3 shows this model for the same detectors as Figure 2, biased atthe standard operation configuration.The excess noise?s spectral signature is similar to Johnson noise. This is not a new phenomenon ? it hasbeen observed in other TESs.21,22 Several articles discuss models of this noise,23,24 noting that it is an expectedfundamental noise from a TES. Although the noise is not modeled in this paper, it is worth noting that thedetectors do not all have the same amount of excess noise at low biases. Figure 2 shows a detector with littleexcess noise at low biases and a detector with substantial excess at low biases. Either way, 100Hz is above thefrequency band of interest, and the excess noise should not increase the overall noise levels as long as it is notaliased into the science band from multiplexing. This will be discussed more in Section 5.2.The photon noise is dominant at low frequencies and is modeled by Equation 3. The noise-equivalent power(NEP) is:NEP2photon = 2h?Qload +2Qload????(3)where ? is the frequency, ??? is the spectral bandwidth. The photon loading Qload can be estimated by thetemperatures of the optics and the sky emissivity. The photon noise in the Figure 3 is consistent with a loadingof 4.5 pW, or 25 Kelvin (Rayleigh-Jeans equivalent) at zenith. This is consistent with what we expect for awarm austral summer day at the South Pole. During the winter observing season, the photon loading is closerto 3 pW for these detectors.The phonon noise also contributes significantly at low frequencies. These are thermodynamic fluctuationsassociated with the thermal conductance.21 This is modeled in Equation 4.NEP2TFN = 4kBT2c GF (Tc, Tbath) (4)where F (Tc, Tbath) accounts for non-linear thermal conductance and is estimated to be ? 0.5 for our configura-tion.20,25 The measured thermal conductances Gc and transition temperature Tc from Table 1 were inputs forthe phonon noise.The Johnson noise, or thermodynamic fluctuations of the electrical resistance, is estimated by Equation 5 atDC:Proc. of SPIE Vol. 8452  84521B-5Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms101 102 103 104 105100101102103104HzpA/?HzNoise Modeled and Measured at R/Rnorm=0.75  101 102 103 104 105100101102103104HzpA/?HzNoise Modeled and Measured at R/Rnorm=0.34  PhotonTES JohnsonShuntPhononAmplifierExcessTotalmeasuredFigure 3: High frequency noise spectra and noise model for a single R/Rnormal. These are the same detectorsas in Figure 2: the detector on the left has excess noise as low biases, while the detector on the right has less.The excess noise is marked as the measured spectra minus the model. The TES bias plotted is what is usedduring normal observations. This is an example at R = 0.75?Rnormal and R = 0.35?Rnormal.NEP2Johnson = NEP2TES +NEP2shunt = 4kbTcRTESI2TES1L 2+ 4kbTshRshI2TES(L ? 1)2L 2(5)The Johnson noise is suppressed by the TES thermal feedback loop gain L , making the Johnson noise a sub-dominate component at low frequencies. The TES loop gain L = P?GT is dependent on the steepness of thetransition ?, which is estimated to be about 100 based on temperature versus resistance data. The current ITESand resistance RTES of the TES were measured using a load curve for calibration. During observations, thecurrent is roughly 10 ?A, the TES resistance is 0.3-0.9 Rnormal, the shunt resistors are 3 m?, and the normalresistances of the TESs are about 60 m?.The contributions from each of the noise terms are given in Table 2. These are the median fits across all ofthe good detectors within in a receiver. This noise was taken in April, 2012, when the optical loading was 2-3.5pW. The receivers with lower Gc have less phonon noise, and the receivers with lower optical efficiency have lessphoton noise.Receiver Rx0 Rx1 Rx2 Rx3 Rx4Photon Noise (aW/?Hz) 33 32 34 27 20Phonon Noise (aW/?Hz) 24 20 24 14 16Johnson Noise (aW/?Hz) 0.8 0.5 0.8 0.4 0.6Amplifier Noise (aW/?Hz) 2.0 2.0 2.4 2.0 2.5Total Noise (aW/?Hz) 41 37 41 32 25Total Noise Aliased at 15 kHz (aW/?Hz) 55 44 63 45 34Total Noise Aliased at 25 kHz (aW/?Hz) 46 39 48 36 29Table 2: Summary Table of detector noise contribution for the Keck Array receivers. Again, there is significantvariation within receivers by detector tile, but the values are averaged here for conciseness.Proc. of SPIE Vol. 8452  84521B-6Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms0 0.2 0.4 0.6 0.8 1101102103RTES/Rnormal?K?sNET per tileFigure 4: The NET per detector tile as a function of TES fractional resistance. Each line is a different tile forall 20 tiles. There is variation in the shape of the NET versus resistance curve. The detectors with little excessnoise at low biases are flat bottomed, while those with significant amount rise in NET at low resistances.5. OPTIMIZATIONSince 2011, we have put a significant amount of effort into improving the sensitivity of the system. The singlelargest, and most obvious, was to add two more telescopes. Two of the existing telescopes were upgraded,including replacing one of the focal planes. We also spent time improving the SQUID feedback servo andincreasing the multiplexing speed.5.1 TES Bias SelectionWe selected the TES biases by sweeping through a range of bias currents, taking elevation nods on the sky tomeasure the optical response, followed by five minutes of noise data taken with the telescope stationary. Figure4 shows the noise-equivalent temperature (NET) versus bias for each detector tile.The TES bias is also constrained on the lower end by when the TES goes unstable. At low biases, the thermaltime constant and the electrical time constants can interfere and cause the TES to go into oscillations.21 TheNET per detector column (common MCE bias line) may still go down because some detectors are very sensitivein that regime. However, the other detectors are unstable and can cause cross talk and other problems withinthe system.5.2 MultiplexingThe noise performance was also improved by increasing the multiplexing speed. We must multiplex quicklyenough for the Nyquist frequency to exceed our noise bandwidth to avoid a large noise aliasing penalty. In 2011,we multiplexed at 15 kHz. We estimated that the noise was degraded by 15-20% by multiplexing at 15 kHz versus25 kHz. Bicep2 has shown a similar increase in sensitivity by moving to 25 kHz.9,20 Learning from Bicep2?sexperience, the Keck Array was able to deploy Nyquist chips with 2 ?H bandwidth limiting inductors on fourout of five focal planes, but the noise was still decreased by multiplexing faster. The limit on multiplexing speedcomes from the time needed for the multiplexing circuit to settle to its new voltage after each row switch.The time-domain SQUIDs switch between 33 rows. At each row, it sets the SQ1 bias, the SQ1 feedback, andthe SQ2 feedback (to appropriately center for each SQ1). This has a settling time. In 2011, the detectors andSQUIDs were allowed to settle for 88 clock cycles before 10 samples were added to form a data point. With a50MHz clock, this means each detector was recorded with a frequency of f = 50MHz/(33 ? 98) = 15kHz. ForProc. of SPIE Vol. 8452  84521B-7Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms0 100 200 300 40010001500200025003000350040004500Raw DataSamples @ 50 MHzRaw Output (ADU)  raw traceoffsetrow switchbegin data0 100 200 300 40010001500200025003000350040004500Raw DataSamples @ 50 MHzRaw Output (ADU)  raw traceoffsetrow switchbegin dataFigure 5: Raw multiplexing time streams. On the left is in the 2011 configuration. On the right is 2012. Theblue line is the raw data trace. At each cyan line, the SQ1 row is switched, and it must settle before data istaken at the green line. The magenta line is the settling point for each detector. The changes of decreasing theswitching time of SQ1 feedback and maximizing the SQ2 dynamical resistance made it so the Keck Array couldmultiplex at 25 kHz, which decreased the aliased noise contribution.Keck Array, the multiplexing frequency was limited by the settling time of the SQUIDs. This is evident in Figure5, which is a raw data timestream as it switches between 4 detectors.The settling times were improved significantly by decreasing the time spent applying the SQ1 feedback andmaximizing the dynamical resistance (Rdyn = ?V/?I) of the SQ2. The first improvement works because thereis a rise time to the switching transients. The amplitudes of the transients were reduced significantly when theswitching time was decreased. The SQ1 feedback switching time had previously been increased in order to allowthe MCE to calculate flux-jumps of the SQ1. The second improvement is to minimize the settling time of thesystem. The settling times are dominated by the SQUID2 to series array time constant of ? = L/Rdyn, whereL is the inductance in that line. The maximal Rdyn turned out to be at a bias of 1.2 times the critical currentIc?max of the SQ2. The critical current Ic?max corresponds to where the SQ2 is no longer superconducting,has the largest amplitude V (?) modulation curve and highest gain and therefore was previously the nominalbiasing point. These two changes resulted in much smaller transients and quicker settling times in the 2012configuration, as seen in Figure 5.5.3 SQUID Feedback Servo ChangesIn normal data taking modes, the MCE servos on the first-stage SQUID. This is because SQUIDs have optimalgain and are the most linear in the middle of their V(?) modulation curve. In 2011, the Keck Array used a basicI-term servo, as is common with the MCE, and as was done with ACT and SCUBA-2.19 This servo was simplyf(n) = e(n) + f(n ? 1), where f is the applied SQ1 feedback at point n and e is the error signal. The newtime-constant limited I-term servo the Keck Array uses is f(n) = e(n)+ b?f(n?1), where b is a decay term lessthan unity. With the basic I-term, the feedback signal can accumulate indefinitely, eventually overflowing. Thisgenerates large amplitude currents in the multiplexer which can interfere with neighboring channels, inducingcrosstalk as large as 0.1 KCMB . The time-constant limited I-term effectively discards old error data from theoverall sum, keeping this term bounded, while still preserving servo linearity.6. INITIAL SENSITIVITY ESTIMATESThe Keck Array has been observing with a full set of receivers and detectors since February, 2012. The initialestimate of the sensitivity of the array is 11.5 ?KCMB?s in the 2012 configuration.Proc. of SPIE Vol. 8452  84521B-8Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsra (deg)dec (deg)150GHz T (?K)  ?50?40?30?20?1001020304050?70?65?60?55?50?45 ?KCMB?150?100?50050100150Figure 6: CMB temperature map for an 8 day subset of data.6.1 Map based estimatesOne method for estimating the sensitivity is with a CMB map.26 Figure 6 is an early season 2012 map of theCMB temperature, coadded over all detectors for an 8 day subset at the end of April. This map will be used forthe rest of the section for calculating estimates of NET. The CMB temperature fluctuations are cross-correlatedwith WMAP to obtain an absolute calibration.1 As was done in Chiang et al.,1 the WMAP maps (Q, W and Vbands) are smoothed with Keck Array?s beam, converted to simulated timestreams, processed with Keck Array?sfiltering and converted back into maps, thus creating ?Keck Array Observed? WMAP maps. In order to avoida noise bias, one of the other WMAP bands is used as a reference. This is written out in Equation 6g =?`?aWMAP?1`m aKeck`m ??`?aWMAP?1`m aWMAP?2`m ?(6)where ` is summed over the range of 30-210 and g is the resulting Keck Array absolute calibration. The gain isflat over this multipole range. The results are the same regardless of which Q, W, or V band maps are used.After calibrating the maps, the sensitivity of the array can be estimated by directly examining the noise withinthe maps. A scan-direction jackknife, the difference map of data taken in the two azimuth scan directions, isused to remove any signal in order to get an estimate of the noise in the maps. The polarization pair differencingremoves most of common mode noise from the atmosphere. In the T maps, when all of the detectors are summed,the 1/f noise contaminates the science band even in the scan-direction jackknife. Because measuring polarizationis the goal of this experiment, the Q and U maps provide a better estimate of the array NET.The noise in the scan-direction jackknife Q and U maps multiplied by the square root of the integration timemap is defined to be the per-detector NET. The signal is divided between the Q and U maps, but this cancels outthe pair differencing operation. The histogram of the resulting map is shown in Figure 7. The per-detector NETfrom this calculation using the 8-day subset of data is approximately 400 ?KCMB?s. The number of effectivedetectors used to make this map is total integration time divided by the integration time for a single detector.Including the data cuts for this time period gives an overall array sensitivity of 11.5 ?KCMB?s in the Q/U mapsin the 2012 configuration. The weather was good during this subset of data, but data is also cut based on otherquality measures such as flux jumps (large SQUID steps), noise stability, and relative gain changes.6.2 Timestream based estimatesAnother method to estimate the sensitivity is by directly analyzing the noise of the timestream in fourier space.26This was also computed on the same 8-day subset of data as the map-based method. The responsivity of theProc. of SPIE Vol. 8452  84521B-9Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms?2000 ?1000 0 1000 2000050100150200250300350400450500Histogram of Noise from Q/U scan?direction jackknife?Kc m b?spixel count  Q=399?K?sQfitU =400?K?sUfitFigure 7: The histogram of the scan-direction jackknife Q/U map times the square root of the total integrationtime map. The integration time is total detector time on each pixel for the entire array, making this is anestimate of the per-detector NET.0 200 400 600 800 1000050100150200250300350400?K?sN per 20?K wide binPer Detector NET  rx0+rx1+rx2+rx3+rx4Figure 8: Histogram of the NET per detector using timestream based estimates. Rx3 and Rx4 have loweroptical efficiencies than the other receivers. We will be upgrading those telescopes with more efficient detectorsfor 2013.Proc. of SPIE Vol. 8452  84521B-10Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/termsdetectors is estimated using the calibration elnods. This depends on the sky temperature, which is calculatedusing the absolute calibrations of our detectors from WMAP as described above. The noise level of each detectorpair is calculated from the polarization pair-differenced timestream in the frequencies of interest (0.1-1 Hz).Figure 8 is the resulting histogram of sensitivities per detector across the array. This method results in a perdetector NET of approximately 440 ?KCMB?s, and an array NET of 11.7 ?KCMB?s for the 2012 configuration.The per-detector NET is 10% higher in this method because of the residual 1/f noise in the data, as seen inFigure 1. However, the overall array sensitivities are comparable, because of the cuts applied while making themaps.ACKNOWLEDGMENTSThe Keck Array projects have been made possible through support from the National Science Foundation (grantNos. ANT-1044978/ANT-1110087) and the Keck Foundation. Detector development has been made possiblewith the Gordon and Betty Moore foundation. We also acknowledge the Canada Foundation for Innovation andBC Knowledge Development Fund for support. We are grateful to Robert Schwarz for spending the winter inthe South Pole for us in both 2011 and 2012, as well as to the South Pole logistics team. We also are gratefulfor the insight and collaboration from the entire Bicep2, SPIDER and Keck Array teams.REFERENCES[1] Chiang, H., Ade, P., Barkats, D., Battle, J., Bierman, E., et al., ?Measurement of CMB Polarization PowerSpectra from Two Years of BICEP Data,? Astrophys.J. 711, 1123?1140 (2010).[2] Guth, A. H., ?Inflationary universe: A possible solution to the horizon and flatness problems,? Phys. Rev.D 23, 347?356 (Jan. 1981).[3] Netterfield, C. et al., ?A measurement by Boomerang of multiple peaks in the angular power spectrum ofthe cosmic microwave background,? Astrophys.J. 571, 604?614 (2002).[4] Komatsu, E. et al., ?Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmolog-ical Interpretation,? Astrophys.J.Suppl. 180, 330?376 (2009).[5] Kamionkowski, M., Kosowsky, A., and Stebbins, A., ?A probe of primordial gravity waves and vorticity,?Phys. Rev. Lett. 78, 2058?2061 (Mar 1997).[6] Seljak, U., ?Measuring polarization in the cosmic microwave background,? The Astrophysical Jour-nal 482(1), 6 (1997).[7] Kovac, J., Leitch, E., Pryke, C., Carlstrom, J., Halverson, N., et al., ?Detection of polarization in the cosmicmicrowave background using DASI,? Nature 420, 772?787 (2002).[8] Keisler, R., Reichardt, C., Aird, K., Benson, B., Bleem, L., et al., ?A Measurement of the Damping Tail ofthe Cosmic Microwave Background Power Spectrum with the South Pole Telescope,? Astrophys.J. 743, 28(2011).[9] Ogburn, R. et al., ?BICEP2 and Keck Array operational overview and status of observations,? TheseProceedings (2012).[10] Vieregg, A. et al., ?Keck Array Optical Performance,? These Proceedings (2012).[11] O?Brient, R. et al., ?Keck Array/SPIDER/BICEP2 detectors,? These Proceedings (2012).[12] Kaufma, J. et al., ?BICEP2 thermal stability,? These Proceedings (2012).[13] Sheehy, C., Ade, P., Aikin, R., Amiri, M., Benton, S., et al., ?The Keck Array: a pulse tube cooled CMBpolarimeter,? Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for AstronomyV 7741(1), 77411R, SPIE (2010).[14] Aikin, R. W. et al., ?Optical performance of the BICEP2 Telescope at the South Pole,? Millimeter, Submil-limeter, and Far-Infrared Detectors and Instrumentation for Astronomy V 7741(1), 77410V, SPIE (2010).[15] Ogburn, IV, R. W. et al., ?The bicep2 cmb polarization experiment,? Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V 7741(1), 77411G, SPIE (2010).[16] Kuo, C., Bock, J., Bonetti, J., Brevik, J., Chattopadhyay, G., et al., ?Antenna-coupled tes bolometerarrays for cmb polarimetry,? Millimeter and Submillimeter Detectors and Instrumentation for AstronomyIV 7020(1), 70201I, SPIE (2008).Proc. of SPIE Vol. 8452  84521B-11Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms[17] Orlando, A., Aikin, R., Amiri, M., Bock, J., Bonetti, J., et al., ?Antenna-coupled tes bolometer arrays forbicep2/keck and spider,? Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation forAstronomy V 7741(1), 77410H, SPIE (2010).[18] de Korte, P. A. J., Beyer, J., Deiker, S., Hilton, G. C., Irwin, K. D., MacIntosh, M., Nam, S. W., Reintsema,C. D., Vale, L. R., and Huber, M. E., ?Time-division superconducting quantum interference device multi-plexer for transition-edge sensors,? Review of Scientific Instruments 74, 3807 ?3815 (Aug 2003).[19] Battistelli, E. S., Amiri, M., Burger, B., Halpern, M., Knotek, S., Ellis, M., Gao, X., Kelly, D., MacIntosh,M., Irwin, K., et al., ?Functional description of read-out electronics for time-domain multiplexed bolome-ters for millimeter and sub-millimeter astronomy,? Journal of Low Temperature Physics 151(3-4), 908?914(2008).[20] Brevik, J. A. et al., ?Initial performance of the bicep2 antenna-coupled superconducting bolometers atthe south pole,? Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for AstronomyV 7741(1), 77411H, SPIE (2010).[21] Irwin, K. and Hilton, G., ?Transition-edge sensors,? in [Cryogenic Particle Detection ], Enss, C., ed., Topicsin Applied Physics 99, 81?97, Springer Berlin / Heidelberg (2005).[22] Cabrera, B., ?Introduction to tes physics,? Journal of Low Temperature Physics 151, 82?93 (2008).[23] Irwin, K., ?Thermodynamics of nonlinear bolometers near equilibrium,? Nuclear Instruments and Methodsin Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 559(2),718 ? 720 (2006). Proceedings of the 11th International Workshop on Low Temperature Detectors.[24] Galeazzi, M., ?Fundamental noise processes in tes devices,? IEEE Transactions on Applied Superconductiv-ity 21, 267?271 (2011).[25] Mather, J. C., ?Bolometer noise: nonequilibrium theory,? Appl. Opt. 21, 1125?1129 (Mar 1982).[26] Brevik, J. et al., ?Noise Performance of the BICEP2 antenna-coupled TES bolometers at the South Pole,?Journal of Low Temperature Physics (LTD-14) 167 (2011).Proc. of SPIE Vol. 8452  84521B-12Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/13/2013 Terms of Use: http://spiedl.org/terms

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