calibration system with cryogenically-cooled loads for cmb polarization detectors

7/27/2019 Calibration System With Cryogenically-Cooled Loads for CMB Polarization Detectors

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Calibration System with Cryogenically-Cooled Loads

for CMB Polarization DetectorsM. Hasegawa,1 O. Tajima,1 Y. Chinone,2 M. Hazumi,1 K. Ishidoshiro,1 and M. Nagai11)Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Oho, Tsukuba,Ibaraki, 305-0801, Japan 2)Astronomical Institute, Graduate School of Science, Tohoku University, Aramaki, Aoba, Sendai, 980-8578,Japan

(Dated: 3 March 2011)We present a novel system to calibrate millimeter-wave polarimeters for CMB polarization measurements.This technique is an extension of the conventional metal mirror rotation approach, however it employscryogenically-cooled blackbody absorbers. The primary advantage of this system is that it can generatea slightly polarized signal (∼ 100 mK) in the laboratory; this is at a similar level to that measured by ground-based CMB polarization experiments observing a ∼ 10 K sky. It is important to reproduce the observingcondition in the laboratry for reliable characterization of polarimeters before deployment. In this paper, wepresent the design and principle of the system, and demonstrate its use with a coherent-type polarimeterused for an actual CMB polarization experiment. This technique can also be applied to incoherent-typepolarimeters and it is very promising for the next-generation CMB polarization experiments.

PACS numbers: 98.80.Es, 07.20.Mc, 95.85.BhKeywords: Cosmic Microwave Background, Polarization, Gravitational Waves, Microwave Receivers, Cali-

bration

I. INTRODUCTION

The faint pattern of cosmic microwave back-ground (CMB) polarization promises to provide new andinteresting information on the universe. The primarygoal of CMB polarization studies in the next decade isto detect the degree-scale B-modes (curl components) in-duced by primordial gravitational waves. The existenceof the primordial gravitational waves is a generic predic-tion of inflation. Therefore the detection of the B-modesis a “smoking-gun” signature of inflation1. Using an ar-ray with ∼ 1, 000 of polarization detectors (hereafter po-larimeters) is essential to discover the B-modes2. For thenext-generation experiments with such a large polarime-ter array, establishing the performance of the detectorsin the laboratory is essential to prepare for observationsin the field.

Our system aims to calibrate three important prop-erties; responsivity, orientation of detector polarizationangle and spurious polarization signal in the instrument.The calibration of these parameters requires a well-characterized artificial polarization signal. The combi-nation of an unpolarized cold load (blackbody absorber)and a metal mirror at room temperature is one of themain approaches3–5 to obtain such a signal. The temper-ature difference between the cold load and the mirror cre-ates a well-characterized polarization signal, ∼ 100 mK(Details are discussed in Sec. II A). In the laboratory,the blackbody absorber tends to be cooled with liquidnitrogen (77 K). However, the large difference betweenthis temperature and that of the sky at the observingsite (∼ 10 K, for example the Atacama desert of north-ern Chile at an altitude of ∼ 5000 m) makes it difficultto characterize the polarimeters in the laboratory. This

is particularly true for detectors with a narrow range of linear response to input load temperature.

To address these issues, we propose an advanced ap-proach for polarimeter calibration. Our method is anextension of the metal mirror rotation approach3–5, how-ever it employs cryogenically-cooled blackbody absorbersinstead of the absorbers cooled with liquid nitrogen. Thissystem provides in the laboratory a load condition similarto the actual observation.

II. PRINCIPLE OF POLARIZATION CALIBRATOR

A. Principle of polarization signal generation

The principle for generating the polarization signal isthe same as the conventional method3–5. Figure 1 showsa schematic view of the developed calibrator system. Theblackbody emitters are cooled with a cryocooler as thecold load with temperature of T load. Unpolarized black-body radiation is emitted from the cold load; it reflectsoff a metal mirror surface, which induces a linearly po-larized component because of the finite emissivity of themirror. The magnitude of the polarization signal (P ) can

be calculated using the following formula,

P = 2

16πνρε0 tan(β ) (T mirror − T load) , (1)

where ν is the frequency of observed radiation, T mirror

and ρ are the temperature and resistivity of the mirror,β is the reflection angle of the radiation, and ǫ0 is thevacuum permittivity. For example, we obtain ∼110 mKpolarization signal when we use an aluminum mirror (ρ ∼2.2 µΩ · cm) with T mirror = 250 K, T load = 10 K and β =45. We can control the signal magnitude by changing ρ

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FIG. 1. Schematic view of the developed calibration system. Unpolarized radiation is emitted from the blackbody absorberscooled with a cryocooler. The radiation reflects off a metal mirror surface placed at the center, and enters a tested polarimeter.The incident radiation is polarized b ecause of the finite emissivity of the mirror. The blackbody absorbers are cylindricallyplaced as shown to the right. The cryocooler in the system has two cooling stages, and a part of absorbers are cooled to bedifferent (higher) temperature using another cooling stage. The mirror can rotate in the vacuum, and the loads at two different

temperatures are alternately presented to the polarimeter.

as well as changing the temperature difference, T mirror −T load.

B. Principle of Polarimeter Calibration

The linear polarization is characterized by two Stokesparameters Q and U 1. Since the value of Stokes pa-rameters depends on the bases of the selected coordinatesystem, the ability to rotate the axis of the polarizationsignal is essential to calibrate the polarimeter responsesunless we calibrate the orientation of the polarization an-gle for the Stokes parameters.

Moreover, the baseline of the polarimeter response fluc-tuates due to a 1/f noise. To measure the response forthe polarization correctly, we have to modulate the polar-ization signal by rotating the mirror; the parallactic angleof the signal axis with respect to the polarimeter varieswith the rotation angle of the mirror (θ). For example,assuming the axis for the Q response of the polarime-ter aligns with the orientation of θ = 0, the Q responsevaries with P cos(2θ), and the U response varies withP sin(2θ) = P cos(2(θ

−π4

)). We can characterize the

responsivity; signal height with respect to the input po-larization signal, and the polarization angle; orientationangle of the polarization axis from the amplitude andthe phase of the sinusoidal response of the polarimeter,respectively.

We are also interested in the spurious polarization of the polarimeter with respect to the total power which isusually dominated by unpolarized temperature. This iscalled I to Q (or U ) leakage where the total power is de-scribed with Stokes I parameter. The actual polarization

response for Q is P cos(2θ)+εI , where ε is the leakage pa-rameter Since I is dominated by T load in most cases, wecan measure the leakage parameter for the polarimeterby changing the T load6. With the two different tempera-ture loads of 10 K and 30 K, we observe a 1 K baselinedifference in the polarization response for ε = 0.05.

The polarimeter can also measure the unpolarized tem-perature response for I as well as for Q and U . We cal-ibrate the response for I by using two different T load s(the Y-factor measurement). This allows us to measure

receiver temperature (T rec) which is the effective temper-ature offset from the intrinsic noise.

C. Expected Polarimeter Response

In general, the polarization angle does not align withthe design value perfectly. The responses of the polarime-ter are defined as described in the following formula inthe unit of mV,

V Q ≡ RQ [ P cos (2(θ − φQ))

+εQ(T load + P ) ] , (2)

V U ≡ RU [ P sin (2(θ − φU ))+εU (T load + P ) ] , (3)

V I ≡ RI [ T load + P + T rec ] , (4)

where Rk (k = Q, U ) and RI are the responsivities(mV/K), φk is the polarization angle and εk is the leak-age parameter for each Stokes parameter response.

Figure 2 shows the polarimeter responses as a func-tion of the rotation angle of the mirror. Here, weassume a configuration with two different temperature



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[degree]θ

-100 0 100 200 300 400

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V

-100

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100LoadT LoadT LoadT

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[degree]θ

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k

V

-0.4

-0.2

0

0.2

0.4

LoadT LoadT LoadT

Q,UV∆

kR×P

FIG. 2. The expected response of total power and polarizationsignal plotted as a function of the rotation angle (θ). The twodifferent temperature pyramid arrays are alternately viewedby the rotating metal mirror.

loads T Lload = 10 K and T Hload = 30 K and the leakage pa-rameter ε = 0.05. The T Lload load covers the 10 ∼ 300

region and other regions are covered by the T Hload load.

The boundary regions between the two loads are maskedin the analysis because it is complicated to estimate theresponse due to the beam profile.

We can extract all the calibration parameters from thesimultaneous fit for each polarimeter response with re-spect to the mirror rotation angle (θ) and the load tem-peratures (T load). In the case T load is constant, the po-larimeter responses V k are simple sinusoidal shape withconstant offsets. Furthermore, in the case εk∆T load ≫ P (where ∆T load ≡ T Hload − T Lload), the leakage parametersεk can be extracted from the baseline difference ∆V k be-tween T Hload and T Lload , i.e. εk = ∆V k/(Rk∆T load).

III. SYSTEM COMPONENTS

A. Cryostat and Cryocooler

A cylindrical cryostat with a dimension of 540 mm di-ameter and 500 mm height houses all of the system com-ponents as shown in Fig. 1. The system is cooled withthe 2-stage Gifford-McMahon cryocooler7 Its cooling ca-pacity in the cryostat is consistent with the specifica-tion (Appendix A). Thermal load for the 1st (2nd) stagein our system is about 18 W (7 W), and we usually op-erate at 30 K (10 K) temperature on the top of the 1st

(2nd) stage.

B. Cold Load – Blackbody Emitter Array

To create the low temperature blackbody radiation,low reflectivity and high thermal conductivity are re-quired for the blackbody emitters. Furthermore, theemitters need to have viscosity (or similar thermal ex-pansion coefficients with the base plate material) to with-

FIG. 3. CR-112 blackbody emitter array as the cold load.

Frequency [GHz]75 80 85 90 95 100 105

R e f l e c t i v i t y [ d B ]

-60

-50

-40

-30

-20

-10

0

CR-112

CV3

FIG. 4. Measured power reflection coefficient of CR-112 andCV-3.

stand the thermal cycling. To fulfill the requirements, weemploy Eccosorb CR-1128 an iron-loaded epoxy as thematerial for the blackbody emitter. To minimize the sur-face reflection, the CR-112 is casted with pyramid-shapegrooves on the front surface. We follow the manufactur-ing processes of the ARCADE experiment9. The pyramidhas a square base of 400 mm2 and height of 58 mm. Toachieve higher thermal conductivity and uniform surfacetemperature, each pyramid has an aluminum core and acopper wire epoxied onto the end of the aluminum core,

running almost to the tip. We use two arrays of the pyra-mids as the cold load (Fig. 3). We use 420 pyramids intotal to surround the inside of the cryostat wall in thesystem.

We confirmed the low reflectivity of the pyramid ar-ray by measurements with commercial millimeter-waveequipment10. The measured reflectivity for the pyramidarray is shown in Fig. 4. It is about −30 dB around the90 GHz frequency region and is comparable to commer-cial absorber material such as CV-38.



Sample title 4

C. Metal Mirror

We adopt β = 45 for the metal mirror in our system.The mirror is hung with a stainless steel shaft that isrotated with a DC motor from the outside of the cryo-stat via a feedthrough11 The maximum rotation speed is∼12 rpm, which corresponds to much higher frequencyof the 1/f noise of the polarimeters for the CMB exper-

iment (several mHz ∼ 100 mHz).We use three metal mirrors, aluminum, steel and stain-

less steel, to vary the polarization signal intensity. It isuseful to evaluate the possible inherent polarization4,12.We obtained zero-consistent inherent polarization in oursystem (Sec. IV D).

Currently, precision of the resistivity (ρ) is the mainuncertainty for the calculation of the polarization signal(P ). The variation of the catalog specification is 20%,corresponding to a 10% uncertainty for the polarizationsignal calculation. Such uncertainty can be reduced witha resistivity measurement in a separate setup.

D. Load and Metal Mirror Temperature

Time [hours]0 2 4 6 8 10 12

e m p e r a t u r e

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50

100

150

200

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300

loadLT

loadHT

Time [hours]0 5 10 15 20 25 30

e m p e r a t u r e

200

220

240

260

280

300

mirrorT(Aluminum)

FIG. 5. Loads and mirror temperatures during the coolingprocess.

Figure 5 shows the temperature of the loads and thealuminum mirror. It takes ∼10 (∼ 30) hours to stabi-lize the temperature of the cold load (mirror) Becauseof the difference of the emissivities for each metal, equi-librium temperatures depend on the mirror material assummarized in Table I. The measured temperatures are

consistent with the thermal calculation in Appendix B.Uniformity of the load surface temperature is con-

firmed to be better than 1 K with DT-670 commer-cial silicon diode thermometers13 The temperature non-uniformity causes only a 0.4% effect for the polarizationsignal while the effect for the unpolarized response isabout 10%. The temperature uniformity can also be con-strained from the flatness of the V I response as a functionof the rotation angle effectively, which is also less than1 K (Sec. IV B).

IV. EVALUATION OF SYSTEM PERFORMANCE

A. Polarimeter for System Evaluation

We evaluate the system performance using the QUIETpolarimeter14. QUIET has an array of pseudo-correlationpolarimeters, each of them employs hybrid couplers to

correlate the two orthogonal polarizations selected by anorthomode transducer in order to directly and simultane-ously measure the Stokes Q, U and I parameters of theincoming signal. A corrugated horn is attached on top of each polarimeter, and its beam width is measured to be∼ 10 (FWHM)15. The beam coverage of this system is∼ 20, and the spill-over power is expected to be less than1%. The responsivity of this polarimeter is ∼ 0.15mV/Kincluding the pre-amplifier gain factor of ∼ 10016 whichwas measured with a different setup using the rotationplate technique under 77 K. In case of QUIET polarime-ters, reflections around the septum polarizer is the mainreason for the I to Q (U ) leakage. A fraction of the

power input on one port of the correlation module wasreflected to the septum polarizer and a fraction of thereflected power re-entered the other port. Typically, theleakage of a QUIET polarimeter is ε ∼ 0.005. To evalu-ate the system performance for the leakage parameter (ε)easily, we insert an extra waveguide between the corru-gated horn and the septum polarizer. This increases thereflection, and the leakage size is increased to ε ∼ 0.05.

B. Total power response

The response for the total power as a function of therotation angle of the mirror is shown in the left panelof Fig. 6. The total power response shows two levels;the upper (lower) level corresponds to 10 K (30 K) loadtemperature. The total power responsivity, RI , is calcu-lated from the timestream with Eq. 4 to be 0.15 (mV/K),which is consistent with the previous measurement dis-cussed in Sec. IVA.

The uncertainty for the total power response is domi-nated by the uniformity of the load temperature, whichis evaluated from the timestream of the total power re-sponse. The RMS of the total power response for theT Lload load is 0.9 K, which is consistent with the RMSon the temperature monitored using thermometers. Thisvariation includes the polarimeter noise which dominatesthe response fluctuation in this test. Thus, this numberstill provides an upper limit on the non-uniformity of the load temperature. So far, the precision for the totalpower responsivity measurement is 7% (1 K uncertaintyboth for T Lload and T Hload), which is already comparablewith the precision obtained using astronomical sources.



Sample title 5

TABLE I. Resistivity (ρ), load temperatures and mirror temperature for each mirror material. P is the calculated polarizationamplitude which corresponds to each T Lload. In case of the stainless steel mirror, we use an aluminum shaft, which has betterheat conductivity than that of a stainless steel shaft. Therefore T mirror is higher than others.

Mirror Material ρ [µΩ · cm ] T Lload [K] T Hload [K] T mirror [K] P [mK]Aluminum (6061) 2.2 12.0 29.7 250.0 114.8Steel (304) 17.1 13.5 30.0 250.0 370.0Stainless Steel (1095) 54.9 14.5 32.1 257.2 591.9

Rotation Angle [Degree]

-100 0 100 200 300 400 T o t a l P o w e r R e s p o n s e [ m V ]

-5

0

5

Rotation Angle [Degree]

-100 0 100 200 300 400 P o l a r i z a t i o n R e s p o n s e [ m V ]

-1.1

-1

-0.9

-0.8

-0.7

FIG. 6. Response of the QUIET polarimeter to the rotating aluminum block. The left panel shows the timestream for a totalpower measurement and the right panel shows the timestream for a polarization measurement. A red dashed line in the rightpanel is a fitted sinusoidal curve.

C. Polarization response

The response for the polarization as a function of rota-tion angle of the aluminum mirror is shown in the rightpanel of Fig. 6. The response shows a clear sinusoidalcurve as a function of the mirror rotation angle. This isthe first demonstration “in the laboratory” for the mod-ulation of the polarization signal (110 mK) with a loadtemperature which is as low as those at the observationsite.

From the amplitude of the curve, we obtain RU =0.12± 0.01(stat)± 0.02(syst) mV/K which is consistentwith the RI . Here the stat term is the statistical un-certainty due to the polarimeter noise and the syst termis the systematic uncertainty derived from the cataloguncertainty of the resistivity (10%, Sec. IIIC) and theload temperature (0.4%). This is the uncertainty for theabsolute scale, not for the relative uncertainty among de-tectors. The relative uncertainty is much more importantfor CMB polarimeters.

For the polarization angle, φU , we extract the angle

with a 0.8 error from the fit, where the error is dom-inated by the polarimeter noise. The system has notbeen limited by the precision of the relative angle mea-surement. However, we have not implemented the en-coder for the mirror rotation angle yet, which limits theabsolute angle measurement. This encoder is needed toachieve the necessary precision of 0.5 for future B-modesmeasurements17.

For the I to Q (or U ) leakage, we can determine theleakage parameter with a precision of 0.005 from Fig. 6.

Again this measurement is limited by the polarimeternoise. There is no systematic limitation for the leakagemeasurement unless the relative uncertainty between RI

and RQ,U becomes significantly large.Just a few tens of seconds of measurements using our

system can provide comparable precision with astronomi-cal source calibration at the observation site, for examplea 20-minute observation for the Crab nebula (Tau A)18.

Our system therefore provides better precision than as-tronomical sources in a given amount of time.

D. Evaluation of Inherent polarization signal in the system

Figure 7 shows the amplitude of the polarized signal forthree different mirror materials. The results show thatthe amplitudes are proportional to the square root of theresistivity as expected, and the system has no inherentpolarized signal within the precision of the measurement.This is the evidence that there is no bias for the polariza-tion responsivity measurement by using the single mirror

setup.

V. DISCUSSION AND SUMMARY

We have developed a polarization calibrator for CMBpolarization receivers. The technique is a simple exten-sion of the conventional rotation metal plate approach,however, it employs ∼10 K cold loads which correspondto the sky temperature at the CMB observation site



Sample title 6

cm]Ωµ[ρ

0 1 2 3 4 5 6 7 8 9

R e s p o n s e ( A r b i t r a r y )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

FIG. 7. The response of the polarized signal is plotted withrespect to the square root of the resistivity of the mirror mate-rial. Here three different materials (Aluminum (•), Steel ()and Stainless steel (∗)) are used.

on the ground (the Atacama desert of northern Chile

at an altitude of ∼ 5000 m). The calibrator can pro-vide a well-characterized polarization signal (∼ 100 mK)which can be modulated by rotation of a mirror. Us-ing a QUIET polarimeter, we demonstrated simultane-ous measurements of the responsivity, orientation of po-larization angle, and spurious polarization signal in theinstrument with sufficient precision. These three param-eters are keys to the success of B-mode observations aswell as sensitivity (noise equivalent temperature: µK

√ s)

of the polarimeter. Our system also provides a way tomeasure noise properties under a comparable load tem-perature condition to the observing site. The estimationbased on our system is thus more “reliable” than that ob-tained using a 77 K load cooled with liquid nitrogen. Oursystem can easily be extended for large detector arraysby scaling up the size of the system.

The precision of the laboratory-based calibration iscomparable with the astronomical source calibrationsat the observation site. This system can establish thepolarimeter performance before deployment, which isimportant for experiments with large detector arrays.Moreover, the precision of calibrations using astronom-ical sources is limited by the beam profile uncertainty.Our system is free from this effect because of the widecoverage-angle of the loads. We have already eliminatedit to less than 1% for the QUIET polarimeter.

We have confirmed that our system works as designed.It will be very useful for the next-generation CMB polar-ization experiments. In this paper, we demonstrated theperformance of the system using a polarimeter based oncoherent amplifiers. By using a different configuration,e.g. a setup in which the reflected emission on the mirrorgoes outside the cryostat, it is possible to use the systemas an external polarized source for a polarimeter withdifferent technology such as a bolometer. With a larger-capacity cryocooler, the system can also be extended to3 K load temperatures. Such a system will be a key tool

in the development of polarimeters for the future satelliteexperiments.

VI. ACKNOWLEDGEMENT

We acknowledge Todd Gaier, Kieran A. Cleary andtheir colleagues at Jet Propulsion Laboratory and Cal-ifornia Institute of Technology for providing low-noisepolarization sensitive modules and valuable advice onthe calibration system. We would like to thank MicheleLimon for valuable information about the cold load. Wealso thank Hogan Nguyen, Fritz DeJongh, Akito Kusakaand Bruce Winstein for their encouragement. We wishto thank Takayuki Tomaru and their colleagues at Cryo-genics Science Center for their cooperation and adviceon the low temperature techniques. We gratefully ac-knowledge the cooperation of Bee Beans TechnologiesCo.,Ltd. This work was supported by MEXT and JSPSwith Grant-in-Aid for Scientific Research on Young Sci-

entists B 21740205, Scientific Research A 20244041, andInnovative Areas 21111002.

Appendix A: Evaluation of Cooling Capacity of Cryocooler

15 20 25 30 35 40 450

2

4

6

8

10

12

14

16

18

20

First stage temperature [K]

S e c o n d s t a g e t e m p e r a t u r e [ K ]

(0.0 W, 0.0 W)

(13.0 W, 0.0 W) (13.0 W, 35.4 W)

(0.0 W, 35.4 W)(0.0 W, 18.0 W)

(7.0 W, 0.0 W)

Operation

FIG. 8. Measured Load map of the cryocooler used in thesystem, SHI-RDK 408S, which is consistent with the sepcifi-cation.

Figure 8 shows the measured load map for the 10 KGifford-McMahon cryocooler (SHI-RDK 408S) used inthe calibrator system. The first (second) stage of the re-frigerator reaches temperature of 22 K (4.6 K) under noexternal thermal load. The calibration system is usuallyoperated at 30 K (10 K) on the first (second) stage. Thethermal load on each stage during the operation is esti-mated to be 18 W (7 W) from the load map measurement.



Sample title 7

! !""#!

! $"%&!! #'!!"! !

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FIG. 9. Schematic diagram of a cryostat for heat transfercalculation on the mirror.

Appendix B: Heat transfer on the metal mirror and mirrortemperature in the system

Figure 9 shows a schematic diagram of the heat trans-fer on the metal mirror. The mirror has a surface area of 0.04 m2 and is supported by a stainless steel shaft (thesurface area divided by the length is 0.09 m). The mirrortemperature instationary state is estimated as the tem-perature where the following heat transfer balances.

1. Qrad : Radiant heat inflow from the cold loads andoutflow.

2. Qcon : Heat conduction from a DC motor throughthe shaft.

Each heat transfer is calculated as follows;

Qrad = σ Amirror

−T 4mirror + T 4load

εmirror (B1)

Qcon =A

L

300KT mirror

k(T )dT (B2)

where σ is Stefan’s constant (5.67 × 10−8Wm−2K−4),Amirror is the surface area of the mirror, T mirror and T loadare the physical temperature of the mirror and the coldload, εmirror is the emissivity of the mirror, A/L is the

ratio of the surface area to the length of the stainlesssteel shaft, and k(T ) is the temperature-dependent ther-mal conductivity of the shaft, respectively. In case we

use an aluminum mirror (εmirror 0.03 ∼ 0.04), the heattransfers are balanced at T mirror of 240 K ∼ 260 K. Thisis consistent with the measured temperature as stated inSec. IIID.

1M. Zaldarriaga and U. Seljak, “An All-Sky Analy-sis of Polarization in the Microwave Background,”Phys. Rev. D55, 1830–1840 (1997), arXiv:astro-ph/9609170.

2J. Bock et al., “Task Force on Cosmic Microwave BackgroundResearch,” (2006), arXiv:astro-ph/0604101.

3S. T. Staggs et al., “Calibrating CMB Polarization Telescope,”AIP Conf. Proc. 609, 183–186 (2002).

4K. Vanderlinde, “New Measurement from the CAPMAP Exper-iment of the CMB E-Mode Power Spectrum at High MultipolesAnd New Limits on B-Mode Power.” Ph.D Thesis, University of Chicago (2008).

5. C. Bischoff e t a l. (CAPMAP), “New Measurements of Fine-Scale CMB Polarization Power Spectra from CAPMAPat Both 40 and 90 GHz,” Astrophys. J. 684, 771–789 (2008),arXiv:0802.0888 [astro-ph].

6In higher order calculation, the I is define with sum of T load andP . In case we use two different temperature loads, the differenceof the load temperature and the polarization signal are definedwith symbols ∆T load and ∆P respectively. Therefore, the varia-tion of I is described as ∆I ≡ ∆T load + ∆P , and ∆I ∼ ∆T loadin most of cases because ∆P ∼ ∆T load/100.

7Sumitomo Heavy Industries ltd., ThinkPark Tower, 1-1 Osaki 2-chome, Shinagawa-ku, Tokyo 141-6025, Japan;www.shi.co.jp/english/index.html .

8Emerson & Cuming Microwave Products, INC., 28 York AvenueRandolph, MA 02368, USA; www.eccosorb.com.

9A. Kogut et al., “Design and Calibration of a Cryo-genic Blackbody Calibrator at Centimeter Wave-lengths,” Rev. Sci. Instrum. 75, 5079–5083 (2004),arXiv:astro-ph/0402580.

10We obtained the signal in W-band region with Agilent E8247C(PSG) CW signal generator and frequency multiplier chain(AMC-10-RFH000). The W-band signal was injected to theblackbody emitter array with an incident angle of 7. The re-flected signal power was measured by a general purpose detector(DXP-10 RPFW0).

11CI Technology, INC., 2-674-2, Tokorozawa, Saitama, 359-1164JAPAN; www2.dango.ne.jp/cikogyo.

12Private Communication with Bruce Winstein (University of Chicago).

13Lake Shore Cryotronics, INC., 575 McCorkle Blvd, Westerville,OH 43082-8699 USA; www.lakeshore.com.

14K. A. Cleary (QUIET), Proc. SPIE 7741, 77412H (2010).15J. Gundersen and W. E., “Millimeter-wave Corrugated Platelet

Feeds,” Journal of Physics: Conf. Ser 155, 012005 (2009).16The typical responsivity of the QUIET polarimeters is 2 ∼

3mV/K. The module used for the test in this paper is a lowgain module which was not used for the CMB observation.

17W. Hu, M. M. Hedman, and M. Zaldarriaga, “Bench-mark parameters for CMB polarization experiments,”Phys. Rev. D67, 043004 (2003), arXiv:astro-ph/0210096.

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Measurements of CMB Polarization Power Spectra at 43GHz in the Multipole Range 25 ≤ ell ≤ 475,” (2010),arXiv:1012.3191 [astro-ph.CO].

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calibration system with cryogenically-cooled loads for cmb polarization detectors

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