CMB Observations with a Compact Heterogeneous 150 GHz Interferometer in Chile

0.32 MB·

by  J. W. Fowler

Draftversion February2,2008
PreprinttypesetusingLATEXstyleemulateapjv.4/9/03
CMB OBSERVATIONS WITH A COMPACT HETEROGENEOUS 150 GHZ INTERFEROMETERIN CHILE
J. W. Fowler, W. B. Doriese,1,6 T. A. Marriage, H. T. Tran,2,7 A. M. Aboobaker, C. Dumont,3 M. Halpern,4
Z. D. Kermish,2 Y.-S. Loh,5 L. A. Page, S. T. Staggs, D. H. Wesley
DepartmentofPhysics,JadwinHall,PrincetonUniversity,P.O.Box708,Princeton,NJ08544.
Draft versionFebruary 2, 2008
ABSTRACT
Wereportonthedesign,firstobservingseason,andanalysisofdatafromanewprototypemillimeter-
waveinterferometer,MINT. MINT consists offour 145GHz SIS mixers operatingin double-sideband
mode in a compact heterogeneous configuration. The signal band is subdivided by a monolithic
5
channelizer,afterwhichthecorrelationsbetweenantennasareperformeddigitally. Thetypicalreceiver
0 ◦ ◦
sensitivityina2GHz bandis1.4mK√s. Theprimarybeamsare0.45 and0.30 FWHM,withfringe
0 ◦
spacingassmallas0.1 . MINT observedthe cosmicmicrowavebackground(CMB)fromCerroToco,
2
in the Chilean Altiplano. The site quality at 145GHz is good, with median nighttime atmospheric

n temperature of 9K at zenith (exclusive of the CMB). Repeated observations of Mars, Jupiter, and
a a telescope-mounted calibration source establish the phase and magnitude stability of the system.
J
MINT is the first interferometer dedicated to CMB studies to operate above 50GHz. The same type

7 of system can be used to probe the Sunyaev-Zel’dovich effect in galaxy clusters near the SZ null
2 at 217GHz. We give the essential features of MINT and present an analysis of sideband-separated,

digitally sampled data recorded by the array. Based on 215 hours of data taken in late 2001, we set
2
anupper limit onthe CMB anisotropyina bandofwidth ∆ℓ=700aroundℓ=1540ofδT <105µK
v
(95% conf.). Increased sensitivity can be achieved with more integration time, greater bandwidth,
7
and more elements.
3
Subject headings: cosmic microwavebackground — instrumentation: interferometers
1
3
0
1. introduction terusingSIS(superconductor-insulator-superconductor)
4
mixers at f >100GHz has the potential to measure the
0 MeasurementsoftheCMBatsmallangularscales(ℓ>
/ 1000) complement those from WMAP (Bennett et al. CMB anisotropy and SZ effects where the point source
h contamination is at a minimum (Toffolatti et al. 1998)
2003) and previous experiments including TOCO
p and where the SZ effect (Sunyaev & Zel’dovich 1970,
(Miller et al. 1999), BOOMERanG (Mauskopf et al.
-
1972) has a characteristic spectral null. However, the
o 2000; Ruhl et al. 2003), MAXIMA (Lee et al. 2001),
r DASI (Halverson et al. 2002), VSA (Grainge et al. technicalcomplicationsareconsiderable,asmightbesur-
t misedbytheexistenceofonlyafewsuchinterferometers
s 2003), and ARCHEOPS (Benoit et al. 2003), allowing
a yet more precise constraints on the standard cosmologi- (e.g., SMA, OVRO, BIMA, IRAM, NRO/NMA).
: We have built and observed with a four element, het-
v calmodel (Spergel et al. 2003). Additionally, such mea-
erogeneous,compact, fully-digital, SIS-basedD-band (
i surements will enable us to understand the transition
X 145GHz) interferometer designed as a prototype for∼a
from the linear to the non-linear growth regimes for the
r formation of cosmic structure. One promising measure- larger, more ambitious instrument. Novel elements of
a the interferometer include the channelizer, a custom mi-
ment technique is interferometry because of the ability
crowave integrated circuit; digital correlators for CMB
to control systematic errors. Existing CMB interfer-
measurements; and mixed antenna sizes. We describe
ometers, CAT (Robson et al. 1993), CBI (Padin et al.
key features of the interferometer, the observations in
2001), DASI (Leitch et al. 2002), IAC (Dicker et al.
Chile, and the data analysis.
1999), VSA (Watson et al. 2003) are based on HEMT
amplifiers(Pospieszalski 1992;Pospieszalskiet al. 1995;
Pospieszalski 1997) and operate at 30GHz where the 2. the millimeter interferometer
contamination from point sources can be large; MMIC
The Millimeter INTerferometer (MINT) is a compact
technology at 90GHz will enable a straightforward
instrument, approximately two meters on a side (with-
switch to higher frequencies. A compact interferome-
outthegroundshield)andcubical. Allfourreceiversare
mountedtoasinglerigidaluminumplatewithfixedrela-
1 Present address: NIST Quantum Electrical Metrology Divi-
tive alignment. The plate sits atopa movable aluminum
sion,325BroadwayMailcode817.03, Boulder,CO80305-3328.
2Presentaddress: DepartmentofPhysics,UniversityofCalifor- cage,as shown in Figure 1. The channelizer, digital cor-
nia,Berkeley,CA94720. relators, data computer, and a calibration noise source
3 Presentaddress: SchoolofMedicine,UniversityofPennsylva- are also mounted on the cage. By moving the entire sig-
nia,Philadelphia,PA19104.
4 Department of Physics and Astronomy, University of British nalpathinunison,we avoidthe potentialphasechanges
Columbia,Vancouver, BC,CanadaV6T1Z4. that result from cable flexure and other moving parts.
5 Present address: Center for Astrophysics and Space Astron- The telescope cage moves on an altitude-azimuth
omy,389UCB,UniversityofColorado,Boulder,CO80309.
6 NRCFellow. mount. Alineara◦ctuatord◦rivesthetelescopeinelevation
7 MillerFellow. over the range 60 to 100 , controllable to the accuracy
◦
of the 17-bit encoder ( 0.005 ). The azimuth drive has
∼
2 J. W. Fowler et al.
Fig. 1.— MINT interferometer. An elevation over azimuth mount positions the cage that holds four Cassegrain antennas.
A ground shield mounted on top of the cage moves with the receivers. External to the cage, and not shown, are a thermal
regulationsystemthatservosthecoolantfortheRFelectronicsandcorrelatorsto±1K,apositioncontrolcomputer,thehelium
compressors, and a 50kW Katolight diesel generator to provide electrical power. The entire experiment fits inside one 20-foot
shippingcrate.
◦
a range of 270 , with an inaccessible zone centered to feed all four antennas. The feeds are characterized in
the north. The azimuth is also instrumented with a 17- Miller et al. (2002). The mirrors were machined from
◦
bit encoder and can be positioned to 0.015 accuracy. aluminum on a computer-controlled lathe. A rigid tri-
∼
A brake on the azimuth bearing allows us to turn off pod of thin (1.6mm) legs made of G-10 composite sup-
theelectricallynoisyazimuthdriveduringfixed-azimuth ports each secondary mirror (see Figure 1). A conical
observing. A ground shield made of aluminum hex cell aluminum radiation shield with an opening half angle of
◦
in the shape of an inverted frustum extends 1.2meters 5 surrounds eachprimary mirror to a height of approx-
above the receiver mounting plate. This shield prevents imately one diameter. The shields are rolled outward at
the receivers from illuminating the ground, either di- the top with a radius of 5λ to limit diffraction and
∼
rectly or through any number of reflections. reduce crosstalk between receivers.
The beam patterns of the two optical systems have
been both measured and computed. Beam maps were
2.1. Optics and Receiver Arrangement
measuredusingachoppedsource(a147GHzGunndiode
MINT uses antennas of two different sizes on its four
with a D-band corrugated feed) and a diode power de-
receivers. A heterogeneous array is unusual in radio in-
tector. The system allowed measurements over a dy-
terferometry. It introduces complications such as com-
namic range of 35dB. Beams were also computed us-
plex effective beams andan“optical”phase that areun- ing the DADRA program(Barnes et al. 2002).9 From a
desirable in most astronomy applications. However, the
spherical wave expansion of the field from a corrugated
faintCMB anisotropyis aweaksignalatthe limit ofde-
feed,DADRAcomputesthecurrentsonthesubreflector.
tectability. We maximize the sensitive area in the aper-
Then,fromthe subreflector,it computes the currentson
ture plane of the four-element prototype array, within
theprimary. Thenetpatternisthesumofthefieldsfrom
structuralconstraints,bycombiningantennasoftwodif-
the feed, subreflector, and primary. We found it neces-
ferent sizes. Mounting the four antennas in a fixed con-
sary to modify DADRA to include reflections from the
figuration on a single plate also improves sensitivity by
primarybackontothesecondary,becausetheMINTsec-
ensuringthatthe baseline separationsinthe (u,v)plane
ondarymirrorhasa largerdiameter thanthe hole in the
stay fixed as the sky rotates. Of course, deep observa-
primary. The small primary hole is desirable, as it puts
tions of a single (u,v) visibility come at the expense of
power onto the sky rather than backward into the de-
mapping.
war,butitmustbeincludedinthecomputation. Exten-
Anon-axisCassegrainmirrorsystemismountedabove
sive measurements on the MINT and similar Cassegrain
each receiver. The inner two receivers have 30cm di-
antennas (e.g., Figure 2) confirm the computed beam
ameter primary mirrors and 6.5cm diameter hyperbolic
shapes.
secondaries. The equivalent focal length is 53.7cm, giv-
ing a focal ratio of f/1.8. The outer two receivers have 2.2. Receivers
Cassegrainoptics of the same shape but larger by a fac- ThereceiverisshownschematicallyinFigure3. Ituses
tor of 1.5 in each linear dimension. Rays from infinity the classic double-sideband superheterodyne configura-
focusneartheentrancetoacoldcylindricalfeedhorn8in- tion (Kraus 1986, e.g.). Other than the external optics,
◦
side the dewar. Identical horns with 17 FWHM beams
9 YRS Associates: Y. Rahmat-Samii, W. Imbriale, & V.
8 CustomMicrowave,Longmont, CO Galindo-Israel1995,[email protected]
CMB Observations with MINT 3
Fig. 2.—(a) Measured beam map of one of the small antennas. The dots are the measurement; the solid line is the DADRA
computedbeam,accountingforthedefocuseffectofmeasuringthebeamatfinitedistance(36meters). Thedataarenormalized
tothecomputedforwardgain. Two-dimensionalbeammaps(notshown)confirmthatthebeamsofbothantennasarecircularly
symmetric. (b) Far-field beams, as computed by DADRA,for thesmall (solid) and large (dashed) antennas.
Fig. 3.—Schematic of the MINTRF chain, calibrator, and phase locking system. The noise calibrator is thetop section; the
skysignalflowsfromlefttorightinthecentersection;andthe145.1GHzoscillatorisproducedandphase-lockedinthebottom
section. The dashed line surroundscryogenically cooled components.
the four receivers are essentially the same. Celestial ra- IRblocker;andthe 4K backshortaretreatedas asingle
diation is focused by the Cassegrain optics onto a single multi-layer system. The spacing between the elements
corrugatedfeed. The feedcouples to a polarizerthatac- andthethicknessofthewindowandquartzwereselected
cepts only right circular polarization. The output of the to maximize the transmission near 145GHz.
polarizersupportslinearTE modeinacircularwaveg- Each SIS is cooled with a CTI-1020 CP refrigera-
11
uide (diameter = 0.173cm). A transformer (Padman tor11 modified with a third stage following the design of
1977) converts it to TE in WR-5.8. The 1mW local Plambeck, Thatte & Sykes (1993). The modifications
10
oscillator10 (LO) at 145.1 GHz is coupled to the signal were made by Cryostar.12 The resulting refrigerators
waveguide at 20dB through a NRAO branch-line cou- are efficient; each has a cooling power of 0.05W at 4K
−
pler (Kerr et al. 1993). On the SIS junction, the LO whendrivenbya2.2kWCTI8200compressor. Thebase
(300nW) and incident field ( 0.2nW) are multiplied temperatureisapproximately3.7K,butthetemperature
≈
together. of the unloaded base varies by 400mK peak-to-peak at
For computing the optical transmission into the feed 25Hz, the operating frequency of the fridge. Reducing
horn, the ambient-temperature, 0.056cm polypropylene thevariationwithahighheatcapacity,highconductivity
vacuum window; the 25K, 0.052cm thick z-cut quartz
11 CTI,HelixTechnologyCorp.,Mansfield,MA
10 ZaxMillimeterWave Corporation,SanDimas,CA 12 CryostarAssociates,Yuma,AZ
4 J. W. Fowler et al.
combination of stainless steel and copper and judicious receiver-months without failure. The receivers are de-
choice of thermal breaks, we were able to servo the cold scribed in more detail by Doriese (2002).
headtemperatureto 2mK. Thislevelofthermalstabil-
±
ity was essential. Even with such temperature control,
2.3. The Channelizers
thermally driven dimensional changes in the cold head
The channelizers subdivide the 4–6GHz IF (interme-
led to a small modulation of the reflection of the LO
diate frequency) signal from each of the receivers into
power from the vacuum window. The modulation could
four 500MHz bands, then downconvert each band to
be monitored through 0.5% variations in the SIS bias
∼ baseband. The channelizers are custom integrated mi-
current.
crowavecircuits designed using Agilent EEsofAdvanced
The SIS was tuned with a backshort coupled through
Design System software.15 Each circuit consists of a
vacuum-tight gears to a computer-controlledmotor out-
specialized layout of etched copper on 0.076cm Duroid
side of the dewar. The SIS is biased with a cryogenic
6200 substrate and drop-in components. Its only con-
NRAO bias-T, which outputs the RF signal. Follow-
ing a 3.5–6.5 GHz cryogenic isolator,13 a 4.1cm piece nectors (apart from power supplies) are on the input
and output. The channelizers are housed in a custom
of stainless steel waveguide leads to an NRAO 3.5–6.5
aluminum enclosure that provides isolation between ad-
GHz, 5–8K noise temperature, 33dB C-Band HEMT-
jacent channels and from the outside environment. The
based amplifier at 14K. The output of the C-band amp
cavitiesbetweenthetracesandenclosurearecoatedwith
feeds through stainless steel coaxial cable to the room-
adhesive-backed,rubberized microwaveabsorber to sup-
temperature electronics where it is amplified by another
presscavitymodes. Thechannelizersforallreceiversare
52dB. Halfthesignaliscoupledtoatotalpowermonitor
mounted as a single, compact (6cm by 30cm by 30cm),
and the other half goes to the channelizer. With a 10K
temperature-controlledunit.
thermalloadasinput(similartotheloadobservedinthe
The splitting is accomplished by a four-way power
field), the approximatelevelofthe total poweroutput is
splitter composed of planar cascaded Wilkinson power
1mW.
dividersfollowedbyplanarbandpassfilters. TheWilkin-
Each receiver is tuned while coupled to a cryogenic,
son splitters use a wide-band, three-segmented design
thermally controllable blackbody load that matches the
(Li, Li & Bosisio 1984). Each bandpass filter is a six-
feed but is electrically and thermally isolated from it. A
poleChebyshevtypemadefromsevencoupledmicrostrip
LabVIEW computer program changes the load temper-
sections (Matthaei, Young & Jones 1980). The realized
ature, SIS bias voltage, and backshort position to find
bandwidth varies from band to band, between 400 and
the optimal bias. In addition to the stable SIS temper-
600MHz. There is no significant variation among the
ature, the ambient electronics were stabilized to 0.1K.
± nominally identical bands in different channelizers.
Repeated tests of the system over multiple cool-downs
Each filter is followed by a commercial surface-mount
showedthattheoptimaltuningpositionwasstable. The
mixer,16 which downconverts the signal to baseband (0–
same tuning procedure worked without changes for all
500MHz), and a surface-mount amplifier. Two local os-
four receivers (A, B, C, D). Table 1 gives the noise tem-
cillatorsignals—oneat4.5GHzandoneat5.5GHz—are
peratureoftheSISsysteminthefourbands. Afterinitial
sufficient to mix the four separate bands to baseband.
tuning, the SIS bias was not retuned during the observ-
Thus half the bands are from the upper side-bands of
ing season.
the LOs andhalf are from the lower. The overallgainof
Toprovideacontinuousrelativecalibration,webuilta
the channelizer is 12dB across all four channels, with
138–142GHzsourcethatinjectsabroadbandnoisesignal
∼
output power in the range +1 to +7dBm. We label the
toward the subreflector of each telescope (Figure 3). A
bands out of the channelizer according to their IF fre-
motor-controlled rotary mechanical switch ensured the
quency: red, yellow, green, and blue. The red band is
“off” state of the source.
4.0to4.5GHzintheIF,andthusnominallycontainsce-
The LOs for all four receivers are phase locked to
lestialinformationfrombothsidebandsofthe SIS:149.1
a 100MHz master clock, which also drives the digitiz-
to149.6GHzand140.6to141.1GHz. Tran (2002)gives
ers and correlators, the LOs in the channelizer and a
further information about the channelizers.
12.1GHz reference signal for the LO locking. In the
ambient-temperature electronics associated with each
receiver, the 145.1GHz LO is phased locked to the 2.4. The Digital Correlators
12.1MHz tone using a circuit based on one given to us
EachMINT digitalcorrelatorprocessesfour 500MHz-
by the SMA project (Hunter et al. 2002) at the Har-
wideanaloginputsignals,onefromeachreceiver;allthe
vard Smithsonian Center for Astrophysics. Each circuit
red bands go to one correlator, for example. Incoming
is based on a type II phase-locked loop, servoing on the
signals are digitized at 1 sample per nanosecond with
twelfth subharmonic of the 12.1GHz–145.1GHz mixing
2-bit resolution. The correlator produces a 16-lag cross-
product.14 TheLOfrequencyiscontrolledbyavaractor,
correlationfunction, which is read into a data computer
an approachthat requiresfar less current than the more
twicepersecond. AnofflineFouriertransformofthecor-
usual Gunn bias does.
relation function produces a cross-power spectrum with
Tosummarize,theoutputsofeachreceiverareaphase-
62.5MHz resolution. A total of four correlators are re-
locked4–6GHzIFsignalandatotalpowermonitor. The
quired to process all sub-bands. The basic design of the
receivers were robust. They operated for a total of 30
correlator was given to us by David Hawkins (Hawkins
2003).
13 PassiveMicrowaveTechnology, Inc.,Camarillo,CAandP&
HLaboratories,SimiValley,CA
14 PacificMillimeterProducts,Golden,CO 15 AgilentTechnologies, PaloAlto,CA
16 Mini-circuits,Brooklyn,NY
CMB Observations with MINT 5
Table 1. Noise Temperature of Four Receivers Using NRAO SIS
mixersa.
BandName IFBand(GHz) TA (K) TB (K) TC (K) TD (K)
Blue 5.5–6.0 40 33 68 29
Green 5.0–5.5 28 22 55 31
Yellow 4.5–5.0 24 19 33 27
Red 4.0–4.5 26 19 32 24
aMeasured in the lab through the channelizer with a regulated blackbody load. The IF band is nominal band of the SIS output; the
bandwidthforeachiscloseto500MHz.
The electronics that compute the 16-lag cross- Observations were made from an altitude of 5200m
correlationfunctions between four analog signalsare de- on Cerro Toco19 (longitude 67◦47′09′′ West, latitude
◦ ′ ′′
signed onto a single 38cm by 38cm, 8-layer, surface- 22 5729 South), a mountain overlooking the high
mount circuit board. The four incoming signals are first Chilean Altiplano near the ALMA and CBI sites. This
processed by identical RF sections that each contain a was the same site used for the MAT/TOCO experiment
variable attenuator, an amplifier, a low pass filter, and (Miller et al. 1999; Torbet et al. 1999). The mountain
a voltage bias. The variable attenuators (M/A-COM isaccessiblefromSanPedrodeAtacama,Chile,byfour-
model AT20-0107) have smallest steps of 0.5dB. They wheel drive vehicle and can be reached from Princeton,
areadjustedbydataacquisitionsoftwaretomaintainthe New Jersey in 24 hours.
rms signal level into the digitizer near 0.28V. This level TheatmosphereattheCerroTocositewasoftenexcel-
optimizes signal-to-noise given our correlator algorithm lent. Duringthe 38calendardaysofthe campaign(2001
andthedigitizerquantizationat 0.25V(Cooper 1970). November 22 through December 29), twenty percent of
±
Resetting the attenuatorshourly wasfound in field tests potentialobservationnightswerelosttoovercastweather
tobesufficient. Thelow-passfilters(Mini-circuitsSCLF- or snow. On the remaining usable nights, the effective
550)havea 3dBpointat605MHzandblockunwanted atmospheric temperature at D-band was below 9K half
−
noise(particularlyleakageofthechannelizerLOs),which theavailabletime. Thefirstandthirdquartileswere7K
otherwise would be aliased into the signal. The voltage and 13K and the minimum observed temperature was
bias of 0.5V is required by the digitizers. 5K. The typical opacity in D-band was therefore only a
−
The RF pre-processor is followed by a commercial few percent. These temperatures exclude the contribu-
1GSPS, 6-bit digitizer (SPT7610).17 The two most sig- tionofthe CMBandcoveronlythe periodfrom23:30to
nificant bits are passed to an ECL demultiplexer, which 10:00UTeachnight(localtimeisUT 3). Datatotaling
−
slows the signal rate to 62.5 MHz on a 32-bit bus. After 215 hours are used in the analysis presented here.
conversion to LVCMOS, the 32-bit data streams from Tworadiocommunicationsystems andautomatedob-
each receiver are fed into a single FPGA (Field Pro- serving software generally permitted remote operation
grammable Gate Array, XCV1000),18 which computes of MINT from an apartment in the nearby town of San
the correlation functions and communicates with a dig- Pedro, 35km away (Miller et al. 2002). One-way data
ital I/O card in the data PC. The FPGA also keeps a transmissionfromthesite(33kbpsdatarate)allowedob-
running count of the digitized values for each receiver— serverstomonitorthedatainrealtime. Aseparate,two-
the “digitizer histograms.” These histograms, which are way,low-bandwidthsystememployedpacketmodems to
read out twice per second, proved very useful as moni- relay commands to the telescope control computer.
tors of the RF power reaching the digital correlator(see
3.2). 3.2. Absolute Calibration
§
The algorithm for the correlator is built around a The digital correlator measures the quantity ρ(τ), the
multiplier-adder kernel. The multiplier is implemented unitless correlationcoefficientof twovoltagesignalsas a
as a 4-bit lookup table, whose values are given by the function of lag τ:
4-level, “deleted middle products” correlator algorithm.
V (t)V (t+τ)
This table has a quantization efficiency of ǫq =0.88 rel- ρ(τ) h a b i ,
ative to an ideal analog correlator (Cooper 1970). ≡ V2(t) V2(t)
h a ih b i
Therack-mountedcorrelatorsforallreceiversfitintoa p
where brackets represent averages over time t. The cor-
box41cmby41cmby20cm. Togetherthefourconsume
relator output is converted from raw bits to ρ following
800W and are cooled with a thermally regulated fluid.
8.3 of Thompson, Moran & Swenson (1998). The next
The correlatorsworkedas designed throughoutthe 2001 §
conversion, from ρ to correlated power or temperatures,
campaign. More details are given by Tran (2002).
requires knowledge of the overall system temperature of
each receiver.
The most robustpowercalibrationcomes fromthe to-
3. observations tal power diodes, which measure power at the IF in a
3GHzband(widerthanbutinclusiveofthesignalband).
3.1. Cerro Toco Site
19 TheCerroTocositeoftheUniversidadCato´licadeChilewas
17 SignalProcessingTechnologies,ColoradoSprings,CO madeavailable through the generosity of Prof. HernanQuintana,
18 XilinxInc.,SanJose,CA Dept. ofAstronomyandAstrophysics.
6 J. W. Fowler et al.
Smallnonlinearitiesinthediodesarecharacterizedinthe “pickoff” mirror adjacent to the dewar window. Some
lab. The linearized voltage is calibrated in the field to powerreflects up to the secondaryand back into the de-
the input temperature, using a combination of hot/cold war. Thecouplingefficiencyisnotmeasuredbutisfound
load tests and sky dips. The hot load is a large piece to be stable. The noise source is sharply cut off above
of Eccosorb at ambient temperature (T 270K); the 145GHz by the bandpass of the Q-band amplifier, with
≈
cold load is the sky at zenith. By measuring the sky the consequence that the noise contains D-band power
power at a range of elevations, we separate the sky tem- only in the MINT lowersideband(139 141GHz). This
−
perature, the receiver temperature, and the receiver re- property is helpful in verifying the sideband separation
sponsivity(voltsperKelvin). Thereceivertemperatures procedure ( 6.4).
§
and responsivities found in this way were consistent in During normal CMB observation, the noise source is
threeseparatemeasurementstakenatCerroTocoovera switched on for 6–8 seconds out of every 450. A longer
three-week period. Assuming that responsivities remain calibration of 30 seconds is performed every hour. The
constant,eachdiodeservesasanindependentmonitorof noisesourceproducespowerequivalentto5–10Kineach
the sky temperature. In practice, all four diodes found receiver, so the correlated signal is observed with high
the same sky temperature to within 0.8K rms, confirm- signal-to-noise in a single 2-second integration period.
ingthatnootherimportantcontributiontothemeasured The magnitude of the noise signal recorded by the in-
power varied significantly during the campaign. terferometer was stable throughout the campaign. On
The sky (atmosphere plus CMB) serves as a variable- most nights, the fractional range of amplitudes was 3%
temperature load, given the Eccosorb and sky-dip cali- (rms) or less in all bands and all baselines. Over the
brations. Thedigitizerhistogramsgivethepowerineach entire campaign, the rms range was 6%. Strong correla-
0.5GHz-wide sub-band. Together, the power and sky tionsintheamplitudesamongallbandsandallreceivers
temperaturepermitanestimationofthereceivertemper- suggestthat the main source of amplitude variation was
ature and responsivity of each sub-band. Although the thenoisesourceitself. Forexample,somevariationisdue
responsivity is found to change in one or a few discrete to the waveguide switch failing to find the same resting
jumps during the campaign for some bands, the noise spot on each repetition.
temperaturesdonotchangesignificantly. Thusthe total The phase stability of the instrument—a critical re-
system temperature in each channel can be determined quirementforanyinterferometer—wasalsomeasuredus-
atanytimesimplybyaddingthisconstantreceivernoise ingthenoisesourceandwasfoundtobe sufficient. Con-
temperaturetothevaryingskytemperature. Thejumps, sideredoverthecampaign,themeasuredphasevariation
of approximately 10–20% in magnitude, occur only be- overtime andacrossfrequencybins wouldcauseaverage
tween nights and are attributed to problems in signal signal loss of 6% in most baselines (corresponding to an
◦
cables or their connectors. rmsphase variationof20 ). The D-C andA-B baselines
This calibration method assumes that several key re- performed better than the others, with average loss of
◦
ceiver properties stay constant: the responsivity of the less than 3% and φ = 12 . We attribute this differ-
rms
total power diodes; the receiver temperature at the ence to the power-splitting scheme in the noise source
◦
diodes; and the receiver temperature in each 0.5GHz- (AandBsignalscomefromthesame90 hybrid),which
wide sub-band. The redundantmeasurementsofthe sky permits a relative phase between the A/B signals and
temperature confirm these assumptions (Doriese 2002). the C/D ones. This observation suggests that the cali-
Observations of Mars and Jupiter are used to estab- bration source itself is responsible for the main part of
lish the forwardgain (including optical efficiency) of the the observed phase variation over time. Therefore, the
receivers. Thegainisrequiredtoconvertbetweenbright- interferometer is more phase-stable than could be mea-
nesstemperatureandthefluctuations inthe CMBphys- sured with this source (a comment that also applies to
◦
ical temperature. Planetary observations are described amplitude stability), and the 12 rms phase variation is
in Section 4. anupperlimitonthestabilityoftheinterferometeritself.
The instrument and sky noise is observed to integrate
3.3. Relative Calibration and Phase Stability downwithrmssignalvaluesscalingast−1/2foraveraging
The phase and amplitude stability of the interferome- times t of up to 2000 seconds in a single night. Longer
ter are monitored using a switchable noise source. The integrationsweretoofewtomakesignificantcomparisons
noiseisproducedbya+20dBENRQ-bandsource20 fol- with the expected scaling law.
lowedbyaseriesofamplifiersprovidingagainof+70dB.
4. observations of the sun, mars and jupiter
This signal enters an isolator, a frequency tripler, and
another isolator (Figure 3). A D-band rotary waveguide Repeated observations of the Sun were used to deter-
switch (controlled by a stepper motor) allows the noise mine the telescope alignmentthroughoutthe Chile cam-
to be turned onor off. The signalis then split four ways paign. Thereceiversweretemporarilycoveredwithstan-
bya180◦ magic-Thybridcouplerandapairof90◦ short dardcorrugatedcardboard2mmthicktoblocktheSun’s
slothybridcouplers. Theresultingfoursignalsarehighly opticalandinfraredradiation. The pointing wasderived
correlated, except that each is phase-delayedby 90◦ rel- from separate maps of each receiver’s total power, not
ative to the next. All components up to and including from interferometry. Common-mode pointing errors can
thepowersplittersarehousedinatemperature-regulated be corrected off line and were determined to approxi-
◦
box. Eachsignaltravelsthroughonemeterofcoin-silver mately0.025 accuracyinelevationandinazimuth. Fol-
D-bandwaveguide,whereitiscoupledintothetelescope lowingan initial alignmentofthe receiversto eachother
optics by an open-ended waveguide illuminating a tiny (whichalsoinvolvedsolarobservations),theywerefound
◦
toberelativelyalignedtowithin 0.02 . Thisanglecor-
20 NoiseCom,Parsippany,NJ responds to approximately 1/6 o∼f the fringe spacing in
CMB Observations with MINT 7
the longest baseline. We noted no significant shifts dur- to deployment). This loss of coherent signal is corrected
ing the campaign. At this level of accuracy, the flatness atthe endof the analysispipeline by scalingupallaver-
and placement of the cardboard shields appear to limit age and rms values.
the measurements. Jupiter was too low in the northern sky during late
During the Chile campaign, Mars was visible nightly 2001 to be visible to MINT in its normal configuration.
in the late afternoon and early evening. When weather After the CMB campaign ended, the ground shield was
andmaintenancepermitted,MINTobservedMarsbyre- removed and replaced by a flat mirror that covered all
peatedly pointing the telescope ahead of Mars’ position receivers. This mirror redirected the beams of each re-
◦
andallowingtheplanettodriftthroughthebeamfor1–2 ceiverby76 inaltitude,allowingobservationofJupiter.
′′
minutes. Approximatelytwentyhoursofdataweretaken The planet’s larger angular diameter (47 ) makes the
on or near Mars. Averaged over the season, the planet’s expected signal much larger than the Mars signal and
′′
angular diameter was 7 . Using the 171GHz temper- easily discerned in a single 2-second data frame. We
ature (Goldin et al. 1997) of 198K, we expect Mars to assume a brightness temperature of 172K for Jupiter,
produce antennatemperature in the small-small,mixed- given by WMAP measurements at 90GHz (Page et al.
size, and large-large baselines of only 1.9mK, 2.9mK, 2003). The Jupiter observations (taken on consecutive
and 4.3mK (the three baselines have forward gains of mornings2002January2–4)confirmallthe mainresults
+51.3dB, +53.1dB, and +54.80dB, according to the of the lower signal-to-noise Mars data, including phase
lossless opticalmodel, and solidangles of 93 µsr, 62 µsr, and amplitude stability, beam sizes, and the reduction
and42µsr). Jupiter wasobservedonly atthe end ofthe in signal (particularly in receiver A) caused by the po-
campaign. larizers.
The Mars data are used to measure the phase versus
frequency profile of the instrument. Since Mars appears 5. observing the anisotropy
as an unresolved point source to MINT, its visibility
5.1. Sky Scan Strategy
phase should be a simple function of its position rela-
tivetothephasecenterofagivenbaseline. Inparticular, An experiment’s sensitivity to CMB anisotropy de-
thephaseshouldbenearlyindependentofthebase-band pends onhowthe observingtime is dividedamongfields
frequency (effects of wavelength variation are small due on the sky. The statistically optimal division requires
to the small fractional bandwidth at D band). With observing each field until a signal-to-noise ratio of one
the phase corrected for the position of Mars, a fiducial is achieved, then moving on to the next. For MINT,
phase φ(ν) is determined by averagingthe complex visi- this meant maximizing the observing time on each field.
bility over many Mars observations. All data, including We used a quasi-tracking strategy which combines the
planetary calibrations and CMB data, are adjusted by stability advantagesof the sky drifting overa stationary
subtractingthefiducialphase. After makingthisadjust- telescope with increased integration time beyond a nor-
ment, it is possible to average complex visibility across mal drift-scan. The telescope was repointed eight times
all frequencies. perhourto observethe samestripofsky(1/8hourwide
The visibilities measured on Mars match the impor- in right ascension) repeatedly. Pointings were made at
tant features ofa point source. The visibility magnitude a fixed azimuth angle and a range of near-zenith eleva-
is approximatelyGaussian(as a function ofpointing an- tions. Although fixed points in the sky curve across a
gleawayfromthe planet)withawidthasexpectedfrom range of azimuth, this effect was small for the limited
the primary beam widths. The visibility phase is also range of elevations used.
consistent with the expected 2πx·u fringes. The phase Table 2 gives the location of the center of each strip
of the setting Mars is stable over the campaign at the usedinthecurrentanalysis,bothineclipticandingalac-
level of 5◦–10◦ rms, depending on the baseline. Even tic coordinates. Although the fields near RA=7h and 8h
◦
in the worst baseline, the computed signal loss due to are within 10 of the galactic plane, they are located
the phase variation is only 3%. The phase is somewhat far from the galactic center and outside other major
less stable during observations of Mars rising (10◦–20◦ components. Additionally, the spectrum of diffuse back-
rms, or 2%–10% loss), but these data are taken during grounds such as interstellar dust falls approximately as
daylight hours and are therefore less indicative of the ℓ−1.5 (Gautier et al. 1992). The galactic contribution in
instrument stability during its nighttime CMB observa- the MINT fields at multipoles ℓ&1000 is negligible.
tions. The effectofscanning continuousstripsis to acquirea
Mars’ visibility magnitude, though stable during the seriesofcomplexvisibilitieswithsignalhighlycorrelated
campaign, does not match the expected magnitude. For betweenneighbors. Simulationsshowthatskystripsw=
◦
all baselines involving receiver A, the magnitude is only 1.875 long observed with a Gaussian primary beam of
◦
33%oftheexpectedvalue;forotherbaselines,theobser- width σb = 0.19 have the same statistical power for
vation is 75% of the expected value. Extensive tests to measuring sky variance as nspot = 4.5 separate spots.
explain the deficit were performed after MINT returned The general relation for all three MINT beam sizes is
to Princeton in 2002. The tests involved direct observa- found to be
w
tion of Jupiter, a high signal-to-noise source, and con- n 1+ .
spot
firmed the signal loss. By switching equipment between ≈ 2.8σb
the receivers, channelizers, and correlators, the deficit
5.2. Data Selection
waslocalized to the poor performance ofthe circular-to-
linearpolarizersatthebaseofthefeeds. Thedegradation The data usedfor CMB analysis areselected basedon
is clearly evident only while observing a known celestial time of day, sky temperature, and nominal receiver op-
source interferometrically (which was not possible prior eration. The noise source calibrations ( 3.3) show that
§
8 J. W. Fowler et al.
Table2. Medianrightascensiona andgalacticcoordinatesforCMB
fieldswith atleast9 hoursobserving timeb.
RA(h,m,s) b(deg) l(deg)
1 3 42 −84.47 161.59
2 3 5 −72.68 202.49
3 2 40 −59.54 212.27
4 2 34 −46.34 218.46
5 2 26 −33.12 223.82
6 2 16 −20.24 229.17
7 2 8 −7.68 234.97
8 2 6 4.37 241.77
9 2 1 15.52 249.94
10 1 47 25.41 260.21
11 1 39 33.31 273.18
12 1 38 38.34 289.07
aThedeclinationofeachstripis23◦2′14′′ south.
bThenominalfieldsarespacedevenlyinrightascension. Thecoordinates givenherearemediansofthedatasurvivingallcuts.
the system phase response is stable from 23:35 UT un- ture averagedoverthe beamsolidangle,ratherthan the
til 10:05 UT. These times correspond approximately to usualfluxdensity. Thisdefinitionamountstoare-scaling
half an hour after sunset and twenty minutes after sun- of the usual visibility by a constant factor λ2/(2kΩ ),
B
rise. Outside these times, the phase variations are likely where Ω is the beam solid angle. We make this non-
B
due to thermal changes in the noise calibration waveg- standard choice even though MINT’s power levels are
uide (which is insulated but not thermally regulated). ultimately calibrated to the flux density received from
Although we believe that the instrument is more stable pointsources(MarsandJupiter). We havefounditcon-
than the calibrator, there is no way to be certain, and venienttoworkinskybrightnesstemperature,aquantity
data are rejected outside this window of 10.5 hours per appropriate to a beam-filling source. In particular, this
night. choice permits quick and transparent comparison with
In addition, the data are cut when the sky brightness non-interferometric CMB experiments and their sensi-
inD-band(includingCMB)exceedsaneffectivetemper- tivities. We use the label V to designate the modified
T
ature of 35K. At higher temperatures, the linear re- visibilitydefinition;allformulasforV canbemultiplied
T
lationship between sky temperature and measured rms by 2kΩ /λ2 to yield the conventional visibility.
B
visibilities breaks down. The sky brightnesscut removes IgnoringthefrequencydependenceoftheCMBbright-
3% of the otherwise valid data, which due to their high nessacrossMINT’snarrowbandandmakingtheflat-sky
noise temperature would have only 1% of the statistical approximationfor smallfields ofview, the complex tem-
weight. perature visibility V at location u in the u v plane
T
−
InstrumentcriteriaincludetestsforlockedPLLs,func- is
tional 4K refrigeration, and properly synchronized cor- V (u) dxA(x)∆T (x)e+2πiu·x, (1)
T B
relator readout. The total data set after all cuts is 215 ≡Z Ω
B
hours long, representing 54% of the available nighttime where x is the two-dimensional position in the plane of
hours. The weather and the instrument are responsible the sky (conjugate to u), A is the primary power beam
for approximately equal shares of the lost time.
of the antennas (normalized to one at its peak), Ω
B
dxA(x)is the beamsolidangle,and∆T is the CM≡B
6. analysis B
bRrightness temperature fluctuation (∆TB = ηRJ∆T).
6.1. Expected CMB Signal for a Heterogeneous The Rayleigh-Jeans factor η converts small physical
RJ
Interferometer temperaturefluctuations∆T tobrightnesstemperatures:
MINThasboth30cm-and45cm-diameterantennas,a ∂T λ2 ∂B x2ex
B
configurationwhichproduceshighcollectingareaforthe η = = ,
RJ ≡ ∂T 2k ∂T (ex 1)2
medium and longest baselines, where the CMB signal is −
small, while permitting the shortest baseline to be only where x hν/(kT). At 145GHz and for T = 2.73K,
≡
160λ. Put another way, the heterogeneous array fills a η = 0.59. Note that the definition of temperature
RJ
largerfractionofthe antenna plane thanwouldanarray visibility (equation 1) leads to a magnitude of V =
T
| |
of small antennas alone. T Ω/Ω for an unresolvedsource of brightness temper-
B B
Given a CMB power spectrum, the expected vari- ature T and solid angle Ω Ω . This fact connects
B B
≪
ance of the interferometer visibility is derived by the CMB observations to the absolute calibration off of
Hobson, Lasenby, & Jones (1995) and White et al. Mars.
(1999) for the case of identical receivers. We consider Apart from constant factors, the visibility is the
herethecalculationforaheterogeneousarray,whichdif- Fourier transform of the product of A and ∆T . By the
B
fers in that the effective beam and its Fourier transform convolution theorem, it is also the convolution of their
are complex. transforms:
We work with a modified “temperature visibility” η
V (u)= RJ(A˜ ∆T)(u).
quantity, which corresponds to a brightness tempera- T Ω ⊗
B
g
CMB Observations with MINT 9
Using this expression for temperature visibility, its ex- With this change, all formulas and statements above
pected covariance matrix has diagonal elements of about A and A˜ hold, except that A˜(u v) becomes
−
CT V∗(u)V (u) (2) the cross-correlation of the two antenna’s voltage pat-
≡h T T i terns in the aperture plane. The resulting beam Ae is,
η 2 in general, complex. The overall phase is unimportant;
= RJ dv A˜(u v)2T2 S(v) (3)
(cid:18)Ω (cid:19) Z | − | cmb it merely adds to any other phase offsets in the sys-
B
tem, which are measured by observing planetary point
using the unitless power spectrum, S(v), defined by sources. Phasevariationacrossthe beam, however,adds
an imaginary part to the beam A and its Fourier trans-
hT˜∗(v)T˜(u)i=Tc2mbS(v)δ(v−u). form A˜. In MINT’s mixed-antenna baselines, the phase
NotethattheFourierpowerspectrumS dependsonlyon oftheeffectivebeamisnearlyconstantwellpastthehalf-
the magnitude ofv and approximatelyequals the spher- powerpointofthemainlobe,sotheimaginarypartofA˜
icalharmonicspectrumC for largeℓ (ifthe spectrumis is of much smaller magnitude than the real part. Even
ℓ
smooth enough): S(v) Cℓ=2πv. so, the imaginary part is included in A˜2 when numeri-
Non-diagonal elemen≈ts of the theory covariance ma- callyintegratingequations4and5,inc|re|asingthetheory
trixareoftwotypes. Twoobservationsmadebyasingle covariance by a few percent.
baselinebutseparatedbyangle∆ontheskyareaccom-
modated with a factor exp(2πi∆·v) in the integrandof 6.2. Approximate Analytic Expression for the Expected
Equation3. Observationsmade by distinct baselinesare Signal
also correlated. In the extreme case of parallel baselines
The theory covariance integrals can be approximated
(such as DA-BC and AC-DB in MINT), the correlation
by taking the effective beams to be Gaussian and the
is complete. The MINT baselines of equal length but
power spectrum to be scale-invariant. The result is use-
different orientations (such as DB and DC) are weakly
ful in illustrating how the CMB signal depends on in-
correlated. The ratio of the magnitude of the covariance
strumentparameters. We assumeaGaussianbeamwith
for DB-DC data to that of the DB-DB data is 18% for
a beam solid angle Ω = 2πσ2. The ratio of the beam
data from a single field (∆ = 0), falling off quickly with G
solidanglesfortheidealizedGaussiantotheactualbeam
increasing field separation ∆. The correlations between
is akin to a main beam efficiency; call it ǫ 2πσ2/Ω .
theshortorthelongbaselines(DAorCB)andanyother g ≡ B
are negligibly small. The transform A˜ of the normalized beam is then
Analysis of the data is more easily done using the real A˜(u)=2πσ2e−2(πσu)2.
and imaginary visibilities separately, leading to the final
covariance elements Let
1 δT2
CRTR = (ηRJ2ΩTc2mb)2 Z dv|A˜(u−v)|2S(v)cos(2π∆·v) S(v)= 2πv2 (cid:18)Tc2mb(cid:19),
B
(4) so that δT2 is a flat-bandpower temperature variance.
and Performing the angular part of the integral over dv
(η T )2 (Equation 3) yields
CT = RJ cmb dv A˜(u v)2S(v)sin(2π∆·v).
RI 2Ω2B Z | − | (5) CRTR = (ηRJǫ2gδT)2 Z dvve−(2πσ)2(u2+v2)I0(8π2σ2uv),
The other combinations obey CT = CT and CT =
II RR IR
−haClfRToIf.thTehsekynevwarifaanctcoerapofpe2arasccinoutnhtesrefoarlctohmepfaocntentthaotf w(DhieergeuIe0zis1t9h9e9;mHoodbifiseodnB&esMsealisfuinngcetrion20o0f2t)h.e fiTrhsitskcinand
V and half in the imaginary. The two formulas are even be simplified with the asymptotic expansion I0(x)
≈
and odd with respect to exchange of the two indexes ex/√2πxforlargex. DefiningU 2πσuandV 2πσv,
(or equivalently, under reflection of ∆). This result can ≡ ≡
be generalized to give the covariance between distinct CT = (ηRJǫgδT)2 dV 1 U 3/2e−(U−V)2.
baselines. RR 2U2 Z √4π (cid:18)V (cid:19)
In words, the covariance for ∆ = 0 is the sky power
spectrumS(v)averagedintwodimensionswithaweight- NotethatrP =λ/(2πσ)isthecharacteristicradiusofthe
ing function A˜(u v)2. Recall thatA(x) is a single re- Gaussian power reception pattern in the antenna plane.
ceiver’s powe|r bea−m, s|o A˜(u v) is the autocorrelation Therefore,U =λu/rP >2foranyrealinterferometer,as
− theseparationλumustbelargerthantheantennadiam-
of the voltage pattern in the antenna plane, offset from
the origin by a distance u corresponding to the baseline eter. TheintegrandaboveissmallexceptnearV ≈U,so
the divergence as V 0 can be ignored (it corresponds
separation in wavelengths. →
toanunphysicaldivergenceintheCMBpowerspectrum
Thecomplicationofmixedantennascanbehandledby
atlargeangularscales,wheretheflat-skyapproximation
extendingtheformulationoftheantennapowerreception
breaks down as well). For U 3.5, the integral evalu-
pattern (Thompson, Moran & Swenson 1998). Starting ≈
instead with the voltage pattern g (x) of antenna j for ates numerically to 0.54, approaching 0.500 in the limit
radiation from angle x, the effectivje power beam A for of large U (large separation). Replacing the Gaussian
e beamwidthσwiththebeamfullwidthathalf-maximum
baseline j-k is
power θFWHM = √8ln2σ (which is more readily gener-
A (x)=g (x)g∗(x). alized to non-Gaussian beams), the simplified estimate
e j k
10 J. W. Fowler et al.
for the covariance matrix is 6.4. Sideband Separation
CT 0.27η2 ǫ2δT2 U−2 (6) The SIS mixers in MINT are inherently double-
RR≈ RJ g
sidebanddevices,mixingskysignalsinbothranges139–
≈0.038 ηR2Jǫ2gδT2/(uθFWHM)2. (7) 141GHz and 149–151GHz down to a single IF band
◦
Equation 7 can be used to estimate the magnitude of at 4–6GHz. By switching a 90 phase shift in and
the CMB signal from any single interferometer baseline, out of the 145.1GHz local oscillator tone every half-
given basic parameters such as baseline length and the second, we separate the signals from the two sidebands.
beamwidthandefficiency. Weexpectthatthe“Gaussian The separation is possible because an LO phase shift
efficiency” ǫ can generally be replaced with the main enters with opposite signs in the IF signals from the
g ′
beam efficiency with little loss of accuracy. two sidebands. If C and C are the correlation func-
′
tions for unshifted and shifted data, then (C+iC ) and
6.3. Expected Signal-to-Noise on the Power Spectrum (C iC′)isolatethe contributionsfromlowerandupper
−
A numerical evaluation of equations 4 and 5 gives a sidebands. This feature is preserved through the chan-
moreaccuratefigurefortheexpectedMINTvarianceper nelizer,wherethe signalsaremixeddownasecondtime.
µK2 of flat bandpower (Table 3). The two-dimensional Thompson, Moran & Swenson (1998)describethetech-
niquein 6.1. Wehaveshownthattheirresultgeneralizes
Fouriertransformofthebeam,A˜,issimplifiedbynoting §
to the cases of unequal power in the two sidebands and
that the antennas and beams are symmetric about the
oflowersidebandconversionatthe secondmixing stage.
optical axis. This symmetry reduces the problem to the
The magnitude and phase of the cosmic signal should
one-dimensionalHankeltransformoftheradialfunction.
be nearly the same in both MINT sidebands.21 There-
Thenumericalresultassumesthebeamshapescomputed
fore, it is not strictly necessary for CMB observation to
by physicaloptics and confirmed by direct measurement
distinguishthesignalsinthetwobands. Wecouldmain-
(Figure 2).
tainaconstantLOphase,effectivelymeasuringonlyone
The noise covariance CN follows straightforwardly
component of the complex sky visibility. Instead, MINT
from the system temperature and the Dicke equa-
determines the full complex visibility with half the ob-
tion (Dicke 1946). The covariance of the real or imagi-
serving time per component. The MINT strategy was
nary output of a complex correlating interferometer is
chosento characterizethe instrument completely and to
T2 guard against possible drifts in the instrumental phase.
CN ≡h∆TB2i= 2ǫ2s∆ysντ, Correctingsuchphasedrifts—ifmeasuredbythecalibra-
q tion source ( 3.3)—requires the complex visibility.
§
where T is the system noise temperature, ǫ is the ef- The sideband separation technique is proved in prac-
sys q
ficiency factor of the digital quantization scheme, ∆ν is tice by observations of the calibration noise source. The
the IF bandwidth, and τ is the effective observing time noisesourceproducespoweronlyinthelowersidebandof
(see for example Thompson, Moran & Swenson (1998) the MINT receivers. The measured cross-power spectra
eq. 6.42). Note that for MINT, τ is only half the of the calibrator shows no power in the upper sideband
elapsed time, because the phase-switching scheme effec- except for small leakage near the band edges, a result of
tively time-shares the correlator between measuring the the limited number of time lags available in the correla-
real and imaginary parts of the correlation. Using a tion function.
typical T = 45K (including atmosphere and CMB),
sys
ǫ =0.88, ∆ν =1.9GHz, and 5 hours of observing time
q 7. anisotropy results
(τ = 9000s) on a CMB field, the noise covariance is
77µK2. 7.1. Data Reduction
Using a set of N 1 Gaussian deviates to estimate
Analysis of the interferometer data is performed in
≫
the variance of the set gives a fractional uncertainty of
Fourier (temporal frequency) space. First, the correla-
2/N. The number of samples N is twice the number tionfunctionρ(τ)isconvertedtobrightnesstemperature
poffieldsobserved,nf,becausethecomplexcorrelationat (as described in 3.2 and 4). The conversion incorpo-
each field gives two independent samples. The variance rates the results§of sky di§ps and the absolute calibra-
CT +CN of the data can be estimated to a fractional tiondeterminedfromMarsobservations. Usingtheside-
uncertainty of 1/√nf, so band separation procedure, data with and without the
◦
90 phase shift in the LO are combined to form a com-
δCT 1 CT +CN
. plexcorrelationfunction. ThediscreteFouriertransform
CT ≈ √nf (cid:18) CT (cid:19) of the 16-lag correlation gives the cross-power spectrum
ofonepairofantennas. Interpretationofthecross-power
The two terms are the sample and noise variances. The
iscomplicatedbythefactthatboththelowestandhigh-
quantityofinterest,δT,isanrmsratherthanavariance;
est frequency bins combine signal from upper and lower
thusiftheerrorissmall,δT hashalfthefractionaluncer-
tainty of CT. Consider the case of MINT observations, sidebands. This complication is not a problem, because
MINT does not currently make use of the spectral infor-
covering n = 50 fields. If sample and noise variance
f
mation in analysis of the CMB data.
contributed equally to the final error (which is statisti-
The “fiducial phase” φ(ν ) found from many Mars
cally optimal for a fixed total observing time), then the j
observations ( 4) is subtracted from each data point.
fractionalerrorexpectedontheCMBsignalδT wouldbe
§
1/√50 15%. Achieving this levelof uncertainty would
≈ 21 Thelowersidebandpowerexceedstheupperby7%forCMB
require76hoursofobservingperfield, approximately12
fluctuations, owingtothefrequencydependence intheconversion
times the time actually available in the 2001 campaign. fromphysicaltobrightnesstemperatures.