CAPMAP: A New Instrument to Measure the E-mode CMB Polarization on Angular Scales of 4 arcmin to 40 arcmin

Denis Barkats

REVIEW 3 major objections 5 minor 158 references

CAPMAP: A New Instrument to Measure the E-mode CMB Polarization on Angular Scales of 4 arcmin to 40 arcmin

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A 90 GHz four-receiver array can reach the microkelvin E-mode CMB signal.

desk verdict A thorough instrument thesis whose sensitivity claim is honest and well-supported, but whose absolute calibration carries an unquantified ±20% systematic that should be flagged. read the letter →

arxiv 2411.18522 v1 pith:MFNEKPSF submitted 2024-11-27 astro-ph.IM astro-ph.CO

Denis Barkats This is my paper · ORCID

classification astro-ph.IMastro-ph.CO

keywords CMBpolarizationE-modecorrelationpolarimeter90GHzreceiverarrayradiometersensitivitychopper-platecalibrationangularpowerspectrumNorthCelestialPolescan

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

CAPMAP is a 90 GHz four-element array of correlation polarimeters built to measure the E-mode polarization of the cosmic microwave background on angular scales from 4 to 40 arcminutes, corresponding to multipoles near 500 to 1500. The thesis argues that the instrument, fielded in January 2003 on the Crawford Hill 7-meter antenna, has enough sensitivity to detect the few-microkelvin polarized signal: the twelve polarization channels reach 1.35 to 1.51 mK√s in total, and fake-chopped sky data show noise that integrates down as 1 over the square root of time. That matters because E-mode polarization is a robust prediction of the standard cosmological picture, and measuring its power spectrum would confirm that picture while adding information that helps break degeneracies among cosmological parameters.

What carries the argument

The central object is the phase-switched heterodyne correlation polarimeter: an orthomode transducer splits incoming radiation into two orthogonal linear polarizations, cryogenic MMIC HEMT amplifiers preserve the relative phase, a local oscillator down-converts the band, and a diode multiplier produces a voltage proportional to one Stokes parameter. An in-line phase switch modulates that output at 4 kHz, above the amplifier 1/f knee, so unpolarized common-mode power and low-frequency gain drift are rejected. The absolute calibration that converts volts into kelvin is carried by the chopper-plate test, whose emitted polarized signal is predicted from the finite conductivity of aluminum through Eq. 3.9.

What would settle it

Compare the chopper-plate-derived absolute sensitivity against an independent calibrator with known polarized flux, such as Tau A at 90 GHz, observed through the same receivers; a disagreement beyond roughly the 20 percent scale set by the resistivity assumption would show the absolute temperature scale is wrong. On the statistical side, the claim that noise integrates down is directly falsified if the RMS of fake-chopped sky data stops following 1 over the square root of the integration time before the full observing period is reached.

Watch

Extended reading notes

Core claim

The paper's central claim is that a four-element W-band correlation-polarimeter array, phase-switched at 4 kHz and pointed at the North Celestial Pole through a 7-meter antenna, is sufficiently sensitive to detect the few-microkelvin E-mode CMB polarization at multipoles 500 to 1500. The demonstration rests on calibration measurements: effective bandwidths near 11 to 14 GHz, polarized gains obtained from chopper-plate tests, and polarization-channel sensitivities of 1.35 to 1.51 mK√s derived from a five-hour stretch of stable sky data. The RMS of fake-chopped sky data declines as 1 over the square root of the integration time out to the longest measured time scales, which is exactly the behavior needed for a real detection in the roughly 250 hours of planned observation.

Load-bearing premise

The absolute temperature scale of the sensitivity claim rests on the assumed 4 microhm-centimeter resistivity of the aluminum chopper plate and on the finite-conductivity emission model in Eq. 3.9, and the thesis itself notes that a 50 percent uncertainty in that resistivity would shift the predicted signal, and therefore every quoted microkelvin sensitivity, by up to 20 percent.

Editorial extensions

If this is right

With total polarization-channel sensitivities of 1.35 to 1.51 mK√s, the four receivers can reach the predicted few-microkelvin E-mode signal in the roughly 250 hours of CAPMAP03 observations.
The white-noise plateau after fake chopping means the scan-synchronous offset, slope, and quadratic removal will not be the dominant error term.
Four-arcminute beams and a pointed, calibrated array place usable sensitivity at multipoles 500 to 1500, where the E-mode power spectrum peaks.
A successful E-mode measurement would directly confirm a robust prediction of the standard cosmological model and complement temperature anisotropy data by breaking parameter degeneracies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the absolute chopper-plate calibration holds, the CAPMAP03 data should yield E-mode band powers at multipoles 500 to 1500, with roughly a 20 percent calibration floor on the overall amplitude traced to the assumed plate resistivity.
The same correlation-polarimeter architecture could be pointed at deeper or smaller patches to push toward higher multipoles, at which point the dominant uncertainty would shift from receiver noise to the absolute calibration scale.
A natural testable extension is to tie the chopper-plate gain scale to an astronomical polarized source such as Tau A observed through the same receivers, converting the flagged resistivity uncertainty into a measured quantity.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a PhD thesis, not a detection paper. It describes the CAPMAP 90 GHz four-element correlation polarimeter array and argues, from lab and sky data, that the instrument is sensitive enough to detect E-mode polarization at ℓ 500–1500. The receiver characterization is genuinely careful: phase matching via in/out-of-phase sweeps, gains from chopper plate and Y-factor tests, sensitivity from the variance of five hours of sky data, and integration-down curves that follow 1/√t. Those curves are convincing evidence that the noise is white on the relevant timescales, and the quoted sensitivities (1.35–1.51 mK√s for the four receivers) are consistent with the independently measured bandwidths and system temperatures.

What's new here are the measured numbers: the phase-matched bandwidths, polarized gains, total-power gains, and sky-noise sensitivities (Tables 3.5, 3.7, 3.8, 3.9). These are real engineering results, presented in enough detail to reproduce. The thesis also credits PIQUE and places CAPMAP in the context of the 2002–2004 polarization experiments; the citation pattern looks fair.

The soft spot is the one you flagged. The absolute temperature scale of the polarization channel gains comes from the chopper plate tests, and those rely on Equation 3.9 with an assumed aluminum resistivity of 4 μΩ cm. The thesis states explicitly in §3.3.2 that the quoted gain errors exclude the systematic from the predicted signal and that a 50% uncertainty in ρ corresponds to a 20% systematic error. Since the Table 3.9 sensitivities are converted from volts to mK using those gains, they carry the same ±20% unquantified absolute calibration uncertainty. The integration-down behavior doesn't test that scale. This doesn't sink the paper—it's an instrument thesis, and the relative noise performance is solid—but anyone using those absolute sensitivities for a detection claim would need to quantify or bound that systematic. Note also that the abstract says 'preliminary analysis indicates' sensitivity, not 'we detect'; the claim is appropriately scoped.

The provided text truncates the observatory calibration and CMB data chapters, so I can't fully vet the Tau A comparison or the final map processing. That's a limitation of the review, not necessarily of the thesis.

Bottom line: this is a solid instrument thesis, worth reading if you work on coherent polarimeter arrays or CMB E-mode history. As a peer-review target, it deserves a serious referee; the main request should be a quantified absolute calibration systematic or a clear caveat on all absolute sensitivities. My own verdict would be conditional acceptance with that revision.

Referee Report

3 major / 5 minor

Summary. The thesis presents the design, construction, laboratory characterization, and first-season deployment of CAPMAP, a four-element 90 GHz correlation-polarimeter array mounted on the 7 m Crawford Hill antenna. It details the RF/IF/LO receiver architecture, the cooled feed optics, the cryostat, the telescope optics and pointing, and the chopper-plate calibration of the polarized gains. The central quantitative claim is that the measured sensitivity of each polarization channel is 1.35–1.51 mK√s (Table 3.9) with noise that integrates down as 1/√t (Fig. 3.20), so that a roughly 250-hour integration should be sufficient to detect the few-μK E-mode CMB polarization at ℓ ≈ 500–1500. No final Cℓ spectrum is presented; the claim is a sensitivity projection.

Significance. If the absolute calibration is correct, this is a valuable instrument paper. The receiver characterization is unusually complete for a thesis: phase matching is verified via in- and out-of-phase sweeps, gains are anchored to an external physical model, and the sky-noise variance and fake-chopped integration curves demonstrate white noise down to hour timescales. The explicit statement of the chopper-plate resistivity systematic, and the use of direct sky data rather than a fitted model, are strengths. The measured noise performance is close to the design value, and the array was one of the few 90 GHz coherent polarimeters probing ℓ ~ 500–1500. The remaining issue is concentrated in the absolute polarization calibration, not in the noise statistics.

major comments (3)

[§3.3.2, Eq. (3.9), Tables 3.7 and 3.9] The absolute scale of the polarization calibration rests exclusively on the chopper-plate model. As the text states, the predicted signal in Eq. (3.9) uses ρ = 4 μΩ cm, and a 50% uncertainty in ρ gives a 20% systematic error; that systematic is explicitly excluded from the quoted gain errors in Table 3.7. Because Table 3.9 converts the measured voltage noise into mK√s using these gains, the headline sensitivities 1.35–1.51 mK√s carry an unquantified ±20% absolute calibration error. This error propagates directly through Eq. (2.1) into the predicted Cℓ error bars and into any future detection significance. The 1/√t integration shown in Fig. 3.20 is unaffected, but it cannot validate the absolute temperature scale. I ask that the authors measure or bound the resistivity of the actual plate, include the resulting systematic in the reported gains and sensitivities, and, if possible, provide an independent cross-check such as the Tau A observation described in §6.5.2.
[§2.1, Fig. 2.3, Table 2.1] The projected detection claim in the abstract is tied to Fig. 2.3, which assumes S = 1000 μK√s and a 1.5 degradation factor borrowed from PIQUE. The measured total sensitivities in Table 3.9 are 1.35–1.51 mK√s, i.e., 35–51% worse than the plotted assumption. Although the resulting realistic per-pixel noise may still be adequate for a band-power detection, the predicted Cℓ errors in Fig. 2.3 should be recomputed with the measured S values and with the calibration systematic from the previous comment; as it stands, the figure overstates the projected significance.
[§6.5.2] The text lists Tau A as a potential independent polarized calibration (Figs. 6.20 and 6.21), but no derived gain comparison from those observations is presented in the available text. If the Tau A analysis exists, it should be used to bound the chopper-plate resistivity systematic; if it does not, the absence of any independent absolute polarization calibration should be stated explicitly as a limitation of the projected sensitivity claim.

minor comments (5)

[Abstract and throughout] The symbol θK appears where μK is intended (e.g., 'few-θ K signal'); replace the unit throughout the manuscript.
[Table 2.1] The column headers repeat 'CAPMAPb'; clarify whether the W-band and Q-band performance columns refer to design estimates for the final array or to the CAPMAP03 configuration.
[Table 3.9] State explicitly that the 'Total' column is the inverse-quadrature combination 1/√(Σ 1/S_i²), not the quadrature sum; the present caption says 'added in quadrature,' which can be misread.
[§3.3.2] The statement that the smallest measurable polarization signal is a factor √2 smaller than Eq. (3.11) depends on the Q = (Tx − Ty)/2 convention; make that dependence explicit in a full sentence rather than in a parenthetical.
[References] Several key calibration references are internal theses or notes ([55], [57], [58], [107]); if this is submitted as a journal paper, those should be publicly available or replaced by published descriptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the sensitivity estimate is measured from sky noise and calibrated with a physical chopper-plate emission model, not fitted to the predicted CMB polarization signal.

full rationale

Walking the derivation chain: the instrument sensitivity S in Eq. (3.10) is the standard radiometer formula S = T_sys/sqrt(delta_nu), and the measured values in Table 3.9 are derived from the variance of 10-second sky data, after converting voltages to temperature using polarized gains obtained from the chopper-plate tests in Section 3.3.2. The chopper-plate predicted signal, Eq. (3.9), comes from a finite-conductivity emission model for an aluminum plate with parameters alpha, beta, T_plate, and T_sky; it does not depend on the CMB polarization amplitude or on any fitted C_l spectrum. The gains are therefore calibrated against an external physical model, not against the quantity being predicted. The predicted C_l errors in Eq. (2.1) then use the measured sensitivity S as an input, which is an empirical instrument characterization rather than a fitted parameter renamed as a prediction. The thesis explicitly flags the leading systematic: "If we conservatively assume a 50% uncertainty on the estimate of the resistivity of Aluminium, this would translate into a 20% systematic error in the expected signal" and notes that the quoted gain errors exclude this systematic. That is a calibration-accuracy concern, not circularity. Citations to the group's earlier PIQUE experiment provide context and comparison (e.g., Table 2.1 and Section 2.1), but the CAPMAP receiver tests, beam measurements, and integration-down curves are independent results and do not reduce to those citations. Figures 3.19 and 3.20 independently demonstrate that the polarization-channel noise integrates down as 1/sqrt(t), consistent with the claimed sensitivity. No load-bearing step in the paper is equivalent by construction to its own inputs, so no circularity is present.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim, instrument sensitivity, rests on measured noise properties and calibration gains. The gains in turn rest on the chopper plate model and an assumed aluminum resistivity with a known but unquantified systematic. No new physical entities are introduced.

free parameters (4)

Chopper plate resistivity rho = 4 micro-ohm cm (assumed)
Assumed for aluminum 6061 in the chopper plate polarization signal calculation (Eq 3.9). The thesis states a 50% uncertainty in this value translates into a 20% systematic error in the predicted signal, which propagates to all polarized gains in Table 3.7.
Polarized gain calibration constants = e.g., A S0 = 21.0 mV/K (Table 3.7)
Fit amplitudes from chopper plate data for each receiver and sub-band. Used to convert voltage noise into temperature sensitivity in Table 3.9. Statistical errors are quoted but systematic (resistivity) is excluded.
Realistic sensitivity degradation factor = 1.5
Adopted from PIQUE in Table 2.1 footnote f to scale ideal senfac to realistic sigma_pix. A hand-chosen fudge factor not derived from CAPMAP data.
System temperature T_rec from Y-factor = 76 to 166 K per arm (Table 3.8)
Derived from in-lab two-load Y-factor tests; used to cross-check sky sensitivities. Depends on load temperatures and linearity assumptions.

assumptions (5)

standard math CMB polarization arises from Thompson scattering of a quadrupole radiation field at last scattering.
Section 1.3.2. Basis for expecting the E-mode signal the instrument targets.
domain assumption The E-mode polarization spectrum is well described by a Lambda-CDM model with WMAP parameters.
Used throughout, for example in Figure 2.3, to set predicted signal levels and required sensitivity.
domain assumption Receiver noise is white and integrates as 1/sqrt(t) after phase switching.
Central to sensitivity statements. Checked empirically in Figures 3.19 and 3.20 for the CAPMAP receivers.
domain assumption Jupiter is an unpolarized calibrator at 90 GHz.
Used in Section 6.3.1, as referenced in the text, to estimate instrumental cross-polarization from beam maps.
domain assumption The chopper plate produces a polarized signal given by Eq 3.9 based on finite-conductivity emission theory.
Section 3.3.2. Depends on the plate being aluminum with resistivity rho and on specular reflection geometry.

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Cite this review

Pith. "Pith review of CAPMAP: A New Instrument to Measure the E-mode CMB Polarization on Angular Scales of 4 arcmin to 40 arcmin." pith.science (2026). https://pith.science/paper/MFNEKPSF

@misc{pith2026241118522,
  author       = {Pith},
  title        = {Pith review of: CAPMAP: A New Instrument to Measure the E-mode CMB Polarization on Angular Scales of 4 arcmin to 40 arcmin},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MFNEKPSF}},
  note         = {Machine review of arXiv:2411.18522}
}

read the original abstract

The CMB polarization is the Everest in the quest to characterize the earliest photons from the Universe. After a long list of ever-decreasing upper limits, a detection of polarization was made in 2002 by the DASI team at ell =~ 500. The experiment described in this thesis is designed to make a more detailed measurements at higher angular resolution. The E-mode polarization power spectrum not only provides a more direct link to the properties of the last scattering surface than the temperature anisotropy but also offers complementary information which can be used to break various degeneracies in the determination of cosmological parameters. Most importantly, the existence of polarization is a robust prediction of the standard cosmological picture so a precise measurement of the CMB polarization should come as a confirmation of the standard model. However, polarization measurements represent an experimental challenge. The weakness of the polarization signal requires both a demanding instrumental sensitivity and focused attention to all sources of systematic error. This thesis describes the design, construction, and testing of a 90 GHz four-element array of correlation polarimeters to probe the E-mode polarization power spectrum at multipoles (ell) ranging from 500 to 1500. The array was fielded in Jan 2003 on the 7-meter Crawford Hill antenna, in Holmdel, New Jersey and observed for two months. The receiver calibration is described in detail, as well as the characterization of the pointing and beams. Preliminary analysis indicates that the instrument is sufficiently sensitive to detect the few micro Kelvin signal of the CMB polarization.

Figures

Figures reproduced from arXiv: 2411.18522 by the authors.

**Figure 1.1.** From [32]. Hubble diagram using distant type-Ia supernovæ as standard candles. Top panel shows apparent magnitude (an indicator of the distance) vs. redshift. Lines show the predictions for different energy contents of the universe. Bottom panel plots the residuals, making it clear that the high redshift supernovæ favor a Λ-dominated universe over a matter-dominated one. unchanged until the first stars began convert… view at source ↗

**Figure 1.2.** Predictions of light element abundances from Big Bang nucleosynthesis and current measurements from [20]. The four curved lines are the calculated predictions of the initial fraction of 4He, Deuterium, 3He, and 7Li relative to Hydrogen, as a function of η. The boxes are the current best measurements. Since the primordial abundances are a function of the initial baryon-to-photon ratio, an observation of any of the a… view at source ↗

**Figure 1.3.** Blackbody curve and CMB spectrum measured by FIRAS [40, 102]. The exquisite agreement is an inevitable confirmation of the thermal origin of the CMB. Any alternative theory must confront this direct measurement. 1.2.2 Spatial distribution The CMB radiation was observed to be isotropic until the DMR instrument on the COBE satellite [129, 13, 146, 85] detected intensity fluctuations on the sky. The largest anisotropy … view at source ↗

Figures from the paper (107 more)

**Figure 1.4.** Figure 1.4: From [62]. left: Compilation of recent CMB power spectrum measurements (excluding WMAP) compared to the best fit ΛCDM model from the first-year WMAP data. Data points include noise and cosmic variance uncertainty but not calibration uncertainty. right: WMAP power spe…

**Figure 1.** Figure 1: shows an example of such a temperature power spect [PITH_FULL_IMAGE:figures/full_fig_p024_1.png]

**Figure 1.5.** Figure 1.5: Experimental status of polarization measureme [PITH_FULL_IMAGE:figures/full_fig_p025_1_5.png]

**Figure 1.** Figure 1: provides an illustration of the acoustic oscilla [PITH_FULL_IMAGE:figures/full_fig_p026_1.png]

**Figure 1.6.** Figure 1.6: Figure by [99]. Acoustic oscillations of different modes in the baryon-photon fluid generate characteristic peaks in the angular power spectrum. The observer is on the left. The gray spots are initial over-densities seeded by inflation. The smallest scales have re-en…

**Figure 1.7.** Figure 1.7: A quadrupolar intensity distribution incident on an electron of the primordial plasma generates a linearly polarized scattered photon. The incoming radiation is not polarized. The size of the lines and their color are redundant and indicate their intensity. This effe…

**Figure 1.** Figure 1: (a)). An electron on the crest will see radiation d [PITH_FULL_IMAGE:figures/full_fig_p028_1.png]

**Figure 1.8.** Figure 1.8: E and B mode polarization pattern from a single Fo [PITH_FULL_IMAGE:figures/full_fig_p030_1_8.png]

**Figure 1.9.** Figure 1.9: Figure by N. Ponthieu [121]. Spectrum of the various foreground emissions for angular scales of 8′ at the galactic anti-center. Although this plot is only for unpolarized emission, it shows that there is a window between 50 and 100 GHz where the CMB dominates the for…

**Figure 1.10.** Figure 1.10: left: WMAP Maximum Entropy Method derived foreground full sky galactic maps [15] for synchrotron (top), free-free (middle), and dust (bottom) emission. The white circle in the Mollweide full sky maps is a 10◦ radius centered on the NCP. The NCP is located at galacti…

**Figure 2.1.** Figure 2.1: Block diagram of photon path. The signal is transmitted via three different methods: free space propagation (squiggly line), waveguide or coaxial transmission line (double line), and analog or digital signal (straight line) [PITH_FULL_IMAGE:figures/full_fig_p035_2_1.png]

**Figure 2.** Figure 2: gives a graphical representation of the angular r [PITH_FULL_IMAGE:figures/full_fig_p037_2.png]

**Figure 2.2.** Figure 2.2: Angular multipole vs frequency coverage of past, current, and planned polarization experiments. Descriptive parameters of these experiments are listed in [PITH_FULL_IMAGE:figures/full_fig_p038_2_2.png]

**Figure 2.3.** Figure 2.3: CMB E-mode (top) polarization and TE correlation (bottom) detections and upper limits. The CAPMAP03 (CAPMAP04) band power predictions are conservative. They assume an instrument with 1000µK √ s (200µK√ s), tint = 250 hrs (500 hrs), θfwhm = 4′ , and Npix = 600 (1300) …

**Figure 2.4.** Figure 2.4: Schematic diagram of CAPMAP correlation polarimeter polarization detection technique (top left). The reader is referred to [113] for an excellent review of the Jones matrix formalism to interpret the measurement of each type of polarimeter. CAPMAP measures a single S…

**Figure 2.6.** Figure 2.6: Typical noise power spectrum of a phase-switched polarization channel showing the white noise plateau and a 1/f component at low frequencies. For CAPMAP receivers, the 1/f knee is at a few mHz. The residual 1/f noise is removed by the scan strategy position chop. A c…

**Figure 2.7.** Figure 2.7: top: Beam window function for four beams with different full widths at half maximum (fwhm) normalized to a C E ℓ spectrum. B 2 l not Bl is plotted. The CAPMAP beam is chosen to be 4′ (0.06◦ ) so the signal is only reduced by a factor of 0.8 at ℓ = 1500. bottom: The r…

**Figure 2.8.** Figure 2.8: (a) Far-field beam co- and cross-polar beam patterns of the 7-meter antenna at 90 GHz. The input to the simulation is a gaussian beam with a -30 dB edge taper (-30 dB at 5.06◦ at the edge of secondary). The co-polar beam pattern is normalized to 0 dB. It otherwise pe…

**Figure 2.9.** Figure 2.9: Cutaway of CAPMAP horn, lens shroud and lens. Drawing is to scale. The lens is 4.83” diameter, with a spherical back surface of radius R1 = 5.5” and front surface radius described by R2 = F (n−1) n−cos θ , with respect to the phase center at the horn aperture. The fo…

**Figure 2.10.** Figure 2.10: Beam expansion as a function of the distance from horn aperture using gaussian beam optics propagation [44]. All distances are to scale. The curvature of the field is only visible in the closeup of the horn (inset) because it is the near-field region. The origin of …

**Figure 2.11.** Figure 2.11: Spot diagrams of the Crawford Hill antenna. The spot diagram are calculated using the CODE V software[25]. The five spots displayed are the dispersion of ∼ 300 rays distributed over the whole primary and focused to (from right to left) the focal point and the four C…

**Figure 2.12.** Figure 2.12: Induced polarization from the telescope mirrors (in mK) for a 1×1 meter area in the focal plane. Contours are spaced by 100 mK. The simulation assumes a sky temperature of 40 K, an isotropic mirror temperature of 300 K, an aluminium resistivity of ρ = 4 µΩ cm at 90 …

**Figure 2.13.** Figure 2.13: View of the focal plane layout in the CAPMAP03 dewar as seen from the secondary. The crosshatch indicates the direction of the E-plane polarization of the main arm of the OMT. The resulting detection axes are at 45◦ from the OMT axes. Each circle represents a lens.…

**Figure 2.** Figure 2: (b) shows the integration time of the azimuth sca [PITH_FULL_IMAGE:figures/full_fig_p055_2.png]

**Figure 2.14.** Figure 2.14: (a) CAPMAP03 azimuth scan pattern on the sky. The axes are in arbitrary degrees and the size of the throw is determined in [PITH_FULL_IMAGE:figures/full_fig_p056_2_14.png]

**Figure 2.** Figure 2: illustrates some of the results. The error on the [PITH_FULL_IMAGE:figures/full_fig_p056_2.png]

**Figure 2.15.** Figure 2.15: Error on the recovered power spectrum as a function of cap size and varying sensitivity. The simulations perform 100 realizations of the sky assuming a Wang theory power spectrum [141] and observed assuming a 0.05◦ FWHM beam and sensitivities varying from σE = 0.1 (…

**Figure 2.16.** Figure 2.16: CAPMAP observes the white region of sky. Overlaid on top is the WMAP 94 GHz full sky map [93] in galactic coordinates. CAPMAP maps a 1◦ diameter cap centered on the NCP. Inset shows the zoomed WMAP region along with the WMAP 94 GHz beam and CAPMAP W-band beam scaled…

**Figure 3.1.** Figure 3.1: Schematic diagram of the CAPMAP correlation polarimeter [PITH_FULL_IMAGE:figures/full_fig_p059_3_1.png]

**Figure 3.2.** Figure 3.2: Photograph of the RF and LO sections of an actual W-band polarimeter. Detailed views with component names are shown in Figures 3.3 and 3.7, and [PITH_FULL_IMAGE:figures/full_fig_p060_3_2.png]

**Figure 3.3.** Figure 3.3: Scale 3D drawing of an RF section of a CAPMAP polarimeter. The RF section is shown in the same orientation as the receiver picture in [PITH_FULL_IMAGE:figures/full_fig_p060_3_3.png]

**Figure 3.4.** Figure 3.4: Photo of one half MMIC LNA housing. The input and output waveguides are visible. The small circuit in the lower center is the actual amplifier. The housing require a precision finish (Appendix B) to ensure a good seal of the two faces when the device is closed. The f…

**Figure 3.** Figure 3: shows a W-band MMIC LNA housed inside its metal body [PITH_FULL_IMAGE:figures/full_fig_p064_3.png]

**Figure 3.5.** Figure 3.5: (a) Typical gain and noise performance of the W-band MMIC amplifiers across the 84-100 GHz band. The typical band-averaged gain is 22 dB and the noise temperature 55 K. (b) Histogram of performance for the 26 devices delivered for CAPMAP03. The eight quietest device …

**Figure 3.6.** Figure 3.6: Noise temperature dependence on the drain current (left) and the physical temperature (right) for CAPMAP MMIC LNAs. 3.1.3 LO Section [PITH_FULL_IMAGE:figures/full_fig_p065_3_6.png]

**Figure 3.7.** Figure 3.7: 3D drawing of the LO section of receiver. The Local Oscillator is only present in one of the receivers (Section 3.1.3) The LO is a narrow-band high-power source at 82 GHz [PITH_FULL_IMAGE:figures/full_fig_p065_3_7.png]

**Figure 3.8.** Figure 3.8: Power amplifier gain curve. The output is linear until approximately 50 mW output power. The maximum output is 120 mW. Figure and tests by P. Hamlington. 100 mW, 82 GHz source alongside receivers sensitive to µW power levels at 84-100 GHz. Initially, each receiver in…

**Figure 3.9.** Figure 3.9: The input [PITH_FULL_IMAGE:figures/full_fig_p068_3_9.png]

**Figure 3.10.** Figure 3.10: One arm of a W-band receiver IF module. Individual components are described in the text. All connections to the preamp are SMA. Only a small part of the preamp card is visible here. The IF section of the radiometer provides the final amplification and filtering of t…

**Figure 3.11.** Figure 3.11: Intrinsic phase difference between the two arms of the multiplier itself. The phase shift can only be removed in small regions but not for the totality of the band. The red dashed lines show for example that the phase can be removed if the full IF bandpass is divide…

**Figure 3.12.** Figure 3.12: left: Cutaway view of the cryostat with the four W-band receivers. The only inaccuracy is the LO distribution system which does not represent the final configuration (described in Section 3.1.3). The 70 K radiation shield is not shown nor are the thermal or electric…

**Figure 3.13.** Figure 3.13: The CAPMAP vacuum window consists of a 0.65 mil polypropylene film on top of a 1/8” Gore-tex layer. The Gore-tex supports the atmospheric pressure while the polypropylene provides the vacuum barrier. Two O-rings on top of the polypropylene create a hermetic seal wit…

**Figure 3.14.** Figure 3.14: (a) Radiative Loading from cryostat window. Assuming the window is at 300 K, and emits in the whole spectrum as a blackbody, the thermal loading on the 70 K stage due to a single CAPMAP 6.26 cm radius window is 7.3 Watts. This provides an upper limit on the thermal …

**Figure 3.15.** Figure 3.15: Summary of different calibration techniques for the CAPMAP instrument [PITH_FULL_IMAGE:figures/full_fig_p081_3_15.png]

**Figure 3.16.** Figure 3.16: Receiver A phase measurements as function of frequency. The phase and response are typical of other receivers as well, although A has the smallest total bandwidth. Top: Raw data for determining the phase properties of the receiver, showing the in- (black) and out-of…

**Figure 3.17.** Figure 3.17: Chopper plate geometry on the telescope. The plate is rotated so as to redirect the beam towards zenith. For clarity, the telescope structure and chopper plate mounting are not shown. Although many calibration techniques were used during the integration and observat…

**Figure 3.18.** Figure 3.18: Receiver B polarization channel response during chopper plate calibration. The sinusoidal oscillation is a result of the chopper plate nutation. During the observing season, four separate chopper-plate data sets (labelled C331, C519a, C519b, C519c) were obtained ope…

**Figure 3.19.** Figure 3.19: Power spectral density of the same 5-hour stretch of data used to calculate the sensitivities in [PITH_FULL_IMAGE:figures/full_fig_p090_3_19.png]

**Figure 3.20.** Figure 3.20: Integration down plots for all twelve polarization channels from data taken on the sky. A one-second fake chop was applied to the data. The figure shows the RMS of the fake-chopped data averaged over different time periods. The RMS expectedly scales as the inverse o…

**Figure 4.1.** Figure 4.1: Picture of telescope showing the location of various elements. The azimuth encoder, azimuth bearing and cable wrap are located in the basement. The two trap doors in the right picture are to access the azimuth motors and the azimuth bull gear. The top trap door is on…

**Figure 4.2.** Figure 4.2: Side view scale drawing of the 7-meter telescope pointing at an elevation of 0◦ . All dimensions are in cm. A ray bundle is drawn from the Cassegrain focus to the secondary with an illumination half angle of 5.06◦ . The origin is at the vertex of the primary. The x-a…

**Figure 4.3.** Figure 4.3: Schematic cut through a gaussian beam showing the equiphase surfaces (dashed lines), beam radius, beam waist, and radius of curvature. circular hole in the focal plane, the choice of feed optics was restricted to a tertiary mirror or a lens attached to a feed horn. T…

**Figure 4.4.** Figure 4.4: Thin lens approximation of the optics. The tertiary mirror refocusses the beam from the Cassegrain focus to the feed horn. at the Cassegrain focus. In this design, the telescope mirrors are approximated as thin lenses as in [PITH_FULL_IMAGE:figures/full_fig_p100_4_4.png]

**Figure 4.5.** Figure 4.5: (a) Picture of the mirror in the CNC mill during fabrication. Note the mirror is mounted at an angle to prevent being cut with the tip of the ball mill. (b) Diagram showing the section of ellipse the tertiary is cut from, along with useful angles. All numbers are in …

**Figure 4.6.** Figure 4.6: Side view of mirror feed system in receiver cab. The room temperature dewar mounting structure is not shown. The vertical line is the left surface of the vertex cab dividing wall. Drawing is to scale. 4The idea for the machining algorithm comes from Simon Dicker, pos…

**Figure 4.7.** Figure 4.7: Az and El velocity request servo loop parameters. azdiff and elDiff are the difference between the commanded and current position in encoder bits (360◦ = 221 bits). AzDtoA and ElDtoA are the requested velocity to the telescope is bits (215 = +10V = 2.16◦ /s in azimut…

**Figure 5.1.** Figure 5.1: Time line of the 2003 observing season. The black blocks represent periods when the telescope was in CMB observing mode. The lines are scheduled observations of Jupiter (red), Taua (green), and sky dips (blue). 91 [PITH_FULL_IMAGE:figures/full_fig_p107_5_1.png]

**Figure 5.** Figure 5: ). The mount of the CAPMAP03 dewar comprises two le [PITH_FULL_IMAGE:figures/full_fig_p108_5.png]

**Figure 5.2.** Figure 5.2: Geometry of the dewar on the cal table. The dewar is facing the secondary. The yoke style mount on either side of the dewar is not yet outfitted with the extra stiffening angled-brackets. See [PITH_FULL_IMAGE:figures/full_fig_p109_5_2.png]

**Figure 5.3.** Figure 5.3: Reference surfaces and angles for dewar alignment. Dewar Alignment The dewar is aligned using first a crude mechanical method to place it in the right position with respect to the focal point, then more finely with a laser to verify the tilt. The goal of the alignmen…

**Figure 5.4.** Figure 5.4: Scan pattern for the actual (left) and ideal (right) pointing. Each plot is centered on NCP. The plots show 10 individual azimuth scans separated by 2.4 hours. The width of each scan is the beam size (0.06◦ ). By having the whole array mispointed with respect to NCP,…

**Figure 5.** Figure 5: (a) shows the azimuth scan pattern as a function of [PITH_FULL_IMAGE:figures/full_fig_p111_5.png]

**Figure 5.5.** Figure 5.5: (a) Initial (black) and nominal (red) azimuth scan pattern. The initial pattern scans a 0.59◦ sky radius region in 10 seconds but has an unexplained velocity glitch before the turn-around points. The scan period was changed to 8 seconds which also reduced the scan ra…

**Figure 5.6.** Figure 5.6: Cooldown temperatures of the 20 K (MMIC temp), 70 K (D shroud temp), and warm stage (LO and power amp temp) of the CAPMAP03 dewar using the 1020 compressor and 1020 cold head. The 70 K stage has not yet stabilized. The dewar is cooled down with metal covers on its wi…

**Figure 5.7.** Figure 5.7: Dewar pressure, and cryogenic and external temperature during the 2003 winter season. The labels indicate the position of the thermometers. The IF thermometer is placed directly on one of the IF amplifiers. There are 8 mirror thermometers placed around the back of th…

**Figure 5.8.** Figure 5.8: Instrument functional block diagram, showing the interconnection between the instrument electronics and receivers. Arrows indicate the direction of the signal. Where possible, the value of the typical bias voltages is indicated. All electronic boxes (ABOB, MMIC Bias …

**Figure 5.9.** Figure 5.9: Timing diagram of the various data acquisition events for a single data sample. The final data rate is approximately 100 Hz. The recorded encoder position comes from the point where the DAQ requests the encoder sample, 4.8 ms earlier than the time stamp of the data s…

**Figure 5.10.** Figure 5.10: Example of a phase shift between the digitization rate and the phase-switch clock. The plot shows a single 4 kHz clock period during which 24 data samples are acquired (black crosses). Had the digitization rate and the 4 kHZ clock been in phase, the first digitized …

**Figure 5.11.** Figure 5.11: (a) Correlation between the phase of the digitized clock signal and the phase of a modulated signal channel (AS0). Falling edge and rising edge (green) radiometer phase show the same behavior. All channels also behave similarly. The phase is defined as the distance …

**Figure 5.12.** Figure 5.12: Relative gain correction for AS0 for all CMB observation during 2003 season. Note that after Feb 27 (day 55), the clock phase is constant during a run and only changes when the readout code is restarted. The largest clock gain variation observed is 0.0025/hour. 5.2.…

**Figure 5.** Figure 5: ). Various schemes were considered, such as send [PITH_FULL_IMAGE:figures/full_fig_p120_5.png]

**Figure 5.13.** Figure 5.13: (a) Flow chart of the connections between the three computers which control the telescope (OBS), the data acquisition (DAQ) and the monitoring (MON). (b) Physical location of the different instrument parts at the telescope. The µcontroller runs in an infinite loop …

**Figure 5.14.** Figure 5.14: Micro-controller flow chart. The µcontroller waits for a strobe signal from the DAQ computer. The strobe signal is a 0.5 ms pulse sent from the DAQ at 100 Hz. When the strobe input goes high, the µcontroller latches the values on its 8 input digital ports (P0 throu…

**Figure 5.15.** Figure 5.15: (a) Az encoder readout vs time (ms). The sudden level shifts are artifacts of the µcontroller transient problems. (b) Diode protection circuit installed in series of each digital input. The diodes clamp the signal between 3.3 + 0.6 V and 0 − 0.6V. The 200 Ω resistor…

**Figure 5.** Figure 5: shows models [46] of the total emission temperat [PITH_FULL_IMAGE:figures/full_fig_p123_5.png]

**Figure 5.16.** Figure 5.16: Cumulative histogram of sky cloud coverage for the 2004 winter season [PITH_FULL_IMAGE:figures/full_fig_p124_5_16.png]

**Figure 5.17.** Figure 5.17: Atmospheric zenith emission temperature vs frequency for different values of PWV. Inset is a zoom on the three CAPMAP frequency bands. Note that although S0 is more affected by the wing of the 60 GHz O2 line than S1 and S2, the variation in PWV does not change the e…

**Figure 5.18.** Figure 5.18: (a) Time series of the total precipitable water vapor (PWV) during the winter 2004 observing season, rebinned in 10 days intervals. These data are derived from the hourly GOES satellite archives. The PWV is the average from a 100 by 100 km square centered on Crawfor…

**Figure 5.19.** Figure 5.19: South Pole, Atacama Chile, and Mauna Kea PWV quartiles. Figure from http://cfa-www.harvard.edu/ aas/tenmeter/pwv.htm [PITH_FULL_IMAGE:figures/full_fig_p126_5_19.png]

**Figure 6.** Figure 6: shows a typical scan, where a 0.8 [PITH_FULL_IMAGE:figures/full_fig_p128_6.png]

**Figure 6.1.** Figure 6.1: left: Telescope azimuth and elevation coordinates (solid line) for a typical Jupiter scan. Jupiter is setting and its position is plotted as the red dashed line. right: Same scan where the telescope azimuth and elevation are converted into co-moving coordinates (X0 a…

**Figure 6.** Figure 6: (b) for a blow up of this plot [PITH_FULL_IMAGE:figures/full_fig_p131_6.png]

**Figure 6.** Figure 6: (b) [PITH_FULL_IMAGE:figures/full_fig_p132_6.png]

**Figure 6.3.** Figure 6.3: (a) Fourier transforms of the raw time-series (black) and baseline (red) of a Jupiter observation. The structure corresponds to the periodic Jupiter signal. The baseline appears as a low-pass filtered version of the original data, with the signal at the scan frequenc…

**Figure 6.4.** Figure 6.4: left: Map and gaussian fit of AD0 total-power channel for a single Jupiter observation. The contour levels are in receiver temperature. The fit contour levels are at -20 dB, -10 dB, and -3 dB from the peak level. This map is made from a 6 minute-long observation. Thi…

**Figure 6.5.** Figure 6.5: Map and fit of DS2 polarization-channel response to a single Jupiter observation. The contour levels are in mK receiver temperature evenly spaced from peak to peak. This quadrupolar feature is the cross-polar pickup of the polarization channel, caused by the lens ant…

**Figure 6.6.** Figure 6.6: Real and simulated time-series of a Jupiter observation as a function of time (in ms). The fake time stream is generated from a noiseless Jupiter signal plus a realization of 1/f noise whose power spectra (slope and level), are tuned to match the average properties o…

**Figure 6.7.** Figure 6.7: Flow Chart of the source observations analysis (left) and the error simulation analysis (right) [PITH_FULL_IMAGE:figures/full_fig_p137_6_7.png]

**Figure 6.8.** Figure 6.8: Beam widths for the 15 processed Jupiter observations of the 2003 season. Each plot has channel D0 in black and D1 in red (gray) for either receivers A, B, C, and D. The horizontal and vertical lines are the weighted means. The large square in the upper right of the …

**Figure 6.9.** Figure 6.9: (a) Amplitude of the dipole versus the amplitude of the quadrupole in the fit to the polarized response to Jupiter. Not only are the two components highly correlated, but also, the amplitudes for the half-grooved lenses (A and D in yellow) are consistently smaller th…

**Figure 6.10.** Figure 6.10: Right-going(red) and left-going(black) scan of Jupiter superimposed vs co-moving azimuth X0 in degrees. The two profiles are shifted by 0.02◦ . This cannot be a real effect as Jupiter must be in one place. It is caused by a shift of the encoder relative to the data …

**Figure 6.11.** Figure 6.11: Deep beam map on receiver A using Jupiter as the source. The top and center plots are the beam maps in linear and dB scale. The bottom plot shows the integration time per bin. No sidelobes are visible down to the noise level of the map, at ∼25 dB below the peak. On …

**Figure 6.12.** Figure 6.12: Refraction in the Earth’s atmosphere bends a light ray towards vertical. Thus, the “apparent elevation” at which a star is observed, α ′ , is always greater than the “true elevation”, α, in the absence of atmosphere. As a guidance, the refraction corrections for a s…

**Figure 6.13.** Figure 6.13: Positions in an az-el map of the sources observed. In black, the 60 star pointing measurements, in red the 15 analyzed Jupiter observations, in blue the 20 Cas A observations, of which only the green ones were detected. No source can be observed below an elevation o…

**Figure 6.** Figure 6: ), using a small optical camera meant to be aligne [PITH_FULL_IMAGE:figures/full_fig_p147_6.png]

**Figure 6.14.** Figure 6.14: (a) ∆Az pointing deltas for the 60 stars observed vs Az and El, along with the best fit pointing solutions. The projections on the Az and El planes are shown in (b) and (c). (d)∆El pointing errors for the 60 stars observed vs Az and El, with the best fit model. Proj…

**Figure 6.15.** Figure 6.15: Measured tilt of the alt-az mount of the telescope. top: Angle of the axis parallel to the secondary arm and best fit −4.8 + 12.5 cos(261 − az) (in millidegrees). bottom: Angle of axis parallel to the elevation axis and best fit 178 + 12.0 cos(351 − az). As expected…

**Figure 6.16.** Figure 6.16: Illustration of the telescope azimuth-axis tilt. The primed coordinate system is rotated counter-clockwise through an angle φ around the X1 axis (the level axis). For a counter-clockwise rotation, the azimuth of the level axis is κ, measured eastward from North, and…

**Figure 6.17.** Figure 6.17: left: Relative position of each of the four beams in the array with respect to the central ray and NCP during the azimuth scans. The underlying grid spacing is 0.1◦ . The ideal configuration would have the NCP at the center of the array but the inadvertent misplacem…

**Figure 6.18.** Figure 6.18: Mosaic of the measured beams. Different noise levels in each receiver map lead to apparent artefacts away from the beam centers. Receiver C which is notably noisy has been binned with three times the bin size, leading to the apparently smaller beam size. Only 6 min …

**Figure 6.19.** Figure 6.19: Atmospheric attenuation for the eight TP channels during the 15 Jupiter observations. As expected, the attenuations for the eight TP channels are identical. The attenuations are plotted at the zenith angle of the observation (from 20◦ to 70◦ elevation), so the zenit…

**Figure 6.20.** Figure 6.20: Published values of the average polarized fraction of Tau A as a function of frequency. The sources in increasing frequency order are [63, 64, 105, 17, 45, 104, 149, 74, 76, 103]. We adopt the mean of all the values, 7.5 ± 1%, for the polarized fraction at 90 GHz as…

**Figure 6.21.** Figure 6.21: Measurement of the polarized signal from Tau A (in counts) as a function of parallactic angle and the best fit curve. The fit model is I + m 2 cos((p − φsource)/2), with the best parameters labeled on the plot. This measurement was made using the PIQUE receiver [56]…

**Figure 7.1.** Figure 7.1: Example map produced with the Healpix pixelisation (Nside = 1024) using ∼450 hours of all the data with receiver B, when it is located west of the NCP. Note that this corresponds approximately to 1/8 of the full CAPMAP03 data set. Gnomic view centered on the NCP in e…

**Figure 7.2.** Figure 7.2: Once the offset, [PITH_FULL_IMAGE:figures/full_fig_p163_7_2.png]

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