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Abstract We present measurements of large-scale cosmic microwave backgroundE-mode polarization from the Cosmology Large Angular Scale Surveyor 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of $82\mu \mathrm{K}\mathrm{arcmin}$, comparable to Planck at similar frequencies (100 and 143 GHz ). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making nonlinearity, being characterized as <3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth $\tau =0.053_{-0.019}^{+0.018}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ > 30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements. 

Front-end polarization modulation enables improved polarization measurement stability by modulating the targeted signal above the low-frequency $1/f$ drifts associated with atmospheric and instrumental instabilities and diminishes the impact of instrumental polarization. In this work, we present the design and characterization of a new 60-cm diameter Reflective Half-Wave Plate (RHWP) polarization modulator for the 90 GHz band telescope of the Cosmology Large Angular Scale Surveyor (CLASS) project. The RHWP consists of an array of parallel wires (diameter 50~µm, 175~µm pitch) positioned 0.88~mm from an aluminum mirror. In lab tests, it was confirmed that the wire resonance frequency ($$f_\mathrm{res}$$) profile is consistent with the target, $139$~Hz$$<154$$~Hz in the optically active region (diameter smaller than 150~mm), preventing the wire vibration during operation and reducing the RHWP deformation under the wire tension. The mirror tilt relative to the rotating axis was controlled to be $<15''$, corresponding to an increase in beam width due to beam smearing of < $0.6''$, %a beam smearing amplitude of $<0.6''$, negligible compared to the beam's full-width half-maximum of $36'$. The median and 16/84th percentile of the wire--mirror separation residual was $$0.048^{+0.013}_{-0.014}$$~mm in the optically active region, achieving a modulation efficiency $$\epsilon=96.2_{+0.5}^{-0.4}\%$$ with an estimated bandpass of 34~GHz. The angular velocity of the RHWP was maintained to an accuracy of within 0.005\% at the nominal rotation frequency (2.5~Hz). The RHWP has been successfully integrated into the CLASS 90 GHz telescope and started taking data in June 2024, replacing the previous modulator that has been in operation since June 2018. 

Abstract The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background (CMB) over ∼75% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. CLASS measures the large angular scale CMB polarization to constrain the tensor-to-scalar ratio and the optical depth to last scattering. This paper presents the optical characterization of the 90 GHz telescope. Observations of the Moon establish the pointing while dedicated observations of Jupiter are used for beam calibration. The standard deviations of the pointing error in azimuth, elevation, and boresight angle are 1.′3, 2.′1, and 2.′0, respectively, over the first 3 yr of observations. This corresponds to a pointing uncertainty ∼7% of the beam’s full width at half-maximum (FWHM). The effective azimuthally symmetrized instrument 1D beam estimated at 90 GHz has an FWHM of 0.°620 ± 0.°003 and a solid angle of 138.7 ± 0.6(stats.) ± 1.1(sys.)μsr integrated to a radius of 4°. The corresponding beam window function drops to $b_{\mathit{\ell }}^2=0.93,0.71,0.14$atℓ= 30, 100, 300, respectively. Far-sidelobes are studied using detector-centered intensity maps of the Moon and measured to be at a level of 10⁻³or below relative to the peak. The polarization angle of Tau A estimated from preliminary survey maps is 149°.6 ± 0°.2(stats.) in equatorial coordinates. The instrumental temperature-to-polarization (T→P) leakage fraction, inferred from per-detector demodulated Jupiter scan data, has a monopole component at the level of 1.7 × 10⁻³, a dipole component with an amplitude of 4.3 × 10⁻³, with no evidence of quadrupolar leakage. 

Polarization modulation is a powerful technique to increase the stability of measurements by enabling the distinction of a polarized signal from dominant slow system drifts and unpolarized foregrounds. Furthermore, when placed as close to the sky as possible, modulation can reduce systematic errors from instrument polarization. In this work, we introduce the design and preliminary drive system laboratory performance of a new 60 cm diameter reflective half-wave plate (RHWP) polarization modulator. The wave plate consists of a wire array situated in front of a flat mirror. Using 50 μm diameter wires with 175 μm spacing, the wave plate will be suitable for operation in the millimeter wavelength range with flatness of the wires and parallelism to the mirror held to a small fraction of a wavelength. The presented design targets the 77-108 GHz range. Modulation is performed by a rotation of the wave plate with a custom rotary drive utilizing an actively controlled servo motor. 

Abstract Measurement of the largest angular scale (ℓ< 30) features of the cosmic microwave background (CMB) polarization is a powerful way to constrain the optical depth to reionization and search for the signature of inflation through the detection of primordialB-modes. We present an analysis of maps covering 73.6% of the sky made from the 40 GHz channel of the Cosmology Large Angular Scale Surveyor (CLASS) from 2016 August to 2022 May. Taking advantage of the measurement stability enabled by front-end polarization modulation and excellent conditions from the Atacama Desert, we show this channel achieves higher sensitivity than the analogous frequencies from satellite measurements in the range 10 <ℓ< 100. Simulations show the CLASS linear (circular) polarization maps have a white noise level of $125\left(130\right)\mu \mathrm{K}\mathrm{arcmin}$. We measure the Galaxy-maskedEEandBBspectra of diffuse synchrotron radiation and compare to space-based measurements at similar frequencies. In combination with external data, we expand measurements of the spatial variations of the synchrotron spectral energy density (SED) to include new sky regions and measure the diffuse SED in the harmonic domain. We place a new upper limit on a background of circular polarization in the range 5 <ℓ< 125 with the first bin showingD_ℓ< 0.023 $\mu {\mathrm{K}}_{\mathrm{CMB}}^2$at 95% confidence. These results establish a new standard for recovery of the largest-scale CMB polarization from the ground and signal exciting possibilities when the higher sensitivity and higher-frequency CLASS channels are included in the analysis. 

Abstract The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background over 75% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. This paper describes the CLASS data pipeline and maps for 40 GHz observations conducted from 2016 August to 2022 May. We demonstrate how well the CLASS survey strategy, with rapid (∼10 Hz) front-end modulation, recovers the large-scale Galactic polarization signal from the ground: the mapping transfer function recovers ∼67% (85%) ofEEandBB(VV) power atℓ= 20 and ∼35% (47%) atℓ= 10. We present linear and circular polarization maps over 75% of the sky. Simulations based on the data imply the maps have a white noise level of $110\mu \mathrm{K}\mathrm{arcmin}$and correlated noise component rising at low-ℓasℓ^−2.4. The transfer-function-corrected low-ℓcomponent is comparable to the white noise at the angular knee frequencies ofℓ≈ 18 (linear polarization) andℓ≈ 12 (circular polarization). Finally, we present simulations of the level at which expected sources of systematic error bias the measurements, finding subpercent bias for the Λ cold dark matterEEpower spectra. Bias fromE-to-Bleakage due to the data reduction pipeline and polarization angle uncertainty approaches the expected level for anr= 0.01BBpower spectrum. Improvements to the instrument calibration and the data pipeline will decrease this bias. 

Abstract The Cosmology Large Angular Scale Surveyor (CLASS) is a four-telescope array observing the largest angular scales (2≲ ℓ ≲ 200) of the cosmic microwave background (CMB) polarization. These scales encode information about reionization and inflation during the early universe. The instrument stability necessary to observe these angular scales from the ground is achieved through the use of a variable-delay polarization modulator as the first optical element in each of the CLASS telescopes. Here, we develop a demodulation scheme used to extract the polarization timestreams from the CLASS data and apply this method to selected data from the first 2 yr of observations by the 40 GHz CLASS telescope. These timestreams are used to measure the 1/ f noise and temperature-to-polarization ( T → P ) leakage present in the CLASS data. We find a median knee frequency for the pair-differenced demodulated linear polarization of 15.12 mHz and a T → P leakage of <3.8 × 10 −4 (95% confidence) across the focal plane. We examine the sources of 1/ f noise present in the data and find the component of 1/ f due to atmospheric precipitable water vapor (PWV) has an amplitude of 203 ± 12 μ K RJ s for 1 mm of PWV when evaluated at 10 mHz; accounting for ∼17% of the 1/ f noise in the central pixels of the focal plane. The low levels of T → P leakage and 1/ f noise achieved through the use of a front-end polarization modulator are requirements for observing of the largest angular scales of the CMB polarization by the CLASS telescopes. 

Abstract The Cosmology Large Angular Scale Surveyor (CLASS) observes the polarized cosmic microwave background (CMB) over the angular scales of 1° ≲θ≤ 90° with the aim of characterizing primordial gravitational waves and cosmic reionization. We report on the on-sky performance of the CLASSQ-band (40 GHz),W-band (90 GHz), and dichroicG-band (150/220 GHz) receivers that have been operational at the CLASS site in the Atacama desert since 2016 June, 2018 May, and 2019 September, respectively. We show that the noise-equivalent power measured by the detectors matches the expected noise model based on on-sky optical loading and lab-measured detector parameters. Using Moon, Venus, and Jupiter observations, we obtain power to antenna temperature calibrations and optical efficiencies for the telescopes. From the CMB survey data, we compute instantaneous array noise-equivalent-temperature sensitivities of 22, 19, 23, and 71 $\mu {\mathrm{K}}_{\mathrm{cmb}}\sqrt{\mathrm{s}}$for the 40, 90, 150, and 220 GHz frequency bands, respectively. These noise temperatures refer to white noise amplitudes, which contribute to sky maps at all angular scales. Future papers will assess additional noise sources impacting larger angular scales.