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A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images., Comment: 17 pages, 6 figures, 1 table; corrections to Appendix A

The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array observing the Cosmic Microwave Background (CMB) at frequency bands centered near 40, 90, 150, and 220 GHz. CLASS measures the CMB polarization on the largest angular scales to constrain the inflationary tensor-to-scalar ratio and the optical depth due to reionization. To achieve the long time-scale stability necessary for this measurement from the ground, CLASS utilizes a front-end, variable-delay polarization modulator on each telescope. Here we report on the improvements in stability afforded by front-end modulation using data across all four CLASS frequencies. Across one month of modulated linear polarization data in 2021, CLASS achieved median knee frequencies of 9.1, 29.1, 20.4, and 36.4 mHz for the 40, 90, 150, and 220 GHz observing bands. The knee frequencies are approximately an order of magnitude lower than achieved via CLASS pair-differencing orthogonal detector pairs without modulation., Comment: Submitted to SPIE Astronomical Telescopes + Instrumentation 2022 Conference (AS22)

The Cosmology Large Angular Scale Surveyor (CLASS) is a polarization-sensitive telescope array located at an altitude of 5,200 m in the Chilean Atacama Desert. CLASS is designed to measure "E-mode" (even parity) and "B-mode" (odd parity) polarization patterns in the Cosmic Microwave Background (CMB) over large angular scales with the aim of improving our understanding of inflation, reionization, and dark matter. CLASS is currently observing with three telescopes covering four frequency bands: one at 40 GHz (Q); one at 90 GHz (W1); and one dichroic system at 150/220 GHz (G). In these proceedings, we discuss the updated design and in-lab characterization of new 90 GHz detectors. The new detectors include design changes to the transition-edge sensor (TES) bolometer architecture, which aim to improve stability and optical efficiency. We assembled and tested four new detector wafers, to replace four modules of the W1 focal plane. These detectors were installed into the W1 telescope, and will achieve first light in the austral winter of 2022. We present electrothermal parameters and bandpass measurements from in-lab dark and optical testing. From in-lab dark tests, we also measure a median NEP of 12.3 $\mathrm{aW\sqrt{s}}$ across all four wafers about the CLASS signal band, which is below the expected photon NEP of 32 $\mathrm{aW\sqrt{s}}$ from the field. We therefore expect the new detectors to be photon noise limited., 10 pages, 6 figures, to appear in Proc. SPIE Astronomical Telescopes and Instrumentation 2022

The BICEP3 Polarimeter is a small aperture, refracting telescope, dedicated to the observation of the Cosmic Microwave Background (CMB) at 95GHz. It is designed to target degree angular scale polarization patterns, in particular the very-much-sought-after primordial B-mode signal, which is a unique signature of cosmic inflation. The polarized signal from the sky is reconstructed by differencing co-localized, orthogonally polarized superconducting Transition Edge Sensor (TES) bolometers. In this work, we present absolute measurements of the polarization response of the detectors for more than $\sim 800$ functioning detector pairs of the BICEP3 experiment, out of a total of $\sim 1000$. We use a specifically designed Rotating Polarized Source (RPS) to measure the polarization response at multiple source and telescope boresight rotation angles, to fully map the response over 360 degrees. We present here polarization properties extracted from on-site calibration data taken in January 2022. A similar calibration campaign was performed in 2018, but we found that our constraint was dominated by systematics on the level of $\sim0.5^\circ$. After a number of improvements to the calibration set-up, we are now able to report a significantly lower level of systematic contamination. In the future, such precise measurements will be used to constrain physics beyond the standard cosmological model, namely cosmic birefringence., Submitted to: SPIE Astronomical Telescopes + Instrumentation (AS22)

We report on the development of a polarization-sensitive dichroic (150/220 GHz) detector array for the Cosmology Large Angular Scale Surveyor (CLASS) delivered to the telescope site in June 2019. In concert with existing 40 and 90 GHz telescopes, the 150/220 GHz telescope will make observations of the cosmic microwave background over large angular scales aimed at measuring the primordial B-mode signal, the optical depth to reionization, and other fundamental physics and cosmology. The 150/220 GHz focal plane array consists of three detector modules with 1020 transition edge sensor (TES) bolometers in total. Each dual-polarization pixel on the focal plane contains four bolometers to measure the two linear polarization states at 150 and 220 GHz. Light is coupled through a planar orthomode transducer (OMT) fed by a smooth-walled feedhorn array made from an aluminum-silicon alloy (CE7). In this work, we discuss the design, assembly, and in-lab characterization of the 150/220 GHz detector array. The detectors are photon-noise limited, and we estimate the total array noise-equivalent power (NEP) to be 2.5 and 4 aW$\sqrt{\mathrm{s}}$ for 150 and 220 GHz arrays, respectively., Comment: 8 pages, 5 figures, Published in J Low Temp Phys

Using the Cosmology Large Angular Scale Surveyor, we measure the disk-averaged absolute Venus brightness temperature to be 432.3 $\pm$ 2.8 K and 355.6 $\pm$ 1.3 K in the Q and W frequency bands centered at 38.8 and 93.7 GHz, respectively. At both frequency bands, these are the most precise measurements to date. Furthermore, we observe no phase dependence of the measured temperature in either band. Our measurements are consistent with a CO$_2$-dominant atmospheric model that includes trace amounts of additional absorbers like SO$_2$ and H$_2$SO$_4$., Comment: 7 pages, 3 figures, published in PSJ

In order to extract cosmological information from observations of the millimeter and submillimeter sky, foreground components must first be removed to produce an estimate of the cosmic microwave background (CMB). We developed a machine-learning approach for doing so for full-sky temperature maps of the millimeter and submillimeter sky. We constructed a Bayesian spherical convolutional neural network architecture to produce a model that captures both spectral and morphological aspects of the foregrounds. Additionally, the model outputs a per-pixel error estimate that incorporates both statistical and model uncertainties. The model was then trained using simulations that incorporated knowledge of these foreground components that was available at the time of the launch of the Planck satellite. On simulated maps, the CMB is recovered with a mean absolute difference of $50��$K; the angular power spectrum is also accurately recovered. Once validated with the simulations, this model was applied to Planck temperature observations from its 70GHz through 857GHz channels to produce a foreground-cleaned CMB map at a Healpix map resolution of NSIDE=512. Furthermore, we demonstrate the utility of the technique for evaluating how well different simulations match observations, particularly in regard to the modeling of thermal dust., 10 pages, 6 figures, submitted to ApJ

The Earth's magnetic field induces Zeeman splitting of the magnetic dipole transitions of molecular oxygen in the atmosphere, which produces polarized emission in the millimeter-wave regime. This polarized emission is primarily circularly polarized and manifests as a foreground with a dipole-shaped sky pattern for polarization-sensitive ground-based cosmic microwave background experiments, such as the Cosmology Large Angular Scale Surveyor (CLASS), which is capable of measuring large angular scale circular polarization. Using atmospheric emission theory and radiative transfer formalisms, we model the expected amplitude and spatial distribution of this signal and evaluate the model for the CLASS observing site in the Atacama Desert of northern Chile. Then, using two years of observations at 32.3 GHz to 43.7 GHz from the CLASS Q-band telescope, we present a detection of this signal and compare the observed signal to that predicted by the model. We recover an angle between magnetic north and true north of $(-5.5 \pm 0.6)^\circ$, which is consistent with the expectation of $-5.9^\circ$ for the CLASS observing site. When comparing dipole sky patterns fit to both simulated and data-derived sky maps, the dipole directions match to within a degree, and the measured amplitudes match to within ${\sim}20\%$., Comment: 13 pages, 7 figures, published in ApJ

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 ($1^\circ\lesssim��\leqslant 90^\circ$) CMB polarization to constrain the tensor-to-scalar ratio at the $r\sim0.01$ level and the optical depth to last scattering to the sample variance limit. This paper presents the optical characterization of the 40 GHz telescope during its first observation era, from 2016 September to 2018 February. High signal-to-noise observations of the Moon establish the pointing and beam calibration. The telescope boresight pointing variation is $, 32 pages, 24 figures, published in ApJ

We present the design, manufacturing technique, and characterization of a 3D-printed broadband graded index millimeter wave absorber. The absorber is additively manufactured using a fused filament fabrication (FFF) 3D printer out of a carbon-loaded high impact polystyrene (HIPS) filament and is designed using a space-filling curve to optimize manufacturability using said process. The absorber's reflectivity is measured from 63 GHz to 115 GHz and from 140 GHz to 215 GHz and is compared to electromagnetic simulations. The intended application is for terminating stray light in Cosmic Microwave Background (CMB) telescopes, and the absorber has been shown to survive cryogenic thermal cycling., 6 pages, 6 figures, 2 tables, accepted to Review of Scientific Instruments

The Cosmology Large Angular Scale Surveyor consists of four instruments performing a CMB polarization survey. Currently, the 40 GHz and first 90 GHz instruments are deployed and observing, with the second 90 GHz and a multichroic 150/220 GHz instrument to follow. The receiver is a central component of each instrument's design and functionality. This paper describes the CLASS receiver design, using the first 90 GHz receiver as a primary reference. Cryogenic cooling and filters maintain a cold, low-noise environment for the detectors. We have achieved receiver detector temperatures below 50 mK in the 40 GHz instrument for 85% of the initial 1.5 years of operation, and observed in-band efficiency that is consistent with pre-deployment estimates. At 90 GHz, less than 26% of in-band power is lost to the filters and lenses in the receiver, allowing for high optical efficiency. We discuss the mounting scheme for the filters and lenses, the alignment of the cold optics and detectors, stray light control, and magnetic shielding., Fixed formatting of abstract; 20 Pages, 11 Figures, SPIE Conference Proceedings

The search for inflationary primordial gravitational waves and the measurement of the optical depth to reionization, both through their imprint on the large angular scale correlations in the polarization of the cosmic microwave background (CMB), has created the need for high sensitivity measurements of polarization across large fractions of the sky at millimeter wavelengths. These measurements are subject to instrumental and atmospheric 1=f noise, which has motivated the development of polarization modulators to facilitate the rejection of these large systematic effects. Variable-delay polarization modulators (VPMs) are used in the Cosmology Large Angular Scale Surveyor (CLASS) telescopes as the first element in the optical chain to rapidly modulate the incoming polarization. VPMs consist of a linearly polarizing wire grid in front of a movable flat mirror. Varying the distance between the grid and the mirror produces a changing phase shift between polarization states parallel and perpendicular to the grid which modulates Stokes U (linear polarization at 45°) and Stokes V (circular polarization). The CLASS telescopes have VPMs as the first optical element from the sky; this simultaneously allows a lock-in style polarization measurement and the separation of sky polarization from any instrumental polarization further along in the optical path. The CLASS VPM wire grids use 50 μm copper-plated tungsten wire with a 160μm spacing across a 60 cm clear aperture. The mirror is mounted on a flexure system with one degree of translational freedom, enabling the required mirror motion while maintaining excellent parallelism with respect to the wire grid. The wire grids and mirrors are held parallel to each other to better than 80 μm, and the wire grids have RMS flatness errors below 50 μm across the 60 cm aperture. The Q-band CLASS VPM was the first VPM to begin observing the CMB full time, starting in the Spring of 2016. The first W-band CLASS VPM was installed in the Spring of 2018.

We analyze simulated maps of the Cosmology Large Angular Scale Surveyor (CLASS) experiment and recover a nearly cosmic-variance limited estimate of the reionization optical depth $\tau$. We use a power spectrum-based likelihood to simultaneously clean foregrounds and estimate cosmological parameters in multipole space. Using software specifically designed to constrain $\tau$, the amplitude of scalar fluctuations $A_s$, and the tensor-to-scalar ratio $r$, we demonstrate that the CLASS experiment will be able to estimate $\tau$ within a factor of two of the full-sky cosmic variance limit allowed by cosmic microwave background polarization measurements. Additionally, we discuss the role of CLASS's $\tau$ constraint in conjunction with gravitational lensing of the CMB on obtaining a $\gtrsim4\sigma$ measurement of the sum of the neutrino masses., Comment: Accepted for publication by ApJ

The Cosmology Large Angular Scale Surveyor (CLASS) aims to detect and characterize the primordial B-mode signal and make a sample-variance-limited measurement of the optical depth to reionization. CLASS is a ground-based, multi-frequency microwave polarimeter that surveys 70% of the microwave sky every day from the Atacama Desert. The focal plane detector arrays of all CLASS telescopes contain smooth-walled feedhorns that couple to transition-edge sensor (TES) bolometers through symmetric planar orthomode transducer (OMT) antennas. These low noise polarization-sensitive detector arrays are fabricated on mono-crystalline silicon wafers to maintain TES uniformity and optimize optical efficiency throughout the wafer. In this paper, we discuss the design and characterization of the first CLASS 93 GHz detector array. We measure the dark parameters, bandpass, and noise spectra of the detectors and report that the detectors are photon-noise limited. With current array yield of 82%, we estimate the total array noise-equivalent power (NEP) to be 2.1 aW$\sqrt[]{\mathrm{s}}$., Comment: 16 pages, 9 figures

The Cosmology Large Angular Scale Surveyor (CLASS) will measure the polarization of the Cosmic Microwave Background to search for and characterize the polarized signature of inflation. CLASS will operate from the Atacama Desert and observe $\sim$70% of the sky. A variable-delay polarization modulator (VPM) modulates the polarization at $\sim$10 Hz to suppress the 1/f noise of the atmosphere and enable the measurement of the large angular scale polarization modes. The measurement of the inflationary signal across angular scales that span both the recombination and reionization features allows a test of the predicted shape of the polarized angular power spectra in addition to a measurement of the energy scale of inflation. CLASS is an array of telescopes covering frequencies of 38, 93, 148, and 217 GHz. These frequencies straddle the foreground minimum and thus allow the extraction of foregrounds from the primordial signal. Each focal plane contains feedhorn-coupled transition-edge sensors that simultaneously detect two orthogonal linear polarizations. The use of single-crystal silicon as the dielectric for the on-chip transmission lines enables both high efficiency and uniformity in fabrication. Integrated band definition has been implemented that both controls the bandpass of the single mode transmission on the chip and prevents stray light from coupling to the detectors., Comment: 7 pages, 5 figures, accepted by the Journal of Low Temperature Physics

The Cosmology Large Angular Scale Surveyor (CLASS) is mapping the polarization of the Cosmic Microwave Background (CMB) at large angular scales ($2, Comment: 11 pages, 5 figures

The Cosmology Large Angular Scale Surveyor (CLASS) is a four telescope array designed to characterize relic primordial gravitational waves from inflation and the optical depth to reionization through a measurement of the polarized cosmic microwave background (CMB) on the largest angular scales. The frequencies of the four CLASS telescopes, one at 38 GHz, two at 93 GHz, and one dichroic system at 145/217 GHz, are chosen to avoid spectral regions of high atmospheric emission and span the minimum of the polarized Galactic foregrounds: synchrotron emission at lower frequencies and dust emission at higher frequencies. Low-noise transition edge sensor detectors and a rapid front-end polarization modulator provide a unique combination of high sensitivity, stability, and control of systematics. The CLASS site, at 5200 m in the Chilean Atacama desert, allows for daily mapping of up to 70\% of the sky and enables the characterization of CMB polarization at the largest angular scales. Using this combination of a broad frequency range, large sky coverage, control over systematics, and high sensitivity, CLASS will observe the reionization and recombination peaks of the CMB E- and B-mode power spectra. CLASS will make a cosmic variance limited measurement of the optical depth to reionization and will measure or place upper limits on the tensor-to-scalar ratio, $r$, down to a level of 0.01 (95\% C.L.).

Observations of the Cosmic Microwave Background rely on cryogenic instrumentation with cold detectors, readout, and optics providing the low noise performance and instrumental stability required to make more sensitive measurements. It is therefore critical to optimize all aspects of the cryogenic design to achieve the necessary performance, with low temperature components and acceptable system cooling requirements. In particular, we will focus on our use of thermal filters and cold optics, which reduce the thermal load passed along to the cryogenic stages. To test their performance, we have made a series of in situ measurements while integrating the third receiver for the BICEP Array telescope. In addition to characterizing the behavior of this receiver, these measurements continue to refine the models that are being used to inform design choices being made for future instruments., Comment: 9 pages, 8 figures, Proceedings of SPIE 2022