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CMB-S4 – the next-generation ground-based cosmic microwave background (CMB) experiment - will significantly advance the sensitivity of CMB measurements and improve our understanding of the origin and evolution of the universe. CMB-S4 will deploy large-aperture telescopes fielding hundreds of thousands of detectors at millimeter wavelengths. We present the baseline optical design concept of the large-aperture CMB-S4 telescopes, which consists of two optical configurations: (i) a new off-axis, three-mirror, free-form anastigmatic design and (ii) the existing coma-corrected crossed-Dragone design. We also present an overview of the optical configuration of the array of silicon optics cameras that will populate the focal plane with 85 diffraction-limited optics tubes covering up to 9 degrees of field of view, up to 1.1 mm in wavelength. We describe the computational optimization methods that were put in place to implement the families of designs described here and give a brief update on the current status of the design effort.
This paper presents recent results of ongoing European Space Agency funded program of work aimed at developing large dielectric lenses suitable for future satellite missions, with a particular focus on requirements for CMB polarimetry. Two lens solutions are being investigated: (i) polymer lenses with broadband multi-layer antireflection coatings; (ii) silicon lenses with surface-structured anti-reflection coating represented by directly machined pyramidal features. For each solution, base materials with and without coatings have been optically characterized over a range of temperatures down to ~10 K. Full lens solutions are under manufacture and will be tested in a bespoke large cryo-optical facility.
In this paper we discuss the modeling, development and testing of the optical bread-board models of the Medium and High Frequency Telescope (MHFT) onboard the LiteBIRD satellite. The future JAXA mission LiteBIRD will search for the signature of primordial gravitational waves through the measurement of the “B-modes” of the cosmic microwave background polarization. MHFT will observe the polarized microwave sky between 89 and 448 GHz by means of two refractive telescopes. The accurate knowledge of their optical properties is fundamental to assess the impact of systematic effects (e.g. beam deformation, side lobes and intensity to polarization leakage) on the future observations. To gain early experience with our test approach, and to provide hints of possible criticalities in the design and characterization of a MHFT-like refractive system, we developed two optical bread-board models. The BB1, a single dielectric lens coupled to a fully characterized W-band corrugated horn, allows us to assess the accuracy and potential limitations of different measurement methods and to verify the reliability of optical simulators in predicting refractive elements and systems, as compared to the precision required by LiteBIRD. The BB2, a 1⁄2-scaled version of the Medium Frequency Telescope, focuses on the modelling and issues of dual-lens coupling, while providing a test-bed to finalize the MHFT optical calibration plan for its higher levels of integration.
Microwave telescopes require an ever-increasing control of experimental systematics in their quest to measure the Cosmic Microwave Background (CMB) to exquisite levels of precision. One important systematic for ground and balloon-borne experiments is ground pickup, where beam sidelobes detect the thermal emission of the much warmer ground while the main beam is scanning the sky. This generates scan-synchronous noise in experiment timestreams, which is difficult to filter out without also deleting some of the signal from the sky. Therefore, efficient modelling of pickup can help guide the design of experiments and of analysis pipelines. In this work, we present an extension to the BEAMCONV algorithm that enables us to generate time-ordered data (TOD) from beam-convolved sky and ground maps simultaneously. We simulate ground pickup for both a ground-based experiment and a telescope attached to a stratospheric balloon. Ground templates for the balloon experiment are obtained by re-projecting satellite maps of the Earth’s microwave emission.
LiteBIRD is the next-generation space mission for polarization-sensitive mapping of the Cosmic Microwave Background anisotropies, with observations covering the full sky in a wide frequency range (34-448 GHz) to ensure high-precision removal of polarized foregrounds. Its main goal is to constrain the contribution of primordial gravitational waves to the curly component of the CMB polarization pattern. The LiteBIRD Medium and High Frequency Telescope (MHFT) will observe the sky in the 89-448 GHz band. Its optical configuration features two separate dual-lens assemblies with 300mm and 200mm apertures, 28° fields of view and diffraction-limited imaging over the whole spectral range. Polarization modulation is achieved through the continuous spinning of a half-wave plate at the optical entrance of each system. The optical studies for MHFT focus on a refined modeling of the telescope elements (lenses, anti-reflection coatings, absorbers, interfaces) to assess their individual effects on the predicted optical behavior of the telescopes. Such studies will provide key inputs for end-to-end simulations and will inform the subsystem and system-level characterization to meet the stringent requirements set for the LiteBIRD success. We describe the progress in MHFT optical modeling and the ongoing efforts to reproduce full Medium Frequency Telescope (MFT) and High Frequency Telescope (HFT) beams for representative focal plane pixels down to the far-sidelobe angular region. Here, systematic effects due to challenging beam measurements and higher order optical coupling between the telescope and the surrounding structures are likely to affect the final level and shape of the beams and thus set compelling requirements for in-flight calibration and beam reconstruction.
LiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection, is a space mission for primordial cosmology and fundamental physics. JAXA selected LiteBIRD in May 2019 as a strategic large-class (L-class) mission, with its expected launch in the late 2020s using JAXA's H3 rocket. LiteBIRD plans to map the cosmic microwave background (CMB) polarization over the full sky with unprecedented precision. Its main scientific objective is to carry out a definitive search for the signal from cosmic inflation, either making a discovery or ruling out well-motivated inflationary models. The measurements of LiteBIRD will also provide us with an insight into the quantum nature of gravity and other new physics beyond the standard models of particle physics and cosmology. To this end, LiteBIRD will perform full-sky surveys for three years at the Sun-Earth Lagrangian point L2 for 15 frequency bands between 34 and 448 GHz with three telescopes, to achieve a total sensitivity of 2.16 μK-arcmin with a typical angular resolution of 0.5° at 100 GHz. We provide an overview of the LiteBIRD project, including scientific objectives, mission requirements, top-level system requirements, operation concept, and expected scientific outcomes.
The Simons Observatory (SO) will be a cosmic microwave background (CMB) survey experiment with three small-aperture telescopes (SATs) and one large-aperture telescope (LAT), which will observe from the Atacama Desert in Chile. In total, SO will field over 60,000 transition-edge sensor (TES) bolometers in six spectral bands centered between 27 and 280 GHz in order to achieve the sensitivity necessary to measure or constrain numerous cosmological quantities. The SATs are optimized for a primordial gravitational wave signal in a parity odd polarization power spectrum at a large angular scale. We will present the latest status of the SAT development.
LiteBIRD has been selected as JAXA’s strategic large mission in the 2020s, to observe the cosmic microwave background (CMB) B-mode polarization over the full sky at large angular scales. The challenges of LiteBIRD are the wide field-of-view (FoV) and broadband capabilities of millimeter-wave polarization measurements, which are derived from the system requirements. The possible paths of stray light increase with a wider FoV and the far sidelobe knowledge of -56 dB is a challenging optical requirement. A crossed-Dragone configuration was chosen for the low frequency telescope (LFT : 34–161 GHz), one of LiteBIRD’s onboard telescopes. It has a wide field-of-view (18° x 9°) with an aperture of 400 mm in diameter, corresponding to an angular resolution of about 30 arcminutes around 100 GHz. The focal ratio f/3.0 and the crossing angle of the optical axes of 90◦ are chosen after an extensive study of the stray light. The primary and secondary reflectors have rectangular shapes with serrations to reduce the diffraction pattern from the edges of the mirrors. The reflectors and structure are made of aluminum to proportionally contract from warm down to the operating temperature at 5 K. A 1/4 scaled model of the LFT has been developed to validate the wide field-of-view design and to demonstrate the reduced far sidelobes. A polarization modulation unit (PMU), realized with a half-wave plate (HWP) is placed in front of the aperture stop, the entrance pupil of this system. A large focal plane with approximately 1000 AlMn TES detectors and frequency multiplexing SQUID amplifiers is cooled to 100 mK. The lens and sinuous antennas have broadband capability. Performance specifications of the LFT and an outline of the proposed verification plan are presented.
LiteBIRD is a JAXA-led Strategic Large-Class mission designed to search for the existence of the primordial gravitational waves produced during the inflationary phase of the Universe, through the measurements of their imprint onto the polarization of the cosmic microwave background (CMB). These measurements, requiring unprecedented sensitivity, will be performed over the full sky, at large angular scales, and over 15 frequency bands from 34 GHz to 448 GHz. The LiteBIRD instruments consist of three telescopes, namely the Low-, Medium-and High-Frequency Telescope (respectively LFT, MFT and HFT). We present in this paper an overview of the design of the Medium-Frequency Telescope (89{224 GHz) and the High-Frequency Telescope (166{448 GHz), the so-called MHFT, under European responsibility, which are two cryogenic refractive telescopes cooled down to 5 K. They include a continuous rotating half-wave plate as the first optical element, two high-density polyethylene (HDPE) lenses and more than three thousand transition-edge sensor (TES) detectors cooled to 100 mK. We provide an overview of the concept design and the remaining specific challenges that we have to face in order to achieve the scientific goals of LiteBIRD.
LiteBIRD is a JAXA strategic L-class mission devoted to the measurement of polarization of the Cosmic Microwave Background, searching for the signature of primordial gravitational waves in the B-modes pattern of the polarization. The onboard instrumentation includes a Middle and High Frequency Telescope (MHFT), based on a pair of cryogenically cooled refractive telescopes covering, respectively, the 89-224 GHz and the 166-448 GHz bands. Given the high target sensitivity and the careful systematics control needed to achieve the scientific goals of the mission, optical modeling and characterization are performed with the aim to capture most of the physical effects potentially affecting the real performance of the two refractors. We describe the main features of the MHFT, its design drivers and the major challenges in system optimization and characterization. We provide the current status of the development of the optical system and we describe the current plan of activities related to optical performance simulation and validation.
Accurate optical modeling is important for the design and characterisation of current and next-generation experiments studying the Cosmic Microwave Background (CMB). Geometrical Optics (GO) cannot model diffractive effects. In this work, we discuss two methods that incorporate diffraction, Physical Optics (PO) and the Geometrical Theory of Diffraction (GTD). We simulate the optical response of a ground-based two-lens refractor design shielded by a ground screen with time-reversed simulations. In particular, we use GTD to determine the interplay between the design of the refractor’s forebaffle and the sidelobes caused by interaction with the ground screen
In this work we describe upgrades to the Spider balloon-borne telescope in preparation for its second flight, currently planned for December 2021. The Spider instrument is optimized to search for a primordial B-mode polarization signature in the cosmic microwave background at degree angular scales. During its first flight in 2015, Spider mapped ~10% of the sky at 95 and 150 GHz. The payload for the second Antarctic flight will incorporate three new 280 GHz receivers alongside three refurbished 95- and 150 GHz receivers from Spider's first flight. In this work we discuss the design and characterization of these new receivers, which employ over 1500 feedhorn-coupled transition-edge sensors. We describe pre-flight laboratory measurements of detector properties, and the optical performance of completed receivers. These receivers will map a wide area of the sky at 280 GHz, providing new information on polarized Galactic dust emission that will help to separate it from the cosmological signal.
The Simons Observatory (SO) is a new experiment that aims to measure the cosmic microwave background (CMB) in temperature and polarization. SO will measure the polarized sky over a large range of microwave frequencies and angular scales using a combination of small (~0.5 m) and large (~6 m) aperture telescopes and will be located in the Atacama Desert in Chile. This work is part of a series of papers studying calibration, sensitivity, and systematic errors for SO. In this paper, we discuss current efforts to model optical systematic effects, how these have been used to guide the design of the SO instrument, and how these studies can be used to inform instrument design of future experiments like CMB-S4. While optical systematics studies are underway for both the small aperture and large aperture telescopes, we limit the focus of this paper to the more mature large aperture telescope design for which our studies include: pointing errors, optical distortions, beam ellipticity, cross-polar response, instrumental polarization rotation and various forms of sidelobe pickup.
The Simons Observatory (SO) will make precision temperature and polarization measurements of the cosmic
microwave background (CMB) using a series of telescopes which will cover angular scales between 1 arcminute
and tens of degrees, contain over 40,000 detectors, and sample frequencies between 27 and 270 GHz. SO will
consist of a six-meter-aperture telescope coupled to over 20,000 detectors along with an array of half-meter
aperture refractive cameras, coupled to an additional 20,000+ detectors. The unique combination of large and
small apertures in a single CMB observatory, which will be located in the Atacama Desert at an altitude of
5190 m, will allow us to sample a wide range of angular scales over a common survey area. SO will measure
fundamental cosmological parameters of our universe, find high redshift clusters via the Sunyaev-Zeldovich effect,
constrain properties of neutrinos, and seek signatures of dark matter through gravitational lensing. The complex
set of technical and science requirements for this experiment has led to innovative instrumentation solutions
which we will discuss. The large aperture telescope will couple to a cryogenic receiver that is 2.4 m in diameter
and over 2 m long, creating a number of interesting technical challenges. Concurrently, we are designing an array
of half-meter-aperture cryogenic cameras which also have compelling design challenges. We will give an overview
of the drivers for and designs of the SO telescopes and the cryogenic cameras that will house the cold optical
components and detector arrays.
The Simons Observatory (SO) will observe the temperature and polarization anisotropies of the cosmic microwave background (CMB) over a wide range of frequencies (27 to 270 GHz) and angular scales by using both small (∼0.5 m) and large (∼6 m) aperture telescopes. The SO small aperture telescopes will target degree angular scales where the primordial B-mode polarization signal is expected to peak. The incoming polarization signal of the small aperture telescopes will be modulated by a cryogenic, continuously-rotating half-wave plate (CRHWP) to mitigate systematic effects arising from slowly varying noise and detector pair-differencing. In this paper, we present an assessment of some systematic effects arising from using a CRHWP in the SO small aperture systems. We focus on systematic effects associated with structural properties of the HWP and effects arising when operating a HWP, including the amplitude of the HWP synchronous signal (HWPSS), and I → P (intensity to polarization) leakage that arises from detector non-linearity in the presence of a large HWPSS. We demonstrate our ability to simulate the impact of the aforementioned systematic effects in the time domain. This important step will inform mitigation strategies and design decisions to ensure that SO will meet its science goals.
The Simons Observatory (SO) is an upcoming experiment that will study temperature and polarization fluctuations in the cosmic microwave background (CMB) from the Atacama Desert in Chile. SO will field both a large aperture telescope (LAT) and an array of small aperture telescopes (SATs) that will observe in six bands with center frequencies spanning from 27 to 270 GHz. Key considerations during the SO design phase are vast, including the number of cameras per telescope, focal plane magnification and pixel density, in-band optical power and camera throughput, detector parameter tolerances, and scan strategy optimization. To inform the SO design in a rapid, organized, and traceable manner, we have created a Python-based sensitivity calculator with several state-of-the-art features, including detector-to-detector optical white-noise correlations, a handling of simulated and measured bandpasses, and propagation of low-level parameter uncertainties to uncertainty in on-sky noise performance. We discuss the mathematics of the sensitivity calculation, the calculator's object-oriented structure and key features, how it has informed the design of SO, and how it can enhance instrument design in the broader CMB community, particularly for CMB-S4.
A common optical design for a coma-corrected, 6-meter aperture, crossed-Dragone telescope has been adopted for the CCAT-prime telescope of CCAT Observatory, Inc., and for the Large Aperture Telescope of the Simons Observatory. Both are to be built in the high altitude Atacama Desert in Chile for submillimeter and millimeter wavelength observations, respectively. The design delivers a high throughput, relatively flat focal plane, with a field of view 7.8 degrees in diameter for 3 mm wavelengths, and the ability to illuminate >100k diffraction-limited beams for < 1 mm wavelengths. The optics consist of offset reflecting primary and secondary surfaces arranged in such a way as to satisfy the Mizuguchi-Dragone criterion, suppressing first-order astigmatism and maintaining high polarization purity. The surface shapes are perturbed from their standard conic forms in order to correct coma aberrations. We discuss the optical design, performance, and tolerancing sensitivity. More information about CCAT-prime can be found at ccatobservatory.org and about Simons Observatory at simonsobservatory.org.
The Simons Observatory will consist of a single large (6 m diameter) telescope and a number of smaller (∼0.5 m diameter) refracting telescopes designed to measure the polarization of the Cosmic Microwave Background to unprecedented accuracy. The large aperture telescope is the same design as the CCAT-prime telescope, a modified Crossed Dragone design with a field-of-view of over 7.8 degrees diameter at 90 GHz. This paper presents an overview of the cold reimaging optics for this telescope and what drove our choice of 350–400 mm diameter silicon lenses in a 2.4 m cryostat over other possibilities. We will also consider the future expandability of this design to CMB Stage-4 and beyond.
We describe 280 GHz bolometric detector arrays that instrument the balloon-borne polarimeter spider. A primary science goal of spider is to measure the large-scale B-mode polarization of the cosmic microwave background (cmb) in search of the cosmic-inflation, gravitational-wave signature. 280 GHz channels aid this science goal by constraining the level of B-mode contamination from galactic dust emission. We present the focal plane unit design, which consists of a 16x16 array of conical, corrugated feedhorns coupled to a monolithic detector array fabricated on a 150 mm diameter silicon wafer. Detector arrays are capable of polarimetric sensing via waveguide probe-coupling to a multiplexed array of transition-edge-sensor (TES) bolometers. The spider receiver has three focal plane units at 280 GHz, which in total contains 765 spatial pixels and 1,530 polarization sensitive bolometers. By fabrication and measurement of single feedhorns, we demonstrate 14.7° FHWM Gaussian-shaped beams with <1% ellipticity in a 30% fractional bandwidth centered at 280 GHz. We present electromagnetic simulations of the detection circuit, which show 94% band-averaged, single-polarization coupling efficiency, 3% reflection and 3% radiative loss. Lastly, we demonstrate a low thermal conductance bolometer, which is well-described by a simple TES model and exhibits an electrical noise equivalent power (NEP) = 2.6 x 10-17 W/√Hz, consistent with the phonon noise prediction.
We present the results of integration and characterization of the Spider instrument after the 2013 pre-flight campaign. Spider is a balloon-borne polarimeter designed to probe the primordial gravitational wave signal in the degree-scale B-mode polarization of the cosmic microwave background. With six independent telescopes housing over 2000 detectors in the 94 GHz and 150 GHz frequency bands, Spider will map 7.5% of the sky with a depth of 11 to 14 μK•arcmin at each frequency, which is a factor of ~5 improvement over Planck. We discuss the integration of the pointing, cryogenic, electronics, and power sub-systems, as well as pre-flight characterization of the detectors and optical systems. Spider is well prepared for a December 2014 flight from Antarctica, and is expected to be limited by astrophysical foreground emission, and not instrumental sensitivity, over the survey region.
KEYWORDS: Digital signal processing, Control systems, Servomechanisms, Telescopes, Actuators, Gyroscopes, Sensors, Electroluminescence, Computer programming, Polarization
We present the technology and control methods developed for the pointing system of the Spider experiment. Spider is a balloon-borne polarimeter designed to detect the imprint of primordial gravitational waves in the polarization of the Cosmic Microwave Background radiation. We describe the two main components of the telescope’s azimuth drive: the reaction wheel and the motorized pivot. A 13 kHz PI control loop runs on a digital signal processor, with feedback from fibre optic rate gyroscopes. This system can control azimuthal speed with < 0.02 deg/s RMS error. To control elevation, Spider uses stepper-motor-driven linear actuators to rotate the cryostat, which houses the optical instruments, relative to the outer frame. With the velocity in each axis controlled in this way, higher-level control loops on the onboard flight computers can implement the pointing and scanning observation modes required for the experiment. We have accomplished the non-trivial task of scanning a 5000 lb payload sinusoidally in azimuth at a peak acceleration of 0.8 deg/s2, and a peak speed of 6 deg/s. We can do so while reliably achieving sub-arcminute pointing control accuracy.
We introduce the light-weight carbon fiber and aluminum gondola designed for the Spider balloon-borne telescope. Spider is designed to measure the polarization of the Cosmic Microwave Background radiation with unprecedented sensitivity and control of systematics in search of the imprint of inflation: a period of exponential expansion in the early Universe. The requirements of this balloon-borne instrument put tight constrains on the mass budget of the payload. The Spider gondola is designed to house the experiment and guarantee its operational and structural integrity during its balloon-borne flight, while using less than 10% of the total mass of the payload. We present a construction method for the gondola based on carbon fiber reinforced polymer tubes with aluminum inserts and aluminum multi-tube joints. We describe the validation of the model through Finite Element Analysis and mechanical tests.
KEYWORDS: Bolometers, Digital signal processing, Analog electronics, Cryogenics, Electronics, Control systems, Physics, Sensors, Telescopes, Signal processing
We present the second generation BLASTbus electronics. The primary purposes of this system are detector readout, attitude control, and cryogenic housekeeping, for balloon-borne telescopes. Readout of neutron transmutation doped germanium (NTD-Ge) bolometers requires low noise and parallel acquisition of hundreds of analog signals. Controlling a telescope's attitude requires the capability to interface to a wide variety of sensors and motors, and to use them together in a fast, closed loop. To achieve these different goals, the BLASTbus system employs a flexible motherboard-daughterboard architecture. The programmable motherboard features a digital signal processor (DSP) and field-programmable gate array (FPGA), as well as slots for three daughterboards. The daughterboards provide the interface to the outside world, with versions for analog to digital conversion, and optoisolated digital input/output. With the versatility afforded by this design, the BLASTbus also finds uses in cryogenic, thermometry, and power systems. For accurate timing control to tie everything together, the system operates in a fully synchronous manner. BLASTbus electronics have been successfully deployed to the South Pole, and own on stratospheric balloons.
An attitude determination system for balloon-borne experiments is presented. The system provides pointing information in azimuth and elevation for instruments flying on stratospheric balloons over Antarctica. In-flight attitude is given by the real-time combination of readings from star cameras, a magnetometer, sun sensors, GPS, gyroscopes, tilt sensors and an elevation encoder. Post-flight attitude reconstruction is determined from star camera solutions, interpolated by the gyroscopes using an extended Kalman Filter. The multi-sensor system was employed by the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol), an experiment that measures polarized thermal emission from interstellar dust clouds. A similar system was designed for the upcoming flight of Spider, a Cosmic Microwave Background polarization experiment. The pointing requirements for these experiments are discussed, as well as the challenges in designing attitude reconstruction systems for high altitude balloon flights. In the 2010 and 2012 BLASTPol flights from McMurdo Station, Antarctica, the system demonstrated an accuracy of < 5’ rms in-flight, and < 5” rms post-flight.
Here we describe the design and performance of the SPIDER instrument. SPIDER is a balloon-borne cosmic
microwave background polarization imager that will map part of the sky at 90, 145, and 280 GHz with subdegree
resolution and high sensitivity. This paper discusses the general design principles of the instrument inserts,
mechanical structures, optics, focal plane architecture, thermal architecture, and magnetic shielding of the TES
sensors and SQUID multiplexer. We also describe the optical, noise, and magnetic shielding performance of the
145 GHz prototype instrument insert.
We describe the cryogenic system for SPIDER, a balloon-borne microwave polarimeter that will map 8% of the
sky with degree-scale angular resolution. The system consists of a 1284 L liquid helium cryostat and a 16 L
capillary-filled superfluid helium tank, which provide base operating temperatures of 4 K and 1.5 K, respectively.
Closed-cycle 3He adsorption refrigerators supply sub-Kelvin cooling power to multiple focal planes, which are
housed in monochromatic telescope inserts. The main helium tank is suspended inside the vacuum vessel with
thermally insulating fiberglass flexures, and shielded from thermal radiation by a combination of two vapor
cooled shields and multi-layer insulation. This system allows for an extremely low instrumental background and
a hold time in excess of 25 days. The total mass of the cryogenic system, including cryogens, is approximately
1000 kg. This enables conventional long duration balloon flights. We will discuss the design, thermal analysis,
and qualification of the cryogenic system.
We describe SPIDER, a balloon-borne instrument to map the polarization of the millimeter-wave sky with degree
angular resolution. Spider consists of six monochromatic refracting telescopes, each illuminating a focal plane
of large-format antenna-coupled bolometer arrays. A total of 2,624 superconducting transition-edge sensors are
distributed among three observing bands centered at 90, 150, and 280 GHz. A cold half-wave plate at the
aperture of each telescope modulates the polarization of incoming light to control systematics. SPIDER's first
flight will be a 20-30-day Antarctic balloon campaign in December 2011. This flight will map ~8% of the sky to
achieve unprecedented sensitivity to the polarization signature of the gravitational wave background predicted
by inflationary cosmology. The SPIDER mission will also serve as a proving ground for these detector technologies
in preparation for a future satellite mission.
Spider is a balloon-borne array of six telescopes that will observe the Cosmic Microwave Background. The 2624
antenna-coupled bolometers in the instrument will make a polarization map of the CMB with approximately
one-half degree resolution at 145 GHz. Polarization modulation is achieved via a cryogenic sapphire half-wave
plate (HWP) skyward of the primary optic. We have measured millimeter-wave transmission spectra of the
sapphire at room and cryogenic temperatures. The spectra are consistent with our physical optics model, and
the data gives excellent measurements of the indices of A-cut sapphire. We have also taken preliminary spectra of
the integrated HWP, optical system, and detectors in the prototype Spider receiver. We calculate the variation
in response of the HWP between observing the CMB and foreground spectra, and estimate that it should not
limit the Spider constraints on inflation.
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