The Simons Observatory: Cryogenic half wave plate rotation mechanism for the small aperture telescopes Open Access

The cosmic microwave background (CMB) radiation is the oldest detectable light in the universe, originating from the epoch of recombination. Its polarization is dominated by parity-even “E-mode” patterns, primarily sourced by density fluctuations in the early universe.^1,2 Primordial tensor perturbations are predicted to produce parity-odd “B-mode” polarization with an angular spectrum peaking at degree scales.^3,4 The rapid expansion of the early universe, called inflation, could produce tensor perturbations.^5–7 

A measurement of the primordial B-mode polarization signature would constrain models of the early universe and contribute to the understanding of physics at grand unified theory (GUT) energy scales.⁸ The primordial B-mode signal is subdominant to both E-modes and several foreground sources, including polarized galactic emission, mainly from synchrotron and thermal dust,^9,10 and E- to B-mode conversion through gravitational lensing.¹¹ Separating primordial B-mode polarization from galactic foregrounds requires a wide frequency coverage, while efficient lensing B-mode separation requires a high resolution and large sky coverage.^12–14 

The Simons Observatory (SO) is a CMB experiment located at Cerro Toco (5200 m) in the Chilean Atacama Desert.^15,16 The nominal observatory consists of three small aperture telescopes (SATs), each with an aperture of 42 cm targeting large angular scales,^17,18 and one large aperture telescope (LAT), with an aperture of 6 m targeting arcminute angular scales.^19–21 The combined arrays of the SATs and the LAT employ over 60 000 transition-edge sensor (TES) bolometers.^22–24 The SATs are designed for the primary science goal of constraining primordial B-modes and, therefore, probe a sufficiently wide range of frequency bands and angular scales. In order to address these requirements, each SAT is sensitive to large angular scales of 30 $<ℓ<$ 300 with 10% fractional sky coverage and has two primary frequency bands with bandwidths ranging from about 20% to 45% of the central frequencies.²⁵ Two SATs cover middle frequencies (MFs), with band centers at 93 and 145 GHz, while the third SAT covers ultra-high frequencies (UHFs), centering at 225 and 280 GHz.

Various modulation techniques have been used in CMB polarization experiments.^26–37 The rapid modulation of incident polarization by a half-wave plate (HWP) is one of the most promising techniques to separate the large scale CMB B-mode polarization signal from large unpolarized atmospheric 1/f noise, while using an instrument with a large optical throughput and a large number of multi-chroic pixels.^38–44 

The SO SATs employ a cryogenic continuously rotating half-wave plate (CHWP) polarization modulator to achieve sensitive observations at large angular scales. In this paper, we describe the requirements, design, and evaluation test results of the SO SAT CHWP rotation mechanism for the MF and UHF bands. The development and study of low frequencies (LFs), having center band frequencies of 27 and 39 GHz, are under way and will be reported elsewhere. Section II provides an overview of the basic functionality of the polarization modulator, Sec. III presents the requirements, Sec. IV presents the design of subsystems, Sec. V presents the results of laboratory performance, and Sec. VI summarizes the development and describes future prospects.

Observing primordial B-modes requires nK sensitivity, especially at degree angular scales. The challenge for ground-based polarimeters is to characterize faint signals in the presence of comparably large-amplitude unpolarized atmospheric fluctuations, in addition to polarized emission from the atmosphere,^46,47 the ground, and the instrument itself. While atmospheric noise is mitigated by the high altitude and low water vapor of the SO site, it is, nevertheless, difficult to control this contamination due to spatial and temporal fluctuations caused by local weather conditions. The atmospheric noise enters the detector time ordered data (TOD) as 1/f noise, reducing sensitivity at large angular scales.^48–51 

Experiments without rapid polarization usually mitigate the atmospheric 1/f noise and reconstruct the linear polarization by differencing detectors with orthogonal antennas.^52–54 However, any mismatched response between orthogonal detectors leads to intensity-to-polarization (I-to-P) leakage, which contaminates the cosmological polarization signal.⁵⁵ 

The CHWP employs a Pancharatnam-style⁵⁶ achromatic HWP (AHWP) composed of three single-crystal sapphire plates. Sapphire was chosen because it has high thermal conductivity and low millimeter-wave absorption. The AHWP allows for coverage of a wide frequency band, and it has been employed in several previous CMB experiments^{34,38,44,57,58} as well as included in the design of planned instruments.⁵⁹ The design of the AHWP is similar to that used in the Simons Array experiment, including the three slabs of sapphire with anti-reflection (AR) coating.⁴² The control of systematic effects from the AHWP is a crucial aspect of HWP polarimetry.^58,60,61 The study of detailed performance and systematics of the SO AHWP is reported by Sugiyama et al.⁶² The design of the rotation mechanism inherits many aspects of the analogous system in the Simons Array experiment.⁴⁴ However, the details of the implementation have been modified according to the unique requirements of the SO SAT receiver, as shown in Fig. 1.

The driving philosophy behind the CHWP system design is to ensure stability, both mechanically and thermally. Since the CHWP is located in the SAT’s main beam (Fig. 1), any unpredictable behavior carries a risk of contaminating the polarization signal from the sky.⁴⁵ Therefore, we require any variation in the CHWP system other than its fast modulation to be small, slowly varying, and measurable where possible. Furthermore, we look for robust design solutions that will withstand years of continuous operation at the Simons Observatory site while minimizing maintenance and telescope downtime. Finally, we develop the CHWP rotation mechanism as a modular system that can be tested with more frequent iterations before being integrated with the complete SAT cryostat. The SAT receiver employs an outer vacuum shell and two thermal shells cooled by two pulse tube coolers (PTCs).⁶³ We refer to the two thermal shells as the PTC1 stage and the PTC2 stage with nominal temperatures of 40 and 4 K, respectively. The CHWP mechanism is mounted on the most skyward flange of the PTC1 stage (Fig. 1).

Table I summarizes the CHWP requirements and achieved values. The system design relies on the heritage of the CHWP for the Simons Array telescopes,⁴⁴ and the requirements qualitatively remain the same. Notable differences to the requirements include: (a) a larger optical throughput requiring an optical diameter of 490 mm and the placement of the HWP optics close to the telescope’s aperture stop, (b) relaxed requirements on the physical volume available to the system, and (c) a larger variation in the gravity vector due to the addition of bore sight rotation about the SAT’s optical axis to the scan strategy, resulting in the rotor alignment requirement.

During normal operation, we require a steady rotation frequency (f_HWP) of 2 Hz or greater in order for the polarization signal to be modulated faster than the 1/f knee of temperature fluctuations in the atmosphere.^41,64 In order to make efficient use of observing time, we require spin-up (spin-down) to (from) this rotation frequency to be achieved in less than 5 min. We also require the peak-to-peak stability of f_HWP to be better than 10 mHz during observations over a standard observation period of several years. Requirements are determined by operational conditions, such as the need to avoid noisy frequency regions in the TES power spectra or resonance frequencies of the mechanical structures in the cryostat.

For modularity, the CHWP rotation mechanism is designed to easily accommodate the front end, window-side, of the cryostat. This constrains the total envelope of the CHWP cryogenic components to be $<950$ mm in diameter and $<246$ mm in height along the optical axis. The total mass requirement of the CHWP, $≤70$ kg, is not tightly constrained, as it is subdominant to the total suspended mass of the cryogenic stages supported by the primary cryo-mechanical truss.⁶⁵ 

CHWP rotation can generate vibrations in the cryostat and heat up the focal plane’s temperature, degrading detector gain stability and introducing 1/f noise. We require no measurable CHWP-induced resonant heating in the focal plane temperature. The vibrational performance is discussed in Sec. V D.

A clear aperture is one of the central requirements for the CHWP system. Special care is taken to prevent any optical interference from moving parts of the rotation mechanism, as any signal modulated at 4f_HWP mimics the incident polarization. To this end, we require all parts other than the sapphire stack to be circularly symmetric and to be outside of the −15 dB line of the 90 GHz beam (Fig. 2). The total power of the beam below the −15 dB level is estimated to be 0.52%. The −15 dB requirement is determined by a physical-optics simulation to ensure that sidelobe scattering from the CHWP components is small compared to that from other optical elements of SAT.⁴⁵ The 90 GHz band is chosen to define the −15 dB line because it gives the most stringent optical requirements compared to other MF and UHF bands.

Given the SAT’s 35° field of view and the diffraction limited beam, these requirements impose an approximated keep-out zone with an opening angle of about 23° extending skyward from the 420-mm diameter aperture stop (Fig. 2). The sapphire stack must be at least 490 mm in diameter at a distance of 40 mm away from the aperture stop, as close to the stop as possible while maintaining sufficient mechanical margin for the PTC2 alumina filter in between.

Finally, the misalignment of the rotor with the optical center must not exceed 5 mm during operation, as any larger misalignment would lead to physical interference or contamination of the beam.

The rotor temperature is required to stay below 85 K to reduce thermal emission, requiring the thermal loading by the CHWP induced IR radiation incident on the PTC2 alumina filter to be subdominant to the total thermal loading on the PTC2 stage.⁶⁶ A lower temperature of the HWP optics reduces the fluctuation and non-uniformity of its emissivity and also helps to reduce the potential systematics in the observed polarization signal.

The stator temperature is required to be below 70 K, which is well below the critical temperature of the superconducting bearing, 95 K (Secs. IV B and V E). The power dissipation on the PTC1 stage is required to be subdominant to the total thermal loading on the PTC1 stage, and in addition, care is taken to effectively heat sink the CHWP stator to the PTC1 stage to reduce temperature gradients generated by the loading from the CHWP system during operation and to improve drive system efficiency by reducing the resistance of the motor drive coils. As such, we keep the thermal load on the PTC1 stage below $∼3$ W during operation. The low-power dissipation is an advantage not only for the cryogenic components but also for the room-temperature components, especially for the experiments conducted at the altitude of 5200 m, where convective air cooling is poor.

Precise measurement of the rotation angle of the HWP is crucial for demodulation in the analysis pipeline. We require that the propagated noise equivalent temperature (NET) of the angular encoder be an order of magnitude smaller than the MF SAT NET goal: 1.4 $μKs$⁠,¹⁵ where we combine the sensitivity at 93 and 145 GHz to be conservative. Assuming a $∼100mK$ constant polarization induced by the vacuum window and the PTC1 alumina filter,⁶⁷ and following a similar calculation to that described in a study by Hill et al.,⁴⁴ this imposes a limit of 3 $μrads$ for the encoder white noise level. In addition to the low encoding noise, robustness in encoding, such as a low rate of data packet loss and of glitches, is crucial.⁶⁸ 

Due to the remote nature of the SO site, we also require that the CHWP system be capable of autonomous operation, including the capability of its diagnostic monitoring system to detect a power interruption to the cryostat and trigger an automatic shutdown procedure, braking and re-gripping of the rotor.

This section describes the mechanical design of the rotation mechanism and highlights its novel aspects. The overall mechanism can be divided into five major components: the HWP, the superconducting magnetic bearing (SMB), the grippers, the motor, and the angle encoder.

As shown in Figs. 1 and 3, the non-rotating cryogenic components of the CHWP mechanism are built onto the most skyward flange of the PTC1 stage. The main non-rotating components are the superconductor ring, the motor system, and the encoder readheads. In addition, an aluminum shell on the outer diameter of the CHWP assembly provides a mounting flange for skyward optical components (the PTC1 stage IR blocking filters and related heat strapping) and creates a cold, well-regulated radiative cavity to help control the rotor temperature.

The CHWP system employs an AHWP with a three-layer-sapphire stack sandwiched by AR layers. Hereafter, we refer to this optical element as the sapphire stack. It has a ∼505 mm diameter, and the total thickness of all five layers is ∼20 mm for the MF band. As shown in Fig. 4, the sapphire stack is held in an aluminum cradle. In the vertical direction, the sapphire stack is held along its circumference between a Spira⁶⁹ gasket (LS-08) and a series of nylon pads. Nylon is chosen for its low wear and friction at cryogenic temperatures.⁷⁰ In the radial direction, the sapphire stack is pressed by a 20° arc-shaped Spira gasket (SS-16). On the opposite side, it is held by two nylon stops, each placed at 120° from the gasket. The radial position is designed to be centered after cooldown, taking into account the contractions and the gasket spring constant.

The cradle is mounted on the rotor baffle, which is shielded from the beam by the stator baffle (Fig. 2). As discussed in Sec. III C, all components except for the sapphire stack, e.g., the cradle aperture and rotor baffle, are designed to intercept the diffracted 90 GHz beam at the −15 dB level or below when the rotor is at any position within the mechanical clearance. The stator baffle intercepts the diffracted beam at the −18.5 dB level at 90 GHz.

The CHWP employs a 550 mm diameter superconducting magnetic bearing.⁷¹ While SMBs have been demonstrated in other CHWP systems for CMB observations,^{39,40,43,44,72} the SO SMB is the largest of its kind developed to date. The SMB is composed of a permanent ring magnet on the rotor and a ring of 61 or 53 disks of yttrium barium copper oxide⁷³ (YBCO) epoxied into an aluminum holder on the stator. The number of YBCO disks is different in two versions of SMBs to make the total levitation force similar, because the levitation force per one YBCO disk is different in two versions. YBCO is a type II superconductor with a transition temperature of ∼90 K, below which the magnetic flux of the rotor is pinned in flux vortices in the disks, resulting in the loss of all but the rotational degree of freedom. The ring magnet of 550 mm inner diameter was manufactured by Shin-Etsu Chemical⁷⁴ and consists of 32 segments of neodymium (NdFeB; N52) fixed in a G10 enclosure. Care was taken in assembly to minimize gaps between the segments in order to maintain an azimuthally symmetric field. The number of YBCO disks and the number of magnet segments that make up the SMB are important design parameters, and making them relatively prime is critical to minimize vibration. This optimization of the SMB design and its vibration performance are discussed in Sec. V D. The friction and stability of this bearing were previously characterized in a study by Sakurai et al.⁷¹ 

While the YBCO disks are above their transition temperature (∼90 K), the rotor is not suspended by the flux-pinning effect and it is necessary to firmly grip it. This is accomplished by a grip-and-release mechanism, referred to hereafter as grippers. The grippers are a set of three linear actuators⁷⁵ with vacuum adapters manufactured by Huntington.⁷⁶ The actuator shafts mate to wedge tips mounted on the stator, which engage with a matching groove on the rotor when extended. This system allows for the precise and repeatable positioning of the rotor with respect to the rigid body of the SAT. The gripper design closely follows the design described in a study by Hill et al.,⁴⁴ with minor modifications. A single gripper can provide a pushing force that is more than twice the weight of the rotor; this is necessary to enable re-gripping and centering at any telescope elevation, as required in Sec. III C.

The three gripper arms each carry spring-loaded contacts or “touch probes” that align with copper flex-circuit traces on the rotor’s outer diameter. These traces connect to a silicon diode thermometer on the rotor. When the grippers hold the rotor, two spring-loaded contacts touch the flex-circuit traces, measuring the rotor temperature. The measurement is only possible while the rotor is being held by the grippers. The measurement method can also be used to determine if the rotor is being held firmly.

The motor system that provides torque to the rotor is similar to that described in a study by Hill et al.,⁴⁴ with an increased number of coils due to the larger diameter of the SAT. The magnetic field from the 120 motor coils couples to the 80 magnet sprockets⁷⁷ on the edge of the encoder plate (Fig. 3), driving rotation. We employ two optical encoder assemblies, each with a set of five photodiodes⁷⁸ mounted on an arm that hangs over a G10 encoder plate on the rotor (Figs. 3 and 5). The LEDs are aligned with a matching set of five IR light-emitting diodes⁷⁹ (LEDs) located below the plate. The encoder plate is slotted at two different radii in order to chop the light emitted by the LEDs. The photocurrent signal chopped by the 40 wider slots drives the motor coils⁸⁰ by providing feedback through the motor drive electronics (Sec. IV E), while the signal chopped by the 570 − 1 = 569 finer slots is fed to the encoder electronics for calculation of the rotation angle of the CHWP (Sec. IV F). One missing finer slot is a reference for marking the rotor’s absolute rotation angle. Two encoder heads are installed at 180° from one another for redundant angle encoding. Data from both encoder heads can be combined to estimate the rotor’s off-center displacement, as described in  Appendix B.

The design of the motor drive electronics closely follows that used in a study by Hill et al.⁴⁴ Here, we highlight the two design improvements. First, a Proportional–Integral–Differential (PID) feedback system is used to further regulate the rotation frequency. For this system, a frequency-to-voltage circuit serves as an input to a PID controller,⁸¹ which adjusts the drive voltage and modulates the motor torque. With the PID enabled, the frequency control system becomes closed loop and is able to account for unexpected changes to motor efficiency. PID parameters are chosen to minimize long-timescale variations.

Second, a phase compensation circuit is used to further improve rotation stability. While the CHWP rotates, the inductance of the motor coils and the counter-electromotive force distort the motor drive current against drive voltage. This distortion acts approximately as an effective phase delay to the motor drive current, and the phase delay increases with the rotation frequency, resulting in poor motor efficiency. The phase compensation circuit corrects for this phase delay. Simply compensating for the delayed phase significantly improves the motor efficiency. We implement a discrete phase compensation in 60° increments through the sign reversal and the phase swapping of the three-phase motor using relay modules. The use of the relay modules eliminates single-point failures and minimizes noise added to the motor coil drive feedback. Phase compensation with 60° increments is not always optimal but is easily achieved and provides sufficient control and efficiency. We automatically activate the phase compensation circuit when the rotation speed exceeds 1 Hz. The performance of the rotation drive control electronics and the evaluation of rotation efficiency are summarized in Secs. V B and V C, respectively.

Data generated by the CHWP’s cryogenic system are routed from the cryostat via four cables to a warm electronics box for processing. Acquisition of the rotor angular time stream requires cleaning and digitizing the raw encoder signals sent from the CHWP. This processing follows the method described in a study by Hill et al.⁴⁴ 

The CHWP system also continuously records information from the motor driver, a Hall probe, and four silicon diode cryogenic thermometers. The diodes are placed on the YBCO superconductor ring, the sapphire stack mount on the rotor, the PTC1 filter plate, the PTC2 filter plate, and the rotor. These diodes are continuously monitored using a Lake Shore model 240.⁸² A Hall probe⁸³ attached to the YBCO assembly continuously measures the magnetic field intensity around the superconductor (Fig. 21). The neodymium magnet in the rotor assembly is the primary magnetic source, and its field varies with changes in rotor temperature and displacement, enabling the Hall probe to monitor both of these properties.⁸⁴ The monitoring and control of the CHWP system are managed by the Observatory Control System.⁸⁵ 

We discuss the thermal and mechanical performances of three CHWPs evaluated at the University of Tokyo and in SAT cryostats at the University of California San Diego, Princeton University, and the Lawrence Berkeley National Laboratory (Fig. 6). Performance is evaluated using a dummy mass that brings the rotor mass to that expected with the full sapphire stack. The dummy mass is coated with epoxy to mimic the thermal conditions in the relevant IR frequencies.

Figure 7 shows the rotor and stator temperatures during a cooldown process. Initially, the rotor is held by the grippers and is primarily cooled by conduction through the grippers’ copper fingers. The rotor temperature lags behind the stator by 10 h, well within the 36 h requirement.

Figure 9 shows the model for an ANSYS thermal simulation, which is used to further characterize the CHWP thermal cavity as well as the heat input to the rotor. For the simulation, we simply model the floating rotor surrounded by the PTC1 aluminum shell and the PTC1 and PTC2 alumina IR filters. Based on our measurements, we set the temperatures of aluminum shell and alumina filters in the simulation to 55, 60, and 4 K, respectively. The infrared emissivity of the alumina IR filter is set to 0.8,⁸⁶ while that of the aluminum shell is set to 0.96. Here, the inside of the aluminum shell is covered with an infrared black body.⁸⁷ Since there is no physical contact, the rotor exchanges heat with other components only by thermal radiation. Figure 8 shows the simulated time series of the rotor temperature with a constant heat input to the floating rotor. By comparing the data with the simulation result, the heat input to the rotor is estimated to be 220 mW when the rotor is floating and 390 mW when the rotor is rotating at 2 Hz. The additional thermal loading on the PTC2 IR filter due to the presence of the rotor is estimated to be 120 mW, which is sufficiently small compared to the cooling capacity of the PTC2 stage, 1.8 W.

Figures 10 and 11 show the performance of the PID control and the phase compensation described in Sec. IV E. When the rotation PID feedback is on, the rotor accelerates to steady rotation at 2 Hz within 7 min and decelerates down to 0 Hz within 3 min. When phase compensation is used in conjunction with the PID, the spin-up time to steady rotation at 2 Hz is reduced to less than 4 min.

Figure 12 demonstrates the stability of the CHWP’s rotation at 2 Hz over 4 days using PID control. The achieved stability of ±5 mHz is well within the required ±10 mHz. Although not tested in-lab, the stability of the PID control loop over even longer timescales is expected to remain below the requirement. We additionally performed an in-lab azimuth scan to demonstrate stable operation of the CHWP under observation-like conditions. The receiver was held at a constant elevation angle of 50° and subject to an angular throw of 12°, a constant scan velocity of 1°/s, and a turnaround acceleration of 1°/s². While the nominal SAT angular throw will be wider, more frequent turnarounds during this test enabled an evaluation of scanning effects on PID performance under more strenuous operating conditions.

Table II summarizes the thermal dissipation of the rotation mechanism to the stator and PTC1 stage. There are four primary sources of thermal dissipation from the CHWP: (a) Joule heating of the driving coils, where the phase compensation of the motor driver (Sec. IV E) plays an important role, (b) hysteresis loss in the SMB, (c) eddy current loss in the SMB, and (d) dissipation from the optical encoders. (a) is characterized by the impedance and the bias voltage of the motor coils, while (b) and (c) are characterized by fitting the spin-down curve, using the method described in a study by Sakurai et al.⁷¹ As noted in Table II, (b) and (c) are dependent on the elevation angle, or the gravity vector direction. Lower elevation angles lead to a larger distance between the YBCO and the magnet ring of the rotor along the optical axis, resulting in a weaker and smoother magnetic field coupled to the YBCO, thus diminishing the loss from hysteresis and eddy currents. The total dissipation from the motor and SMB (a + b + c) is measured by comparing the loading on the PTC1 stage when the CHWP is operating and when it is not. The power dissipation of the optical encoders is mainly from the LEDs, which is estimated to be smaller than 1 W based on the bias current and voltage.

(a) is reduced by optimizing the phase compensation angle of the drive motor (Sec. IV E). The phase compensation angle was optimized using the power consumption of the motor driving voltage source,⁸⁸ which includes dissipation both inside and outside of the receiver. Figure 14 shows the power consumed by the voltage source as a function of the phase compensation angle of the drive motor. The power consumption with a 2-Hz rotation achieves minimum at 60°. With a motor drive phase compensation of 60°, the power consumption is reduced from 3.6 ± 1.0 to 0.8 ± 0.1 W, and the dissipation of the motor on the stator is reduced from 3.1 ± 1.0 to 0.5 ± 0.1 W. This results in a total power dissipation of $≤1.6$ W, summing motor dissipation with that of the LEDs, which is below the requirement of 3 W.

As we discuss in Sec. V E, the elevation-dependent off-center displacement of the rotor induces a phase shift between the measurements of the two encoders. Because the motor drive voltage source uses feedback from the encoder to regulate its output (Sec. IV E), the rotation efficiency is dependent on this elevation-dependent phase shift and also on the rotation direction, resulting in the systematic variation in the Joule heat of the driving coils and the power consumption by the voltage source. As shown in Fig. 14, the rotation efficiency is sensitive to the phase shift of the motor when phase compensation is not activated but is insensitive when 60° of phase compensation is activated. Therefore, the phase compensation enables us to achieve robust rotational efficiency regardless of changes to the off-center displacement and rotation direction. The systematic variation in the thermal dissipation of the rotation mechanism is negligible compared to the elevation-dependence of the PTC’s cooling capacity.⁸⁹ 

The characteristic vibration frequencies of the SMB are key parameters for the vibrational performance of the CHWP. From the mass of the rotor and the displacement we evaluate in Sec. V E, the spring constants of the SMB parallel and perpendicular to the optical axis are estimated to be 5.2(8.4)× 10⁵ and 9.1(17) × 10⁴ N/m, respectively, for 48(61) YBCO tiles. From these values, we determine the corresponding characteristic vibrational frequencies to be 7(9) and 9(13) Hz, respectively, which are in agreement with the results of Sakurai et al.⁷¹ 

The primary instrumental parameter that impacts the vibrational performance is the number of YBCO disks of the SMB. Throughout our evaluation of the SAT’s susceptibility to CHWP induced vibrations, our design of the SMB evolved from 48 disks to 53 or 61. This section presents their comparison. We employ two methods to characterize vibration, one by using a three-axis accelerometer⁹⁰ mounted on the cryostat near the rotation mechanism and the other by measuring the temperature increase of the 100-mK focal plane stage while sweeping through CHWP rotation frequencies.

Figure 15 shows the spectrogram of the vibration parallel to the optical axis. We do not observe significant vibration perpendicular to the optical axis. Vibrations were measured at frequencies equal to f_HWP multiplied by the number of coils (=120) or the number of YBCO disks (=48, 53) multiplied by an integer. In the 48-disk setup, the 96th harmonic of f_HWP was the largest vibrational mode. 96 is the least common multiple of the number of YBCO disks (=48) and the number of NdFeB magnet segments (=32), and this relationship yielded vibrational coupling that produced higher amplitude vibration. In the 53-disk setup, the number of YBCO disks and the number of NdFeB magnets are relatively prime (do not have common divisors larger than 1) and we did not observe vibrational mode associated with their coupling.

The influence of vibration on the focal plane temperature in two representative SMBs with different numbers of YBCO disks is shown in Fig. 16. The rotation of CHWP was monotonically swept in frequency from 0.5 to 2.3 Hz over a 12 h duration while measuring the temperature of the cryogenic stages. Since these two SMBs are tested in SATs with different instrumentation, a direct comparison of the thermal sensor noise is not possible; however, the resonant heating response observed in a 48-disk setup is not seen in a 53-disk setup.

There are two degrees of freedom that we consider important for the alignment of the CHWP rotation mechanism: alignment along the optical axis, involving displacement perpendicular to the plane of the SMB, and center alignment, involving displacement along the SMB plane. In this section, we discuss the alignment performance along these degrees of freedom, in addition to the effect of temperature on alignment. The quality of the rotor alignment is determined both by the initial centering established by the grippers and by the stiffness of the SMB.

Because the magnetic flux-pinning acts as a restoring force with a finite spring constant, when the rotor is released from the grippers, it displaces due to gravity, finding a new equilibrium position that depends on the elevation angle. Due to its azimuthal symmetry, the SMB is most stiff along the optical axis.⁴⁰ The off-center displacement produces a phase shift between the two angle encoders, resulting in a difference between the calculated and actual rotational angle and the encoded angle. Therefore, the evaluation of off-center displacement is particularly important.

The stiffness of the SMB is the product of the critical density current of the YBCO, the magnetization of the NdFeB permanent magnet ring, and a constant determined by the geometry of the SMB. A temperature increase from 50 to 85 K results in ∼90% reduction in the critical density current⁹¹ and ∼10% reduction in the magnetization.⁹² Thus, by measuring the temperature dependence of the rotor displacement, we can determine the temperature dependence of the stiffness and obtain the maximum operating temperature of the SMB.

Each of the three primary CHWP alignment considerations can be evaluated independently. Alignment along the optical axis is characterized at 50 K with the methods described in  Appendix B. The largest displacement occurs at an elevation angle of 90°, resulting in a displacement of 2.0 ± 0.3 mm, which is well within the designed clearance of 5 mm.

The center alignment is evaluated using the method described in  Appendix B. Figure 17 shows the measured off-center displacement at different elevation angles and for SMBs with different numbers of YBCO disks. The off-center displacement was measured seven times at an elevation of 90°, and the initial alignment accuracy was found to be ≤1 mm. Inaccurate initial centering by the grippers while cooling through the YBCO transition produces a non-zero displacement at an elevation of 90°. As Fig. 17 shows, the off-center displacement decreases as the number of YBCO disks is increased and is smaller than 3.5 mm with 61 YBCO disks at elevation angles larger than 20°.⁹³ This satisfies the requirement for optical and mechanical clearance of ≤5 mm even when combined with the initial alignment accuracy ≤1 mm.

Finally, the temperature dependence of the displacement (Fig. 18) is evaluated to determine the maximum operating temperature through the following three steps:

1. The temperature of the YBCO is gradually increased to 85 K. The off-center displacement is constant up to 70 K but rapidly increases after reaching 70 K.

2. The YBCO temperature is gradually lowered from 85 K. The off-center displacement does not change throughout this process.

3. The YBCO temperature is gradually increased to observe where the off-center displacement starts to increase again. The off-center displacement remains the same up to ∼85 K but begins to rapidly increase when the temperature rises above 85 K.

With this test, we find that the maximum operating temperature of the SMB is not the transition temperature of the YBCO (∼95 K) but 70 K. This temperature requirement is satisfied with sufficient margin under the normal operating conditions of our system. We additionally find that, if the off-center displacement occurs due to the temperature increase, it cannot be restored by simply lowering the temperature of the YBCO. Once the displacement has occurred, it is retained unless the SMB is brought to a higher temperature. In order to re-center the rotor, it is necessary to grip it at the center and warm up the YBCO disks above their transition temperature, followed by a re-cooling to flux-pin the rotor in the correct position.

There are two primary sources of angle encoding inaccuracy: the timing jitter of the data acquisition system and noise in the encoder readout. The total noise should correspond to less than 3 $μrads$ (Sec. III E).

We have presented the requirements, design, and performance of the CHWP rotation mechanism for the Simons Observatory Small Aperture Telescopes. This work advances the field of cryogenic polarization modulators for mm-wave and sub-mm astronomical observations by introducing the largest diameter CHWP constructed to date. The aperture size of the CHWP system was previously constrained by the size of the rotor’s magnet ring. By overcoming the manufacturing limitations of the SMB and optimizing the optical design, the size of the system is now limited by the largest available size of sapphire plate.⁹⁶ This work has also advanced the CHWP rotation drive techniques to improve operational efficiency and introduced new methodologies for characterizing CHWP systems, which enabled an improvement in the SMB to reduce vibration and evaluate the rotor displacement.

The CHWP for LFs is currently under development and will have different design parameters. The center alignment of the rotor will be more challenging since the LF HWP sapphire stack is a factor of 3–4 thicker and thus $∼15$ kg heavier than the MF HWP. Meanwhile, the LF band enjoys significantly less atmospheric fluctuations than the higher frequency bands, and thus, the requirements on the CHWP rotation frequency can be relaxed.

Three CHWPs have been built and evaluated for three SATs, and three additional CHWPs are planned to be built. The CHWP performance satisfies all requirements, including a 478 mm clear aperture, a rotor temperature of <70 K, a stator temperature of <60 K, <1.6 W of dissipation during continuous operation, rotation frequencies up to 3 Hz, rotation stability within 5 mHz, rotor alignment within 5 mm, and 0.07 $μrads$ of the encoded angle noise. The presented CHWPs are expected to be deployed to the Chilean observation site and to see first light in 2023. This development contributes not only to the SO project but also to the design and trade study for future experiments, such as CMB-S4.^97,98

The presented CHWP development was supported by JSPS KAKENHI, Grant Nos. JP18H01240, JP19H00674, JP19K14732, JP21J11179, JP22H04913, JP23H00105, and JP23H01202; JSPS Core-to-Core program, Grant No. JPJSCCA20200003; World Premier International Research Center Initiative (WPI), MEXT, Japan; and International Research Center Formation Program to Accelerate Okayama University Reform (RECTOR). Work at LBNL was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Contract No. DE-AC02-05CH11231, a grant from the Simons Foundation under Award No. 457687, B.K., and a grant from the Gordon and Betty Moore Foundation under Grant No. GBMF7939. K.Y. acknowledges the support from XPS, WINGS Programs, the University of Tokyo. J.S. acknowledges the support from the International Graduate Program for Excellence in Earth-Space Science (IGPEES) and the JSR Fellowship, the University of Tokyo. D.S. acknowledges the support from FoPM, WINGS Program, the University of Tokyo. We thank Paul Barton at the Lawrence Berkeley National Laboratory for designing the motor drive electronics. We thank Sean Adkins for his advice and assistance in improving the CHWP control system. We thank the reviewers, whose suggestions clarify discussions throughout this paper.

The authors have no conflicts to disclose.

K. Yamada: Methodology (equal); Resources (equal); Investigation (equal); Validation (equal); Software (equal); Writing – original draft (lead). B. Bixler: Methodology (equal); Resources (equal); Investigation (equal); Validation (equal); Software (lead); Writing – original draft (supporting). Y. Sakurai: Conceptualization (equal); Methodology (equal); Resources (equal); Investigation (equal); Validation (equal); Software (equal); Funding Acquisition (supporting); Writing – original draft (equal). P. C. Ashton: Conceptualization (equal); Methodology (equal); Resources (equal); Investigation (equal); Validation (equal); Writing – original draft (equal). J. Sugiyama: Methodology (equal); Resources (equal); Investigation (equal); Validation (equal); Software (supporting); Writing – original draft (supporting). K. Arnold: Project Administration (equal); Supervision (equal); Funding Acquisition (supporting). J. Begin: Investigation (supporting); Validation (supporting); Writing – review & editing (supporting). L. Corbett: Investigation (supporting); Validation (supporting). S. Day-Weiss: Investigation (supporting); Validation (supporting); Writing – original draft (supporting). N. Galitzki: Supervision (supporting); Investigation (supporting); Validation (supporting); Writing – review & editing (supporting). C. A. Hill: Conceptualization (equal); Methodology (supporting); Software (equal); Writing – review & editing (supporting). B. R. Johnson: Supervision (supporting); Funding Acquisition (supporting); Writing – review & editing (supporting). B. Jost: Writing – review & editing (supporting). A. Kusaka: Project Administration (equal); Supervision (lead); Conceptualization (equal); Investigation (supporting); Validation (supporting); Funding Acquisition (lead); Writing – original draft (supporting). B. J. Koopman: Software (equal). J. Lashner: Software (equal). A. T. Lee: Project Administration (equal); Conceptualization (supporting); Supervision (supporting); Funding Acquisition (supporting). A. Mangu: Investigation (supporting); Validation (supporting). H. Nishino: Software (equal); Writing – review & editing (supporting). L. A. Page: Project Administration (equal); Conceptualization (supporting); Supervision (supporting); Investigation (supporting); Validation (supporting); Funding Acquisition (supporting); Writing – review & editing (supporting). M. J. Randall: Investigation (supporting); Validation (supporting). D. Sasaki: Investigation (supporting); Software (supporting); Writing – review & editing (supporting). X. Song: Investigation (supporting); Validation (supporting). J. Spisak: Investigation (supporting); Validation (supporting); Writing – original draft (supporting). T. Tsan: Investigation (supporting); Validation (supporting). Y. Wang: Investigation (supporting); Validation (supporting). P. A. Williams: Investigation (supporting); Validation (supporting).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Here, we elaborate on the methods used to make the displacement measurements summarized in Sec. V E. Displacement measurements along the optical axis are made using the gripping mechanisms (Sec. IV C) and a Hall probe (Sec. IV F) installed below the rotor’s magnet ring. The measurement begins by pointing the receiver at an elevation of 90° and fully gripping the rotor. The actuators controlling the gripper positions are then retracted, allowing the rotor to sink along the optical axis. The gripper head geometry is designed such that the retraction distance corresponds directly to the rotor displacement, and changes in the Hall probe’s measured field are monitored. The total displacement of the rotor is estimated from the distance the grippers have moved while the Hall probe changes linearly. Figure 21 shows a schematic of the measurement setup and the measured magnetic field of the rotor magnet as the grippers are gradually retracted. The systematic error of the displacement is ±0.3 mm, resulting from changes in the Hall probe sensitivity and the rotor magnet’s field caused by temperature drifts during the measurement.

The measurement accuracy of the encoder angle shift due to off-center displacement is 0.02°, which is negligible compared to the required accuracy of the polarization angle calibration. The SAT platform will rotate the boresight ±60°. Since the phase shift between the pair of encoders is at its maximum when the boresight angle is 0°, the requirement of the accuracy of the polarization angle is satisfied at any boresight angle.

Successful operation of the CHWP requires paying careful attention to a number of system characteristics. This section presents a summary of the precautions we learned to take while building the CHWP and evaluating its performance.

Physical interference of the rotor is the most common inhibitor of CHWP rotation. This interference can be caused by misplaced or loose screws, nuts, tape, motor sprocket magnets, encoder or motor cables, or multi-layer insulation. To avoid the risk of physical interference, the use of nuts and tape is minimized, the screws are secured with a threadlocker (LOCTITE 263), and the motor sprocket magnets are secured with epoxy (Stycast 2850 FT). Moreover, the magnetic screws or mechanical parts, including 304 stainless steel, must not be used. This is because the rotor’s magnet ring is strong enough to dislodge them and cause physical interferences.

Care must also be taken in the operation of electrical devices, including the encoders, motors, and grippers. Protective measures for electrical devices are crucial, such as the protection circuit for the optical encoders, the current limit function for the motor drive power source, and the limit switch for the grippers. Finally, drastic temperature changes must be avoided, while the encoder LEDs are biased, as exposure to rapidly changing environments can cause degradation.