LEO-CalSat for the calibration of W-band ground-based CMB polarization experiments

Introduction: The current generation of ground- and space-based Cosmic Microwave Background (CMB) telescopes demands highly precise calibration procedures. However, commonly used celestial polarized sources, such as Tau-A, are not characterized with the level of accuracy required for these experiments. This limitation has motivated several initiatives aimed at developing well-characterized artificial signal sources onboard aerial platforms, enabling observations from the telescopes’ far-field.

Methods: In this context, we propose the deployment of a polarized signal source operating in the W-band (75–110 GHz) onboard a dedicated calibration satellite, referred to as CalSat, in Low Earth Orbit (LEO). This platform would facilitate the calibration of ground-based CMB polarization experiments with significantly improved accuracy compared to traditional celestial sources. During calibration operations, the LEO-based CalSat would emit purely polarized microwave radiation from the far field, directed toward the CMB telescopes.

Results: Moreover, LEO-CalSat could also contribute to the calibration of space-based missions operating at the second Lagrange point (L2) by enhancing the characterization of polarized celestial sources, while simultaneously increasing the Technology Readiness Level (TRL) for the future deployment of a calibration satellite at L2. Various launch and satellite platform options are currently under consideration, including Spectrum shuttles and/or MIURA launchers, as well as micro-satellites such as UPMSat-4 and CubeSats.

Discussion: The anticipated launch date for the LEO-CalSat mission, which targets an orbital altitude of at least 400 km, is initially scheduled for the first half of 2026. Within our collaboration, the Universidad Politécnica de Madrid (UPM) team is responsible for the satellite’s design and development, while the IFCA/IPMU team is tasked with the development of the payload signal source.

1 Introduction

The high sensitivity that the new generation of ground-based (Abazajian et al., 2019; Ade et al., 2019; Mennella et al., 2023) and space-based (LiteBIRD Collaboration et al., 2023; Hanany et al., 2019) CMB polarization experiments must achieve to detect the primordial B-mode signal requires highly precise calibration processes. Celestial polarized sources (such as Tau-A) are not characterized with the required accuracy, while the strongest non-polarized sources (like Jupiter) barely reach the required noise floor for the characterization of the intensity optical beam.

This paper aims to provide an overview of the benefits of using a calibration satellite (CalSat) in a low Earth orbit (LEO) for ground-based experiments. Several examples of experiments have been considered, but a detailed calibration strategy has not been carried out, for instance regarding the quantity of detector crossings or the required net calibration time and corresponding total observation period for a given calibration goal, as this would require the consideration of each experiment particularities like, for instance, their focal plane configuration. This kind of analysis is left for future works dedicated to each particular experiment interested in the proposed calibration tool. However, some examples can be found in (Casas et al., 2021; Bermejo-Ballesteros et al., 2022) for calibrating a space mission similar to LiteBIRD.

In recent years, several proposals for the development of low-cost calibration satellites have been put forward (Johnson et al., 2015; Casas et al., 2021; Ritacco et al., 2024). A common aspect among these proposals is that, during calibration, the sources onboard the satellite emit purely polarized microwave radiation toward the CMB instruments from the telescopes’ far field. In the case of the authors of this work, a CalSat for a space mission at L2 (L2-CalSat) was proposed, and preliminary studies were conducted (Casas et al., 2021; Bermejo-Ballesteros et al., 2022). Figure 1 shows some views of the CubeSat proposed in that work.

Figure 1

Figure 1. Exterior view (a) and exploded view (b) of the preliminary design for L2-CalSat published in (Casas et al., 2021). ADCS is the Attitude Determination and Control System and PDU is the Power Distribution Unit. Published with permission from the authors.

This work focuses on a current effort for the development of a LEO-CalSat with application to ground-based experiments (Johnson et al., 2015). The interest is twofold. On one hand, it aims to achieve well-calibrated ground-based experiments to enhance and optimize their results. On the other hand, these well-calibrated ground-based experiments can support the calibration of L2 missions by providing improved knowledge of celestial calibrators (Aumont, J. et al., 2020; Ritacco, A. et al., 2022), while also increasing the TRL of the calibration satellites for future applications in CMB polarization missions at L2 (LiteBIRD Collaboration et al., 2023; Hanany et al., 2019).

Several months before submitting this work, the authors had an opportunity to use a new rocket (Spectrum from ISAR) to launch a microSAT (UPMSat-3) with a calibration source as part of the payload. Unfortunately, the development timeline of the source was not well aligned with the rocket’s scheduled launch dates, initially expected between Q4 2023 and Q1 2024. However, a new satellite platform (UPMSat-4) is planned to be developed by IDR and it is one of the shortlisted candidates in the Spark Program of PLD’s MIURA-5 rocket. The Spark Program is an initiative of the private company PLDSpace to launch SmallSats in support of educational, institutional and commercial payloads, using the new launcher MIURA-5. This represents a new opportunity for developing our LEO-CalSat proposal, as it has been selected as one of the payloads for the rocket’s second launch. This new platform is quite different from the CubeSat in Figure 1 because UPM-Sat4 is expected to be a microsatellite, similar to the previous UPM-Sat3. However, the navigation and communication instrumentation, as well as the electrical power units, may be very similar. Two UPM-Sat platforms have been successfully launched and flown in recent years, and a third is about to be launched. Therefore, there are no expected issues regarding the platform’s maturity or performance.

As a consequence, we are currently working with the MIURA option, targeting a launch date in the first half of 2026, for a LEO-CalSat intended for ground-based experiments operating in the W-band (75–110 GHz). In this case, the satellite is expected to be in a low Earth Sun-sunchronous orbit (SSO), targeting an altitude of at least 400 km, and will transmit purely polarized reference signals to ground-based experiments operating in a coincident frequency band (see Figure 2). The mission’s lifetime is estimated to be around 1 year, based on the reported altitude. The planned application focuses on the Atacama and Tenerife sites, due to the observational limitations imposed by the Sun-synchronous LEO orbit for the South Pole (see next Section).

Figure 2

Figure 2. CalSat signal view from a ground-based telescope. The horn antenna beam of the signal source is represented in red, together with the corresponding solid angle $\mathrm{\Omega }$ that is seen from the telescope.

2 Sun-synchronous orbits

SSOs are those in which the angle between the orbital plane and the earth-sun axis, $\alpha$, is kept constant. This can be achieved when the precession rate $\mathrm{\Omega }$ equals the mean motion of the Earth around the Sun (see Fig. 4.19 in (Curtis, 2021)).

The equation that describes the average rate of change of the $\mathrm{\Omega }$ angle is:

$\dot{\mathrm{\Omega }}=-\left[\frac{3\sqrt{\mu }{J}_2{R}^2}{2{\left(1-e^2\right)}^2{a}^{\frac{7}{2}}}\right]\cos \left(i\right)(1)$

where R is the radius of the Earth; $\mu$ is the gravitational parameter; $a$, $e$ and $i$ are the semi-major axis, eccentricity and inclination of the SSO, respectively; and $J_2$ is the coefficient for the second zonal term related to the oblateness of the Earth.

For SSOs, due to power generation needs, the inclination and altitude are linked. For LEO altitudes, the inclination is usually between 96° and 98°. As a consequence, visibility at the poles is limited because the satellite passes close to the horizon, especially if the orbit is low, which is likely in an experimental launch as the one we plan to use.

In Figure 3a the Sun-synchronous condition is shown, where we have used Equation 1. As we can see, as the orbital altitude increases, the inclination also increases in an almost linear relation.

Figure 3

Figure 3. (a) Inclination vs. altitude plot. An Earth radius equal to 6,378 km, an eccentricity of 0°, and the constant values described in the text, have been considered. Due to cost considerations, a typical altitude range between 400 and 600 km can be expected for LEO-SSOs. (b) EA measured by an observer in a pole as a function of the orbit altitude.

In our case, for a LEO-CalSat with an orbit altitude of 400 km, the corresponding inclination is 97°. In the mission design, we selected 400 km as the target altitude for CalSat, since this is an easily viable orbit for a new launcher like the one that will be used (MIURA-5 from PLD). Using Equation 1 we can also calculate the orbital period. For this orbital altitude it is 1.54 h, which means that LEO-CalSat travels around the earth 15.6 times per day. This represents a relatively high orbital velocity (3.9 arcmin/second). However, considering the tracking speed of medium-sized telescopes–such as those of the QUIJOTE experiment (Rubiño-Martín et al., 2017), which have a 2.25 m aperture and can track objects at about 12°/second–it is clear that, except perhaps for the largest telescopes (e.g., ACT (Qu et al., 2024) or SPT (Sobrin et al., 2022), most CMB polarization experiments should be able to track the satellite if extended calibration time is needed. As a reference, in Section 4.3, LEO-CalSat observation time will be shown for three selected experiments operating in an static mode (without tracking the CalSat) and for 1 month of total observation time. If more calibration time is needed, a geostationary orbit such as that proposed in (Ritacco et al., 2024) can clearly be more beneficial when the CalSat is placed within the telescope’s field of view (FoV).

On the other hand, a low SSO does not ensure good visibility from experiments located at the poles. In our case, with an altitude of 400 km, LEO-CalSat would be visible at a maximum elevation angle of about 23°, as shown in Figure 3b. As a consequence, we have discarded the calibration of CMB experiments located at the South-Pole (for instance SPT), and have instead focused on other observatories such as those in Atacama (Chile) or Izaña (Tenerife, Spain). Also, it’s important to note that, even for altitudes of more than 1,400 km, the elevation angle observed from the poles do not reach even 40°. Therefore, for experiments at the South Pole, polar LEO orbits, such as those proposed in (Johnson et al., 2015), would be a better option. Figure 4 shows a comparison of the projection of one orbit, as proposed in this work (Figure 4a), over the South Pole, with a second orbit similar to that proposed in (Johnson et al., 2015) (Figure 4b). These orbits were obtained using the SpaceCalcs webpage. However, polar orbits (and geostationary ones) are more expensive in terms of launch and maintenance costs.

Figure 4

Figure 4. (a) SSO LEO projection over the South Pole. The orbit considers an altitude of 400 km and an inclination of 97°. (b) Polar LEO projection over the South Pole. The orbit considers an altitude of 500 km and an inclination of 90°.

3 Payload: calibration source

Two reference signal source versions have been implemented using commercial components. The first one follows the scheme of Figure 5, and is composed of a frequency synthesizer, a $\times 6$ frequency multiplier with signal attenuation and modulation capabilities, a Band-Pass Filter (BPF), a directional coupler, a zero-bias detector to monitor the emitted power, a horn antenna, and a wire grid polarizer (not shown in the schematic).

Figure 5

Figure 5. Proposed initial scheme of the W-band calibration source. A frequency synthesizer generates sinusoidal signals at frequencies that are multiplied to emit in the W-band. The Zero Bias Detector (ZBD) provide the value of the emitted signal power.

This version of the calibration source (see the picture in Figure 6a) have been characterized in the laboratory. It has been proved that it can emit around 20 dB m (100 mW) of power within the WR10 standard bandwidth (75–110 GHz, see Figure 6b). However, it is more suitable for laboratory testing and poses power consumption issues and mechanical integration challenges due to the limited available space (2U) onboard LEO-CalSat.

Figure 6

Figure 6. (a) Picture of the laboratory version W-band signal source. (b) Output power of the source as a function of the frequency at three different stages: At the multiplier output (blue), at the coupler ouput (Orange) and after bandpass filtering (green).

The second version (see picture of Figure 7a) has been optimized in terms of size, volume, and power consumption but, in return, it also emits less power (6 dB m, 4 mW; see Figure 7b). This version is based on a frequency multiplier with an integrated Voltage Controlled Oscillator (VCO), avoiding the need of using a frequency synthesizer. The power shown in the plot is given as a function of the control voltage (Vc) applied to the frequency multiplier. The shown voltage range corresponds to the complete frequency range of the bandwidth of interest (75–110 GHz). Figure 7b, shows the power emitted with (in green) and without (in blue) BPF.

Figure 7

Figure 7. (a) Picture of the W-band signal source optimized version. (b) Output power of the source as a function of the control voltage and for two cases: with and without pass-band filter.

The mass is approximately 1 kg, and the maximum power consumption is 9 W. As mentioned previously, the volume is less than 2U (10 $\times$ 10 $\times$ 20 cm; see Figure 8). In comparison, the first source version presents a higher mass, a power consumption of 15 W, and its volume can hardly be adjusted to 2U, even when disassembling the electronic components located inside the black box of Figure 6a.

Figure 8

Figure 8. Representation of the optimized source in the volume of 2U.

As we will see in the next Section, depending on the experiment’s sensitivity, it is expected that Signal-to-Noise (SNR) values around 30 dB will be achievable using both calibration source versions. It is also important to note that the SNR level achievable on the polarization angle is of the same order of magnitude as that because the emitted reference signals are 100% polarised. This also depends on the polarisation efficiency of the instrumentation to be calibrated, but for simplicity we can assume that this is also very close to 100%, meaning that the polarisation angle SNR level would not be affected in practice.

4 Calibration mission impact

4.1 Received power, detector saturation and SNR

A set of different experiments observing (or expected to observe) in the W-band, and placed in the observatories of Izaña (LSPE-STRIP (collaboration et al., 2021)), Atacama (AdvACT (Ward et al., 2016), CLASS (Datta et al., 2024)) and South-Pole Telescope (SPT-3G (Benson et al., 2014), BICEP (Hui et al., 2018)), has been considered for the calculation of SNR values provided by the proposed calibration signal source (Soneira Landín, 2023). Although the South-Pole experiments are not in an optimal situation to be calibrated with LEO-CalSat, they have been included in this analysis just for reference. This section focuses on saturation power due to the kind of detectors that are generally used in most of the experiments considered in this work. Such detector use to be bolometers implemented in superconducting technologies, and with designs optimized to maximize sensitivity. However, their linear operating power range (or dynamic range) use to be quite narrow, and they saturate when receiving power levels only about 2–3 times higher than their expected nominal optical load (i.e., of the same order of magnitude). Under these circumstances, as saturation should be avoided wherever possible, it is more convenient to consider the saturation power of the detectors instead of their linear operating power range. At the power level of the first version of the source (Figure 6), it has been proved that about 20 dB of signal attenuation is needed to avoid saturation in most telescopes. To that end, studies on atmospheric attenuation and the power received by detectors of the mentioned experiments have been carried out considering the use of the previously mentioned BPF. Taking into account around 70 mW of emitted power, the atmosphere of different sites and sensitivity values from the bibliography of the experiments, some preliminary received power results have been obtained (see Figure 9) and compared with detectors power saturation values (some values are reported in Table 4).

Figure 9

Figure 9. (a) Atmospheric absortion (losses, dB) in the W-band for different observatories and elevations. (b) Received power by the detectors of different experiments considering the first source version with band-pass filter.

SNR values for the first version of the source without attenuation are shown in the last column of Table 1. These values have been calculated considering a worst-case scenario in terms of atmospheric noise and only one second of integration time. Additionally, aspects like emitted power, orbit altitude (400 km), telescope elevation angle $(\alpha )$, atmospheric loss, telescope gain and optical efficiency, and detector NEP values (also in Table 1) have been also considered in the calculation. Applying 20 dB attenuation, SNR values between 10 and 35 dB are expected, most of them being, in fact, around 30 dB. It’s important to note that the second version of the source alleviates the saturation issue because the maximum emitted power level is about 14 dB lower (Figure 7). So, in such a case, signal attenuation could be avoided, achieving SNR values between 16 and 41 dB. Also, for this second source, most of the SNR values would be around 36 dB. Taking the reported SNR values into account, and analysis results presented in previous works (Casas et al., 2021; Johnson et al., 2015), expectations for a calibration strategy that covers the various aspects required by CMB experiments (polarisation angle, efficiency, beam ellipticity, side lobes, etc.) seems very promising. Quantitative expectations of the accuracy of the mentioned optical aspects will be studied during next months, for particular focal plane configurations of experiments interested in the proposed calibration tool.

Table 1

Table 1. Signal-to-noise calculation provided by LEO-CalSat reference signal relative to an upper limit for the atmospheric noise. $\alpha$ is the elevation angle of each telescope we have entered into the calculations. The temperature is estimated to be 282 K in Tenerife, 267 K in Atacama, and 224 K at the South-Pole.

It can be noted that some of the experiments included in both Table 1 and Figure 9 (for example, ACT or SA/PB2) have already been decommissioned. However, current experiments such as those operating in the Simons Observatory would obtain similar SNR results. For example, SO-LAT (Xu et al., 2021) is very similar to ACT in terms of telescope size, observatory site, and NEP detectors, and the BICEP Array case is also similar to SO-SATs (Galitzki et al., 2024). The only experiment without a current representative is SA/PB2, but we think it is interesting to present their results to demonstrate a wider variety of telescope sizes. In any case, the last two tables consider ACT to be equivalent to SO-LAT and focus on three experiments expected to observe the frequency band of the proposed LEO-CalSat in the coming years.

4.2 Polarization angle accuracy and reference signal visibility

The approach assumed in this work regarding the polarization angle accuracy that can be achieved thanks to LEO-CalSat is the same as that published in (Johnson et al., 2015), where the authors claim an uncertainty in the polarization angle of 0.05°. This uncertainty would be dominated by the accuracy of the Attitude Determination and Control System (ADACS). This level of accuracy can be achieved by aligning the polariser transmission axis to the ADACS reference system with micron precision using standard precision metrology tools. This work assumes a CalSat navigation system similar to that published in (Casas et al., 2021), where the proposed ADACS can provide an accuracy of one arcminute (0.017°).

On the other hand, regarding signal visibility, we show some LEO-CalSat simulated SSOs projected on the Earth’s surface (see Figure 10, (Mejía Jirón, 2022)). The orbits have been estimated using the GMAT software, demonstrating the wide visibility coverage that an SSO is able to provide for diverse observatories around the planet. Although they are difficult to identify in the Figure due to the density of the represented orbits, the observatories best suited to use the proposed calibration system (Atacama and Tenerife) are indicated with an arrow and a black point surrounded by a circle. The orbital parameters of the simulated dawn–dusk SSO with a starting date of 20 March 2023 are shown in Table 2.

Figure 10

Figure 10. LEO-CalSat orbits projected on Earth (in red lines) during 30 days, to show the wide visibility coverage that the proposed SSO is able to provide for diverse observatories around the planet. In particular, the Atacama and Tenerife observatories have been pointed out using two yellow arrows and white plots.

Table 2

Table 2. Orbital parameters of a dawn-dusk SSO at 20th of March 2023.

From these simulations, orbit trajectories within the Field of View (FoV) of some of the previously considered experiments have been calculated. At this point we have focused in the experiments placed in Tenerife and Atacama observatories, considering the course of 1 month. The achieved results are shown in Figure 11.

Figure 11

Figure 11. LEO-CalSat trajectories for different experiments: (a) CLASS, (b) LSPE-STRIP, (c) ACT. Each panel shows 1 month of observation, assuming a circular FoV pointed at the zenith. The lines constructed by the points represent the trajectories of the satellite, with the different colors indicating individual observing days.

In this simulations, just for simplicity, circular FoVs and telescopes pointing at the zenith have been considered. Although this is a rather unrealistic scenario, as previously noted in the introduction of this work, its objective is to highlight the potential benefits of the proposed calibration tool for various experiments, rather than to provide a detailed calibration strategy for each one.

Table 3 summarizes the corresponding potential calibration time for each experiment. From these results it seems clear that, if it is not possible to extend calibration observations during several months, this kind of calibration observations is not optimal for experiments with large telescopes and small FoV such as ACT. However, as has been previously noted, smaller telescopes are able to track the satellite orbits, allowing for extended calibration times.

Table 3

Table 3. Number of observations in 1 month and information about the observation time for each experiment.

A last aspect to comment regarding visibility simulations is that, after performing a large number of them, it has been noticed that the potential number of observations (second column in Table 3) depends slightly on the simulation’s initialization time (the initial time that the satellite starts to orbit). However, this dependence introduce an uncertainty in the results of about a 5$\%$, which it is not considered a significant impact on the results presented in this work.

4.3 Thermal control

Another important aspect to consider is the thermal emission from the spacecraft, which can be received by the detectors as an additional optical load, thereby limiting their sensitivity. In this context, the received thermal power has been calculated, considering solar panels at 39 °C (Casas et al., 2021) and with an area similar to that of the UPMSat-2 walls. For the case of the three experiments previously considered and also for different frequencies the results are shown in Table 4, where the absorbed thermal power $(P_{\text{ab}})$ is compared with the detector saturation values $(P_{\text{sat}})$. We use $P_{\text{sat}}$ as a rough reference of the noise equivalent power (NEP) since it is proportional to the total optical load $(P_{\text{tot}})$ of the detectors which, in turn, is typically a factor between 2 and 3 smaller than $P_{\text{sat}}$. It is worth noting that $P_{\text{sat}}$ is always several orders of magnitude higher than the thermal power received from the spacecraft, $P_{\text{abs}}$. Consequently, this contribution is not a limiting factor for the detectors’ sensitivity, since the total optical load corresponding to the detectors NEP is on the same order of magnitude as $P_{\text{sat}}$.

Table 4

Table 4. Absorbed thermal power and saturation power by the detectors of the different experiments and frequencies. All the power values are in pW.

Finally, the thermal emission due to the temperature of the signal source’s antenna has also been analyzed. Specifically, it has been calculated for the previously considered worst case scenario, determined by the telescope size. This corresponds to the ACT/SO-LAT experiments; thus Figure 12 presents the results for the most pessimistic case. The plots show that the highest thermal power absorbed by the ACT detectors remain orders of magnitude below the saturation power level–even at the highest frequencies and with the (clearly unrealistic) antenna temperature of 200 °C.

Figure 12

Figure 12. Absorbed power by the ACT/SO-LAT experiment due to the thermal emission of the horn antenna and as a function of its temperature. It has been considered each frequency band at which ACT operates.

5 Conclusion

In this work, we propose the use of a low-cost satellite equipped with a 90 GHz reference signal source as a payload, aimed at calibrating ground-based CMB polarization experiments. An additional objective is to increase the TRL for the development of an auxiliary satellite dedicated to the calibration of space missions at the second Lagrange point (L2). The proposed LEO-CalSat is expected to be implemented as either a CubeSat or a micro-satellite, operating in a low Earth SSO at an altitude of approximately 400 km, in order to minimize mission costs.

Two versions of the signal source, covering the W-band frequency range (75–110 GHz), have been preliminarily developed and tested. The first version is primarily intended for laboratory validation, while the second has been optimized in terms of mass, volume, and power consumption, making it suitable for integration as the payload of LEO-CalSat. The calibration signal can be spectrally confined to the 90–100 GHz range using a band-pass filter (BPF), which also serves to suppress harmonic distortion. Experimental results demonstrate that SNR values of approximately 30 dB (i.e., a factor of 1,000) can be achieved without saturating the detectors.

Furthermore, the satellite’s visibility has been shown to be well-suited for CMB polarization experiments located at both the Tenerife and Atacama sites, particularly for telescopes with apertures $\le 3$m. Although LEO-CalSat will also be visible from the South Pole, the low elevation angles result in suboptimal conditions due to atmospheric distortion effects on the calibration signal.

Finally, it has been demonstrated that the spurious thermal emission from LEO-CalSat remains several orders of magnitude below the saturation threshold of the detectors–even for large-aperture telescopes such as the Atacama Cosmology Telescope (ACT)– and is therefore negligible for smaller instruments, which are even more likely to benefit from the proposed calibration system.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

FC: Writing – review and editing, Writing – original draft. EM-G: Writing – review and editing, Writing – original draft. JC: Writing – review and editing, Writing – original draft. GP-C: Writing – review and editing, Writing – original draft. IS-R: Writing – original draft, Writing – review and editing. LC: Writing – original draft, Writing – review and editing. PV: Writing – original draft, Writing – review and editing. BB: Writing – review and editing, Writing – original draft.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The authors would like to acknowledge financial support from the Spanish MCIN/AEI/10.13039/501100011033, project ref. PID 2022-139223OB-C21 and PID 2022-139223OB-C22 (funded also by European Union NextGenerationEU/PRTR), and from CSIC/Momentum program (funded by Secretaría de Estado de Digitalización e Inteligencia Artificial–Ministerio para la Transformación Digital y de la Función Pública, by means of Red. es, and with funds of the “Plan de Recuperación”, European Union NextGenerationEU).

Acknowledgements

The authors would like to acknowledge the contributions of the Master Thesis students Luis Fernando Mejía Jirón and Cayetano Soneira Landín, that were supervised by the corresponding author of this article during the completion of their Master Thesis. Also, IFCA team would like to acknowledge the help of David Moya with the design and fabrication of some mechanical parts of the calibration source.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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References

Abazajian, K., Addison, G., Adshead, P., Ahmed, Z., Allen, S. W., Alonso, D., et al. (2019). CMB-S4 science case, reference design, and project plan. arXiv e-prints, arXiv:1907.04473.10.48550/arXiv.1907.04473

Google Scholar

Ade, P., Aguirre, J., Ahmed, Z., Aiola, S., Ali, A., Alonso, D., et al. (2019). The simons observatory: science goals and forecasts. J. Cosmol. Astropart. Phys. 2019, 056. doi:10.1088/1475-7516/2019/02/056

CrossRef Full Text | Google Scholar

Allys, E., Arnold, K., Aumont, J., Aurlien, R., Azzoni, S., Baccigalupi, C., et al. (2023). Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey. Prog. Theor. Exp. Phys. 2023, 042F01. doi:10.1093/ptep/ptac150

CrossRef Full Text | Google Scholar

Aumont, J., Macías-Pérez, J. F., Ritacco, A., Ponthieu, N., and Mangilli, A. (2020). Absolute calibration of the polarisation angle for future cmb b-mode experiments from current and future measurements of the crab nebula. A&A 634, A100. doi:10.1051/0004-6361/201833504

CrossRef Full Text | Google Scholar

Benson, B. A., Ade, P. A. R., Ahmed, Z., Allen, S. W., Arnold, K., Austermann, J. E., et al. (2014). “Spt-3g: a next-generation cosmic microwave background polarization experiment on the south pole telescope,” in Millimeter, submillimeter, and far-infrared detectors and instrumentation for astronomy VII. Editors W. S. Holland, and J. Zmuidzinas, 9153. doi:10.1117/12.2057305

CrossRef Full Text | Google Scholar

Bermejo-Ballesteros, J., Cubas, J., Casas, F., and Martínez-González, E. (2022). Alternative analytic method for computing mean observation time in space-telescopes with spin-precession attitude motion. AIP Conf. Proc. 2611, 050007. doi:10.1063/5.0120161

CrossRef Full Text | Google Scholar

Casas, F. J., Martínez-González, E., Bermejo-Ballesteros, J., García, S., Cubas, J., Vielva, P., et al. (2021). L2-calsat: a calibration satellite for ultra-sensitive cmb polarization space missions. Sensors 21. doi:10.3390/s21103361

PubMed Abstract | CrossRef Full Text | Google Scholar

collaboration, T. L., Addamo, G., Ade, P., Baccigalupi, C., Baldini, A., Battaglia, P., et al. (2021). The large scale polarization explorer (lspe) for cmb measurements: performance forecast. J. Cosmol. Astropart. Phys. 2021, 008. doi:10.1088/1475-7516/2021/08/008

CrossRef Full Text | Google Scholar

Curtis, H. D. (2021). “Chapter 4 - orbits in three dimensions,” in Orbital mechanics for engineering students. Butterworth-heinemann, aerospace engineering. Editor H. D. Curtis, 181–229. doi:10.1016/B978-0-12-824025-0.00004-0

CrossRef Full Text | Google Scholar

Datta, R., Brewer, M. K., Couto, J. D., Eimer, J., Li, Y., Xu, Z., et al. (2024). Cosmology large angular scale surveyor (class): 90 ghz telescope pointing, beam profile, window function, and polarization performance. Astrophysical J. Suppl. Ser. 273, 26. doi:10.3847/1538-4365/ad50a0

CrossRef Full Text | Google Scholar

Galitzki, N., Tsan, T., Spisak, J., Randall, M., Silva-Feaver, M., Seibert, J., et al. (2024). The simons observatory: design, integration, and testing of the small aperture telescopes

Google Scholar

[Dataset] Hanany, S., Alvarez, M., Artis, E., Ashton, P., Aumont, J., Aurlien, R., et al. (2019). Pico: probe of inflation and cosmic origins

Google Scholar

Hui, H., Ade, P. A. R., Ahmed, Z., Aikin, R., Alexander, K. D., Barkats, D., et al. (2018). “Bicep array: a multi-frequency degree-scale cmb polarimeter,” in Millimeter, submillimeter, and far-infrared detectors and instrumentation for astronomy IX. Editors J. Zmuidzinas, and J.-R. Gao, 49, 49. doi:10.1117/12.2311725

CrossRef Full Text | Google Scholar

Johnson, B. R., Vourch, C. J., Drysdale, T. D., Kalman, A., Fujikawa, S., Keating, B., et al. (2015). A cubesat for calibrating ground-based and sub-orbital millimeter-wave polarimeters (calsat). J. Astronomical Instrum. 04, 1550007. doi:10.1142/S2251171715500075

CrossRef Full Text | Google Scholar

Mejía Jirón, L. F. (2022). Satélite de calibración para experimentos ultrasensibles de la polarización del fondo cósmico de microondas desde tierra. Master’s thesis. Santander: University of Cantabria (UC).

Google Scholar

Mennella, A., Arnold, K., Azzoni, S., Baccigalupi, C., Banday, A., Barreiro, R. B., et al. (2023). The European low frequency survey

Google Scholar

Qu, F. J., Sherwin, B. D., Madhavacheril, M. S., Han, D., Crowley, K. T., Abril-Cabezas, I., et al. (2024). The atacama cosmology telescope: a measurement of the DR6 CMB lensing power spectrum and its implications for structure growth. ApJ 962, 112. doi:10.3847/1538-4357/acfe06

CrossRef Full Text | Google Scholar

Ritacco, A., Adam, R., Ade, P., Ajeddig, H., André, P., Artis, E., et al. (2022). Crab nebula at 260 ghz with the nika2 polarimeter: implications for the polarization angle calibration of future cmb experiments. EPJ Web Conf. 257, 00042. doi:10.1051/epjconf/202225700042

CrossRef Full Text | Google Scholar

Ritacco, A., Bizzarri, L., Savorgnano, S., Boulanger, F., Pérault, M., Treuttel, J., et al. (2024). Absolute reference for microwave polarization experiments. The cosmocal project and its proof of concept. Publ. Astronomical Soc. Pac. 136, 115001. doi:10.1088/1538-3873/ad8aed

CrossRef Full Text | Google Scholar

Rubiño-Martín, J. A., Génova-Santos, R., Rebolo, R., Aguiar, C.-C. J. M., Gómez-Reñasco, F., Gutiérrez, C., et al. (2017). “The QUIJOTE experiment: project status and first scientific results,” in Highlights on Spanish astrophysics IX. Editors S. Arribas, A. Alonso-Herrero, F. Figueras, C. Hernández-Monteagudo, A. Sánchez-Lavega, and S. Pérez-Hoyos, 99–107.

Google Scholar

Sobrin, J. A., Anderson, A. J., Bender, A. N., Benson, B. A., Dutcher, D., Foster, A., et al. (2022). The design and integrated performance of SPT-3G. ApJS 258, 42. doi:10.3847/1538-4365/ac374f

CrossRef Full Text | Google Scholar

Soneira Landín, C. (2023). Fuente de calibración embarcada en satélite para experimentos del Fondo Cósmico de Microondas desde tierra. Master’s thesis. Santander: University of Cantabria (UC).

Google Scholar

Ward, J. T., Austermann, J., Beall, J. A., Choi, S. K., Crowley, K. T., Devlin, M. J., et al. (2016). “Mechanical designs and development of TES bolometer detector arrays for the advanced ACTPol experiment,” in Millimeter, submillimeter, and far-infrared detectors and instrumentation for astronomy VIII. Editors W. S. Holland, and J. Zmuidzinas (Bellingham, WA: Society of Photo-Optical Instrumentation Engineers (SPIE)), 9914. doi:10.1117/12.2233746

CrossRef Full Text | Google Scholar

Xu, Z., Adachi, S., Ade, P., Beall, J. A., Bhandarkar, T., Bond, J. R., et al. (2021). The simons observatory: the large aperture telescope (lat). Res. Notes AAS 5, 100. doi:10.3847/2515-5172/abf9ab

CrossRef Full Text | Google Scholar