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Characterization of the Polarization Beam Response of SPT-3G Using Point Sources

This paper presents direct measurements of the SPT-3G camera's polarized beam response using 100 extragalactic point sources, revealing minimal sidelobe depolarization and offering alternative explanations for frequency-dependent residuals previously observed in cosmological power spectrum analyses.

Original authors: T. de Haan, M. Archipley, N. Huang, A. J. Anderson, B. Ansarinejad, L. Balkenhol, D. R. Barron, K. Benabed, A. N. Bender, B. A. Benson, F. Bianchini, L. E. Bleem, S. Bocquet, F. R. Bouchet, L. Bryant

Published 2026-07-21

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CC BY 4.0

Original authors: T. de Haan, M. Archipley, N. Huang, A. J. Anderson, B. Ansarinejad, L. Balkenhol, D. R. Barron, K. Benabed, A. N. Bender, B. A. Benson, F. Bianchini, L. E. Bleem, S. Bocquet, F. R. Bouchet, L. Bryant, E. Camphuis, M. G. Campitiello, J. E. Carlstrom, J. Carron, C. L. Chang, P. Chaubal, P. M. Chichura, A. Chokshi, T. -L. Chou, A. Coerver, T. M. Crawford, C. Daley, K. R. Dibert, M. A. Dobbs, M. Doohan, A. Doussot, D. Dutcher, W. Everett, C. Feng, K. R. Ferguson, N. C. Ferree, K. Fichman, A. Foster, S. Galli, A. E. Gambrel, R. W. Gardner, F. Ge, N. Goeckner-Wald, R. Gualtieri, F. Guidi, S. Guns, N. W. Halverson, E. Hivon, A. Y. Q. Ho, G. P. Holder, W. L. Holzapfel, J. C. Hood, A. Hryciuk, F. Keruzore, A. R. Khalife, L. Knox, M. Korman, K. Kornoelje, C. -L. Kuo, K. Levy, Y. Li, A. E. Lowitz, C. Lu, G. P. Lynch, T. J. Maccarone, A. S. Maniyar, E. S. Martsen, F. Menanteau, M. Millea, J. Montgomery, Y. Nakato, T. Natoli, G. I. Noble, Y. Omori, A. Ouellette, Z. Pan, P. Paschos, K. A. Phadke, A. W. Pollak, K. Prabhu, W. Quan, M. Rahimi, A. Rahlin, C. L. Reichardt, M. Rouble, J. E. Ruhl, E. Schiappucci, A. C. Silva Oliveira, A. Simpson, J. A. Sobrin, A. A. Stark, J. Stephen, C. Tandoi, B. Thorne, C. Trendafilova, C. Umilta, J. D. Vieira, A. G. Vieregg, A. Vitrier, Y. Wan, N. Whitehorn, W. L. K. Wu, M. R. Young, J. A. Zebrowski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, glowing baby picture, taken just 380,000 years after the Big Bang. This "baby picture" is called the Cosmic Microwave Background (CMB), and it's the oldest light in existence. But this light isn't just a simple glow; it's polarized, meaning the light waves are vibrating in specific directions, like a rope being shaken up and down versus side to side. By studying these vibrations, scientists can decode secrets about how the universe began, how it expanded, and what invisible stuff (like dark matter) is holding it together.

However, reading this ancient message is incredibly difficult because our telescopes aren't perfect cameras. Just like a cheap pair of glasses might blur the edges of a picture or make a bright star look like a fuzzy blob with weird halos, a telescope's "beam" (its point spread function) can distort the light it collects. If the telescope smears the light in a way that accidentally changes the direction of the vibrations, it creates a fake signal that looks like a real cosmic mystery. To trust what we see in the sky, we have to know exactly how our telescope blurs things, down to the tiniest detail.

This is where the South Pole Telescope's third-generation camera, SPT-3G, comes in. It's a massive, high-tech eye staring at the sky from the bottom of the world, designed to map that cosmic baby picture with incredible precision. But there was a nagging question: when the telescope looks at the "halos" around bright stars (called sidelobes), does it smear the polarization just as much as it smears the brightness? Previous studies suggested the answer might be "no"—that the telescope might be "depolarizing" the light in those outer rings, effectively washing out the cosmic signal. If true, this would mean our previous maps of the universe were slightly off, and we needed to fix our math to see the truth.

In this paper, the team decided to stop guessing and start measuring. Instead of trying to infer the telescope's behavior from the complex cosmic background itself, they used 100 bright, distant galaxies as natural test lights. Think of these galaxies as lighthouses in a foggy sea. By looking at how the telescope sees the light from these lighthouses, the team could directly measure how the "fog" (the telescope's beam) affects the polarization. They built a sophisticated model to fit the data, essentially asking, "If we shine a polarized light here, what does the telescope see?"

The results were a surprise to the previous models. The team found that the telescope's sidelobes are actually very good at preserving polarization. They measured a value called $\beta_{pol}$ , which acts like a score for how well the telescope keeps the polarization intact in its outer rings. A score of 1.0 means perfect preservation, while 0.0 means total loss. Their measurements showed scores of $0.89 \pm 0.10$ at 95 GHz, $1.08 \pm 0.10$ at 150 GHz, and $0.90 \pm 0.22$ at 220 GHz. In plain English, these numbers are all very close to 1.0, suggesting that the telescope is not washing out the polarization in the way the previous cosmological analyses had feared.

This creates a bit of a detective story. Earlier studies, which looked at the entire cosmic background, had strongly suggested that the telescope was causing a problem (a "depolarization" effect) to make the data from different frequencies match up. But this new, direct measurement says, "Actually, the telescope is doing a great job." The authors explain that this isn't necessarily a contradiction, but rather a puzzle. The difference might be a statistical fluke, or it might mean that the mathematical models used to describe the telescope's beam need to be more sophisticated than the simple "on/off" switch they used before. It could also mean there are other hidden errors in the data that aren't related to the beam at all.

Ultimately, this paper doesn't say the universe is broken or that the telescope is perfect; it just says the specific fear that the telescope's outer rings are destroying the polarization signal is likely unfounded. The team validated their findings with rigorous tests, checking their math with different methods and even simulating the process to ensure they weren't fooling themselves. While the "why" behind the discrepancy with earlier studies remains an open question, the direct evidence is clear: the SPT-3G camera is holding onto the polarization of those distant lighthouses much better than we thought, giving us more confidence that the cosmic secrets we are trying to unlock are real, not just telescope artifacts.

Technical Summary: Characterization of the Polarization Beam Response of SPT-3G Using Point Sources

Problem Statement
Precise measurements of Cosmic Microwave Background (CMB) polarization require rigorous control of instrumental systematics. For the South Pole Telescope's third-generation camera (SPT-3G), which observes in three frequency bands (95, 150, and 220 GHz), the instrumental beam—the point spread function—directly affects CMB power spectrum measurements. While the central, diffraction-limited main beam is well-understood, the extended beam response (sidelobes) may possess polarization properties distinct from the main beam due to non-ideal optical effects such as scattering, reflections, and mirror imperfections.

Previous SPT-3G cosmological analyses (e.g., F. Ge et al. 2025; E. Camphuis et al. 2026) introduced a phenomenological parameter, $\beta_{pol}$ , to quantify the degree of polarization preserved in beam sidelobes. In this model, $\beta_{pol} = 1$ implies identical temperature and polarization beam responses, while $\beta_{pol} = 0$ implies the sidelobes are completely depolarized. Indirect constraints derived from CMB power spectrum consistency across frequency bands favored significant depolarization ( $\beta_{pol} < 1$ ), with best-fit values around 0.5–0.6. However, these constraints were derived indirectly by marginalizing over $\beta_{pol}$ within the cosmological analysis, potentially absorbing other frequency-dependent residuals. A direct, independent measurement of $\beta_{pol}$ is required to test this interpretation and provide robust priors for future cosmological constraints.

Methodology
This work presents the first direct measurements of $\beta_{pol}$ using observations of 100 bright, polarized extragalactic point sources observed by SPT-3G during the 2019–2023 seasons.

Data Processing: Time-ordered data (TOD) were processed into Stokes $T, Q, U$ maps. A critical step involved the deconvolution of bolometer time constants at the TOD level to separate optical beam properties from detector response characteristics. Instrumental temperature-to-polarization leakage was removed using empirically constructed templates. These templates were generated via an iterative procedure: normalizing source maps by peak temperature flux, averaging to isolate static leakage patterns, fitting and subtracting the best-fit astrophysical polarization models, and reconstructing the templates.
Beam Parameterization: The analysis employs two beam models:
1. A flexible, data-driven regularized B-spline model (hybridized with a central Gaussian) to characterize the radial profile without strong physical assumptions.
2. The $\beta_{pol}$ model, which interpolates between a physical-optics main beam ( $B_{main}$ ) and a full beam profile ( $B_{full}$ ) measured in temperature (combining point source and Saturn data). The polarization beam is modeled as $B_{pol}(r) = (1 - \beta_{pol})B_{main}(r) + \beta_{pol}B_{full}(r)$ .
Fitting Framework: A simultaneous fitting framework optimizes both beam parameters and source properties (position and Stokes amplitudes) across all 100 sources. The likelihood is formulated in Fourier space using a precision matrix that accounts for instrumental noise, primary CMB fluctuations, and band-to-band correlations. The analysis utilizes JAX for automatic differentiation and GPU acceleration to handle the high-dimensional parameter space (up to ~1600 parameters).
Uncertainty and Validation: Parameter uncertainties are estimated using bootstrap resampling (200 realizations). The robustness of the results is validated through extensive systematic tests, including:
- Comparison of Fourier-space vs. real-space $\chi^2$ formulations.
- Bayesian posterior sampling (MCLMC) vs. frequentist optimization.
- Variations in leakage template construction (weighting schemes).
- Alternative covariance matrix models (white noise, data-driven).
- Temperature beam validation (fitting $\beta_T$ to temperature data, where $\beta_T$ is expected to be 1.0).

Key Results
The direct measurements yield the following values for $\beta_{pol}$ :

95 GHz: $0.89 \pm 0.10$
150 GHz: $1.08 \pm 0.10$
220 GHz: $0.90 \pm 0.22$

These results indicate minimal sidelobe depolarization, consistent with $\beta_{pol} = 1$ (identical temperature and polarization beams) within approximately $1\sigma$ for all bands. The joint measurement of the three bands deviates from the $\beta_{pol}=1$ hypothesis by a Mahalanobis distance of $1.5\sigma$ (p-value 0.54), indicating statistical consistency with no depolarization.

The results are robust across all systematic variations. For instance, the Bayesian posterior means align closely with the frequentist maximum-likelihood estimates, and different leakage weighting schemes produce variations $< 0.2\sigma$ . The temperature beam validation confirmed the methodology's accuracy, recovering $\beta_T \approx 1.0$ with residuals consistent with numerical limitations.

Significance and Implications
The paper identifies an apparent discrepancy of $1.3\sigma$ between these direct measurements (favoring $\beta_{pol} \approx 1$ ) and the indirect constraints from previous cosmological analyses (favoring $\beta_{pol} \approx 0.5$ ). The authors attribute this difference to the fact that the point-source analysis derives its constraining power from higher multipoles than the power spectrum analysis.

The paper concludes that the frequency-dependent residuals observed in previous power spectrum analyses can be explained by one of three possibilities:

A statistical fluctuation in the cosmological analysis.
The need for more sophisticated polarized beam models beyond the simple $\beta_{pol}$ parameterization.
The presence of systematics other than beam depolarization.

This work provides a critical, independent check on instrumental systematics, demonstrating that the SPT-3G polarized beam response is largely consistent with the temperature response, thereby challenging the interpretation that significant sidelobe depolarization is the sole driver of inter-frequency power spectrum inconsistencies.

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