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Recovering unbiased CMB polarization maps using modern ground-based experiments with minimal assumptions about atmospheric emission

Simon Biquard1,2,3,*, Josquin Errard1, and Radek Stompor1,2

  • *Contact author: simon.biquard@manchester.ac.uk
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Phys. Rev. D 112, 123511 – Published 4 December, 2025

DOI: https://doi.org/10.1103/wdsm-kbhn

Abstract

We present a study of unbiased reconstruction of cosmic microwave background (CMB) polarization maps from data collected by modern ground-based observatories. Atmospheric emission is a major source of correlated noise in such experiments, complicating the recovery of faint cosmological signals. We consider estimators that require only minimal assumptions about the properties of the unpolarized atmospheric emission, instead exploiting hardware solutions commonly implemented in modern instruments, such as pairs of orthogonal antennas in each focal plane pixel, interleaving of the antenna orientation from pixel to pixel, and polarization signal modulation via a continuously rotating half-wave plate (HWP). We focus on two techniques: (i) statistical downweighting of low-frequency atmospheric signals and (ii) pair differencing (PD), which involves differencing the signals collected by two detectors in the same focal plane pixel. We compare their performance and contrast them with the idealized case where the atmospheric signal is perfectly known and can be cleanly subtracted. We show that PD can be derived from the maximum likelihood principle under very general assumptions about the atmospheric signal and is therefore optimal in terms of map sensitivity for essentially any such signal. Remarkably, in the absence of instrumental systematics, but with reasonable variations of detector noise properties, PD yields polarized sky maps with noise levels only slightly worse (typically a few percent) than the ideal reference case. While the downweighting method could in principle match or surpass this performance, it requires highly accurate models of the atmospheric signal, which are not readily available. The performance of PD will be affected by instrumental systematics and those leaking the atmospheric signal to the difference time stream may have particularly adverse impact. However, we expect that some of these effects, as shown in the case of gain mismatch, are efficiently mitigated by a continuously rotating HWP and, therefore, that in the context of modern CMB experimental setups PD could provide a competitive, numerically robust, and efficient practical solution for CMB polarization mapmaking without the need for atmospheric modeling.

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References (70)

  1. P. Ade, J. Aguirre, Z. Ahmed, S. Aiola, A. Ali, D. Alonso, M. A. Alvarez, K. Arnold, P. Ashton, J. Austermann et al., J. Cosmol. Astropart. Phys. 02 (2019) 056.
  2. E. Allys, K. Arnold, J. Aumont, R. Aurlien, S. Azzoni, C. Baccigalupi, A. J. Banday, R. Banerji, R. B. Barreiro et al. (LiteBIRD Collaboration), Prog. Theor. Exp. Phys. 2023, 042F01 (2023).
  3. P. A. R. Ade, M. Aguilar, Y. Akiba, K. Arnold, C. Baccigalupi, D. Barron, D. Beck, F. Bianchini, D. Boettger et al. (Polarbear Collaboration), Astrophys. J. 848, 121 (2017).
  4. P. A. R. Ade, Z. Ahmed, R. W. Aikin, K. D. Alexander, D. Barkats, S. J. Benton, C. A. Bischoff, J. J. Bock, R. Bowens-Rubin et al. (Keck Array and BICEP2 Collaborations), Phys. Rev. Lett. 121, 221301 (2018).
  5. R. Keisler, S. Hoover, N. Harrington, J. W. Henning, P. A. R. Ade, K. A. Aird, J. E. Austermann, J. A. Beall, A. N. Bender, B. A. Benson et al., Astrophys. J. 807, 151 (2015).
  6. U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 (1997).
  7. R. Brout, F. Englert, and E. Gunzig, Ann. Phys. (N.Y.) 115, 78 (1978).
  8. A. H. Guth, Phys. Rev. D 23, 347 (1981).
  9. A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).
  10. P. A. R. Ade, Z. Ahmed, M. Amiri, D. Barkats, R. B. Thakur, D. Beck, C. Bischoff, J. J. Bock, H. Boenish et al. (BICEP/Keck Collaboration), Phys. Rev. Lett. 127, 151301 (2021).
  11. M. Tristram, A. J. Banday, K. M. Górski, R. Keskitalo, C. R. Lawrence, K. J. Andersen, R. B. Barreiro, J. Borrill, L. P. L. Colombo, H. K. Eriksen et al., Phys. Rev. D 105, 083524 (2022).
  12. P. A. R. Ade, R. W. Aikin, M. Amiri, D. Barkats, S. J. Benton, C. A. Bischoff, J. J. Bock, J. A. Brevik, I. Buder et al. (BICEP2 Collaboration), Astrophys. J. 792, 62 (2014).
  13. P. A. R. Ade, Y. Akiba, A. E. Anthony, K. Arnold, M. Atlas, D. Barron, D. Boettger, J. Borrill, S. Chapman et al. (Polarbear Collaboration), Astrophys. J. 794, 171 (2014).
  14. F. Ge, M. Millea, E. Camphuis, C. Daley, N. Huang, Y. Omori, W. Quan, E. Anderes, A. J. Anderson, B. Ansarinejad et al., Phys. Rev. D 111, 083534 (2025).
  15. Y. Li, J. R. Eimer, K. Osumi, J. W. Appel, M. K. Brewer, A. Ali, C. L. Bennett, S. M. Bruno, R. Bustos, D. T. Chuss et al., Astrophys. J. 956, 77 (2023).
  16. Y. Li, J. Eimer, J. Appel, C. Bennett, M. Brewer, S. M. Bruno, R. Bustos, C. Chan, D. Chuss, J. Cleary et al., Astrophys. J. 986, 111 (2025).
  17. C. Hervías-Caimapo, K. Wolz, A. La Posta, S. Azzoni, D. Alonso, K. Arnold, C. Baccigalupi, S. Biquard, M. L. Brown, E. Calabrese et al., J. Cosmol. Astropart. Phys. 06 (2025) 055.
  18. R. Stompor, A. Balbi, J. D. Borrill, P. G. Ferreira, S. Hanany, A. H. Jaffe, A. T. Lee, S. Oh, B. Rabii, P. L. Richards et al., Phys. Rev. D 65, 022003 (2001).
  19. E. Keihänen, R. Keskitalo, H. Kurki-Suonio, T. Poutanen, and A.-S. Sirvio, Astron. Astrophys. 510, A57 (2010).
  20. R. Dünner, M. Hasselfield, T. A. Marriage, J. Sievers, V. Acquaviva, G. E. Addison, P. A. R. Ade, P. Aguirre, M. Amiri, J. W. Appel et al., Astrophys. J. 762, 10 (2012).
  21. D. Poletti, G. Fabbian, M. Le Jeune, J. Peloton, K. Arnold, C. Baccigalupi, D. Barron, S. Beckman, J. Borrill, S. Chapman et al., Astron. Astrophys. 600, A60 (2017).
  22. H. El Bouhargani, A. Jamal, D. Beck, J. Errard, L. Grigori, and R. Stompor, Astron. Comput. 39, 100576 (2022).
  23. C. Pryke, P. Ade, J. Bock, M. Bowden, M. L. Brown, G. Cahill, P. G. Castro, S. Church, T. Culverhouse et al. (QUaD Collaboration), Astrophys. J. 692, 1247 (2009).
  24. J. A. Zebrowski, C. L. Reichardt, A. J. Anderson, B. Ansarinejad, M. Archipley, L. Balkenhol, P. Barry, K. Benabed, A. N. Bender, B. A. Benson et al., arXiv:2505.02827.
  25. W. Hu, M. M. Hedman, and M. Zaldarriaga, Phys. Rev. D 67, 043004 (2003).
  26. D. O’Dea, A. Challinor, and B. R. Johnson, Mon. Not. R. Astron. Soc. 376, 1767 (2007).
  27. M. Shimon, B. Keating, N. Ponthieu, and E. Hivon, Phys. Rev. D 77, 083003 (2008).
  28. P. A. R. Ade, R. W. Aikin, D. Barkats, S. J. Benton, C. A. Bischoff, J. J. Bock, J. A. Brevik, I. Buder, E. Bullock et al. (BICEP2 Collaboration), Astrophys. J. 814, 110 (2015).
  29. D. B. Thomas, N. McCallum, and M. L. Brown, Mon. Not. R. Astron. Soc. 491, 1960 (2020).
  30. G. Hinshaw, C. Barnes, C. L. Bennett, M. R. Greason, M. Halpern, R. S. Hill, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer et al., Astrophys. J. Suppl. Ser. 148, 63 (2003).
  31. B. R. Johnson, J. Collins, M. E. Abroe, P. a. R. Ade, J. Bock, J. Borrill, A. Boscaleri, P. de Bernardis, S. Hanany, A. H. Jaffe et al., Astrophys. J. 665, 42 (2007).
  32. O. P. Lay and N. W. Halverson, Astrophys. J. 543, 787 (2000).
  33. C. L. Kuo, P. a. R. Ade, J. J. Bock, C. Cantalupo, M. D. Daub, J. Goldstein, W. L. Holzapfel, A. E. Lange, M. Lueker, M. Newcomb et al., Astrophys. J. 600, 32 (2004).
  34. J. Errard, P. A. R. Ade, Y. Akiba, K. Arnold, M. Atlas, C. Baccigalupi, D. Barron, D. Boettger, J. Borrill, S. Chapman et al., Astrophys. J. 809, 63 (2015).
  35. S. Naess, Y. Guan, A. J. Duivenvoorden, M. Hasselfield, Y. Wang, I. Abril-Cabezas, G. E. Addison, P. A. R. Ade, S. Aiola, T. Alford et al., arXiv:2503.14451.
  36. S. Hanany and P. Rosenkranz, New Astron. Rev. 47, 1159 (2003).
  37. S. Spinelli, G. Fabbian, A. Tartari, M. Zannoni, and M. Gervasi, Mon. Not. R. Astron. Soc. 414, 3272 (2011).
  38. S. Takakura, M. A. O. Aguilar-Faúndez, Y. Akiba, K. Arnold, C. Baccigalupi, D. Barron, D. Beck, F. Bianchini, D. Boettger, J. Borrill et al., Astrophys. J. 870, 102 (2019).
  39. Y. Li, J. W. Appel, C. L. Bennett, R. Bustos, D. T. Chuss, J. Cleary, J. D. Couto, S. Dahal, R. Datta, R. Dünner et al., Astrophys. J. 958, 154 (2023).
  40. A. Coerver, J. A. Zebrowski, S. Takakura, W. L. Holzapfel, P. A. R. Ade, A. J. Anderson, Z. Ahmed, B. Ansarinejad, M. Archipley, L. Balkenhol et al., Astrophys. J. 982, 15 (2025).
  41. T. E. Montroy, P. a. R. Ade, J. J. Bock, J. R. Bond, J. Borrill, A. Boscaleri, P. Cabella, C. R. Contaldi, B. P. Crill, P. de Bernardis et al., Astrophys. J. 647, 813 (2006).
  42. K. W. Yoon, P. a. R. Ade, D. Barkats, J. O. Battle, E. M. Bierman, J. J. Bock, J. A. Brevik, H. C. Chiang, A. Crites, C. D. Dowell et al., in Millimeter and Submillimeter Detectors and Instrumentation for Astronomy III (SPIE, Bellingham, 2006), Vol. 6275, pp. 508–525.
  43. W. C. Jones, T. E. Montroy, B. P. Crill, C. R. Contaldi, T. S. Kisner, A. E. Lange, C. J. MacTavish, C. B. Netterfield, and J. E. Ruhl, Astron. Astrophys. 470, 771 (2007).
  44. C. L. Kuo, J. J. Bock, J. A. Bonetti, J. Brevik, G. Chattopadhyay, P. K. Day, S. Golwala, M. Kenyon, A. E. Lange, H. G. LeDuc et al., in Millimeter and Submillimeter Detectors and Instrumentation for Astronomy IV (SPIE, Bellingham, 2008), Vol. 7020, pp. 415–428.
  45. J. R. Hinderks, P. Ade, J. Bock, M. Bowden, M. L. Brown, G. Cahill, J. E. Carlstrom, P. G. Castro, S. Church, T. Culverhouse et al., Astrophys. J. 692, 1221 (2009).
  46. Z. Ahmed, M. Amiri, S. J. Benton, J. J. Bock, R. Bowens-Rubin, I. Buder, E. Bullock, J. Connors, J. P. Filippini, J. A. Grayson et al., in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII (SPIE, Bellingham, 2014), Vol. 9153, pp. 540–551.
  47. S. W. Henderson, R. Allison, J. Austermann, T. Baildon, N. Battaglia, J. A. Beall, D. Becker, F. D. Bernardis, J. R. Bond, E. Calabrese et al., J. Low Temp. Phys. 184, 772 (2016).
  48. C. M. Posada, P. A. R. Ade, Z. Ahmed, K. Arnold, J. E. Austermann, A. N. Bender, L. E. Bleem, B. A. Benson, K. Byrum, J. E. Carlstrom et al., Supercond. Sci. Technol. 28, 094002 (2015).
  49. N. Stebor, P. Ade, Y. Akiba, C. Aleman, K. Arnold, C. Baccigalupi, B. Barch, D. Barron, S. Beckman, A. Bender et al., in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VIII (SPIE, Bellingham, 2016), Vol. 9914, pp. 363–371.
  50. A. Kusaka, T. Essinger-Hileman, J. W. Appel, P. Gallardo, K. D. Irwin, N. Jarosik, M. R. Nolta, L. A. Page, L. P. Parker, S. Raghunathan et al., Rev. Sci. Instrum. 85, 024501 (2014).
  51. A. Ritacco, N. Ponthieu, A. Catalano, R. Adam, P. Ade, P. André, A. Beelen, A. Benoît, A. Bideaud, N. Billot et al., Astron. Astrophys. 599, A34 (2017).
  52. S. Takakura, M. Aguilar, Y. Akiba, K. Arnold, C. Baccigalupi, D. Barron, S. Beckman, D. Boettger, J. Borrill, S. Chapman et al., J. Cosmol. Astropart. Phys. 05(2017) 008.
  53. T. Essinger-Hileman, A. Kusaka, J. W. Appel, S. K. Choi, K. Crowley, S. P. Ho, N. Jarosik, L. A. Page, L. P. Parker, S. Raghunathan et al., Rev. Sci. Instrum. 87, 094503 (2016).
  54. M. L. Brown, A. Challinor, C. E. North, B. R. Johnson, D. O’Dea, and D. Sutton, Mon. Not. R. Astron. Soc. 397, 634 (2009).
  55. M. Rashid, M. L. Brown, and D. B. Thomas, Mon. Not. R. Astron. Soc. 532, 2309 (2024).
  56. T. W. Morris, E. Battistelli, R. Bustos, S. K. Choi, A. J. Duivenvoorden, J. Dunkley, R. Dünner, M. Halpern, Y. Guan, J. van Marrewijk et al., Phys. Rev. D 111, 082001 (2025).
  57. K. M. Gorski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelman, Astrophys. J. 622, 759 (2005).
  58. J. R. Stevens, N. Goeckner-Wald, R. Keskitalo, N. McCallum, A. Ali, J. Borrill, M. L. Brown, Y. Chinone, P. A. Gallardo, A. Kusaka et al., in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX (2018), p. 136, arXiv:1808.05131.
  59. D. Alonso, J. Sanchez, and A. Slosar (LSST Dark Energy Science Collaboration), Mon. Not. R. Astron. Soc. 484, 4127 (2019).
  60. H. El Bouhargani, Ph.D. thesis, Université Paris Cité, 2021.
  61. A. Kusaka, J. Appel, T. Essinger-Hileman, J. A. Beall, L. E. Campusano, H.-M. Cho, S. K. Choi, K. Crowley, J. W. Fowler, P. Gallardo et al., J. Cosmol. Astropart. Phys. 09 (2018) 005.
  62. P. A. R. Ade, R. W. Aikin, D. Barkats, S. J. Benton, C. A. Bischoff, J. J. Bock, J. A. Brevik, I. Buder, E. Bullock et al. (BICEP2 Collaboration), Phys. Rev. Lett. 112, 241101 (2014).
  63. N. McCallum, D. B. Thomas, M. L. Brown, and N. Tessore, Mon. Not. R. Astron. Soc. 501, 802 (2020).
  64. M. Monelli, E. Komatsu, T. Ghigna, T. Matsumura, G. Pisano, and R. Takaku, J. Cosmol. Astropart. Phys. 05 (2024) 018.
  65. G. Patanchon, H. Imada, H. Ishino, and T. Matsumura, J. Cosmol. Astropart. Phys. 04 (2024) 074.
  66. A. Zonca, L. P. Singer, D. Lenz, M. Reinecke, C. Rosset, E. Hivon, and K. M. Gorski, J. Open Source Softwaare 4, 1298 (2019).
  67. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith et al., Nature (London) 585, 357 (2020).
  68. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright et al., Nat. Methods 17, 261 (2020).
  69. J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007).
  70. M. L. Waskom, J. Open Source Softwaare 6, 3021 (2021).

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Phys. Rev. D 112, 123511– Published 4 December, 2025
  • Received 25 September 2025
  • Accepted 17 November 2025
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