Closure Statistics in Interferometric Data
Open accessAbstract
Interferometric visibilities, reflecting the complex correlations between signals recorded at antennas in an interferometric array, carry information about the angular structure of a distant source. While unknown antenna gains in both amplitude and phase can prevent direct interpretation of these measurements, certain combinations of visibilities called closure phases and closure amplitudes are independent of antenna gains and provide a convenient set of robust observables. However, these closure quantities have subtle noise properties and are generally both linearly and statistically dependent. These complications have obstructed the proper use of closure quantities in interferometric analysis, and they have obscured the relationship between analysis with closure quantities and other analysis techniques such as self calibration. We review the statistics of closure quantities, noting common pitfalls that arise when approaching low signal to noise due to the nonlinear propagation of statistical errors. We then develop a strategy for isolating and fitting to the independent degrees of freedom captured by the closure quantities through explicit construction of linearly independent sets of quantities along with their noise covariance in the Gaussian limit, valid for moderate signal to noise, and we demonstrate that model fits have biased posteriors when this covariance is ignored. Finally, we introduce a unified procedure for fitting to both closure information and partially calibrated visibilities, and we demonstrate both analytically and numerically the direct equivalence of inference based on closure quantities to that based on self calibration of complex visibilities with unconstrained antenna gains.
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A full set of closure phases is highly redundant (not linearly independent).
“Because a full set of closure phases is highly redundant ( i.e., the set is not linearly independent; see Blackburn et al. 2020 ) , we use eht-imaging ( Chael et al. 2016, 2018 ) to construct a minimal nonredundant set within every snapshot.”
From First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass (2022) · cites this paper as Blackburn et al. 2020
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Self-citation
- Authors
- Blackburn, L., Pesce, D. W., Johnson, M. D., Wielgus, M., Chael, A. A., Christian, P., & Doeleman, S. S.
- Affiliations
- Harvard University (US)
- Princeton University (US)
- University of Arizona (US)
- ORCID
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 2020-05-01
- Volume
- 894
- Issue
- 1
- Pages
- 31
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W3022389365
- Cited by
- 71
- References
- 25
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 12 · 2023: 6 · 2022: 16 · 2021: 14 · 2020: 10
- FWCI
- 5.27
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- The Astrophysical Journal (publishedVersion)
- UA Campus Repository (The University of Arizona) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- NSF (AST-1440254, AST-1614868)
- GBMF (GBMF-5278)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Radio Astronomy Observations and Technology
- Physical Sciences › Physics and Astronomy › Instrumentation › Astronomy and Astrophysical Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Adaptive optics and wavefront sensing
- Keywords
- closure phases, interferometric visibility, antenna gain calibration, self-calibration, noise covariance, Gaussian approximation, radio interferometry
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