Closure Statistics in Interferometric Data
Closure Statistics in Interferometric Data
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DOI：
10.3847/1538-4357/ab8469
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
L. Blackburn;D. Pesce;Michael D. Johnson;M. Wielgus;A. Chael;P. Christian;S. Doeleman
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文献类型：
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作者：
L. Blackburn;D. Pesce;Michael D. Johnson;M. Wielgus;A. Chael;P. Christian;S. Doeleman
干涉能见度反映了干涉阵列中天线记录的信号之间的复杂相关性，它携带有关远距离源的角度结构的信息。虽然幅度和相位方面的未知天线增益可能会妨碍对这些测量的直接解释，但称为闭合相位和闭合幅度的某些可见性组合与天线增益无关，并提供一组方便的稳健可观测值。然而，这些闭合量具有微妙的噪声特性，并且通常是线性和统计相关的。这些复杂情况阻碍了干涉分析中闭合量的正确使用，并且模糊了闭合量分析与自校准等其他分析技术之间的关系。我们回顾了闭包量的统计数据，注意到由于统计误差的非线性传播而接近低信噪比时出现的常见陷阱。然后，我们开发了一种策略，通过显式构造线性独立的量集及其在高斯极限内的噪声协方差，来隔离和拟合闭包量捕获的独立自由度，这对中等信噪比有效，并且我们证明，当忽略此协方差时，模型拟合具有有偏后验。最后，我们引入了一个统一的程序来拟合闭合信息和部分校准的能见度，并且我们在分析和数值上证明了基于闭合量的推理与基于具有无约束天线增益的复杂能见度的自校准的推理的直接等价性。
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.