Polarization calibration of interferometric observations is a costly procedure and, in some cases (e.g., a limited coverage of parallactic angle for the calibrator), it may not be possible to be performed. To avoid this worst-case scenario and expand the possibilities for the exploitation of polarization interferometric observations, the use of a new set of calibration-independent quantities (the closure traces) has been proposed. However, these quantities suffer from some degeneracies, so their use in practical situations may be rather limited. In this paper, we explore the use of closure traces on simulated and real observations, and show that (with the proper selection of fitting parameters) it is possible to retrieve information of the source polarization using only closure traces and constrain spatially resolved polarization. We carry out the first application of closure traces to the brightness modelling of real data, using the ALMA observations of M87 conducted on the April 2017 EHT campaign, quantifying a gradient in the Faraday rotation (FR) along the source structure (the M87 jet). This work opens the possibility to apply similar strategies to observations from any kind of interferometer (with a special focus on VLBI), from which quantities like differential Rotation Measure (RM) or the spatially resolved polarization can be retrieved.
Closure phases are critical in astronomical interferometry. However, their uncertainties are difficult to compute numerically. We provide a method to efficiently compute interferometric closure phase distributions in terms of an approximate distribution that is valid in the low signal-to-noise ratio regime. This is done by first showing that the true phase distribution is well approximated by the von Mises distribution, then performing a convolution of three von Mises distributions. The resulting approximation is superior than the normal distribution for all signal-to-noise ratios and, being f…
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 dependen…
Interferometric imaging now achieves angular resolutions as fine as 10 microarcsec, probing scales that are inaccessible to single telescopes. Traditional synthesis imaging methods require calibrated visibilities; however, interferometric calibration is challenging, especially at high frequencies. Nevertheless, most studies present only a single image of their data after a process of "self-calibration," an iterative procedure where the initial image and calibration assumptions can significantly influence the final image. We present a method for efficient interferometric imaging directly using …
New massively redundant low frequency arrays allow for a novel investigation of closure relations in interferometry. We employ commissioning data from the Hydrogen Epoch of Reionization Array to investigate closure quantities in this densely packed grid array of 14m antennas operating at 100 MHz to 200 MHz. We investigate techniques that utilize closure phase spectra for redundant triads to estimate departures from redundancy for redundant baseline visibilities. We find a median absolute deviation from redundancy in closure phase across the observed frequency range of about 4.5deg. This value …
A Formalism for Calibrating the Instrumental Polarization of Radio Interferometric Arrays at Meter Wavelengths using Unpolarized Sky: A Demonstration using the MWA Observations
Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one dimensional interferometric intensity measurement equation, albeit in a different Fourier space. As a result, familiar concepts in two dimensional intensity interferometry designed to correctly account for a range of instrumental conditions can be translated to the analysis of Faraday dispersion. In particular, we show how to model the effect of channel averaging during Faraday…
Closure phase is the phase of a closed-loop product of correlations in a $\ge 3$-element interferometer array. Its invariance to element-based phase corruption makes it invaluable for interferometric applications that otherwise require high-accuracy phase calibration. However, its understanding has remained mainly mathematical and limited to the aperture plane (Fourier dual of image plane). Here, we lay the foundations for a geometrical insight. we show that closure phase and its invariance to element-based corruption and to translation are intricately related to the conserved properties (shap…
For transient sources with timescales of 1-100 seconds, standardized imaging for all observations at each time step become impossible as large modern interferometers produce significantly large data volumes in this observation time frame. Here we propose a method based on machine learning and using interferometric closure products as input features to detect transient source candidates directly from the spatial frequency domain without imaging. We train a simple neural network classifier on a synthetic dataset of Noise/Transient/RFI events, which we construct to tackle the lack of labelled dat…
A New Method for Aperture Masking Interferometric Imaging: Demonstration with the JWST
National Radio Astronomy Observatory（国家射电天文台）；Astrophysics Group, Cavendish Laboratory, Univ. of Cambridge（剑桥大学卡文迪许实验室天体物理组）；ALBA - CELLS Synchrotron Radiation Facility（阿尔巴-CELLS同步辐射设施）；Commonwealth Scientific and Industrial Research Organisation (CSIRO), Space & Astronomy（联邦科学与工业研究组织（CSIRO）空间与天文部门）
The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope collaboration utilized the novel concept of "closure traces", that are immune to element-based aberrations. We take a fundamentally new approach to this promising tool of polarimetric VLBI, using ideas from the geometric phase and gauge theories. The multiplicative distortion of polarized signals at the individual elements are represented as gauge transformations by general $2\times 2$ complex matrices, so the closure traces now appear as gauge-invariant qu…
We present the calibration and reduction of Event Horizon Telescope (EHT) 1.3mm radio wavelength observations of the supermassive black hole candidate at the center of the radio galaxy M87 and the quasar 3C 279, taken during the 2017 April 5-11 observing campaign. These global very long baseline interferometric observations include for the first time the highly sensitive Atacama Large Millimeter/submillimeter Array (ALMA); reaching an angular resolution of 25 micro-as, with characteristic sensitivity limits of ~1 mJy on baselines to ALMA and ~10 mJy on other baselines. The observations present…
