This is the third installment in a series of papers in which we investigate calibration artefacts. Calibration artefacts (also known as ghosts or spurious sources) are created when we calibrate with an incomplete model. In the first two papers of this series we developed a mathematical framework which enabled us to study the ghosting mechanism itself. An interesting concomitant of the second paper was that ghosts appear in symmetrical pairs. This could possibly account for spurious symmetrization. Spurious symmetrization refers to the appearance of a spurious source (the anti-ghost) symmetrically opposite an unmodelled source around a modelled source. The analysis in the first two papers indicates that the anti-ghost is usually very faint, in particular when a large number of antennas are used. This suggests that spurious symmetrization will mainly occur at an almost undetectable flux level. In this paper, we show that phase-only calibration produces an anti-ghost that is $N$-times (where $N$ denotes the number of antennas in the array) as bright as the one produced by phase and amplitude calibration and that this already bright ghost can be further amplified by the primary beam correction.
This work investigates a particular class of artefacts, or ghost sources, in radio interferometric images. Earlier observations with (and simulations of) the Westerbork Synthesis Radio Telescope (WSRT) suggested that these were due to calibration with incomplete sky models. A theoretical framework is derived that validates this suggestion, and provides predictions of ghost formation in a two-source scenario. The predictions are found to accurately match the result of simulations, and qualitatively reproduce the ghosts previously seen in observational data. The theory also provides explanations…
This paper presents a fast algorithm for full-polarisation, direction dependent calibration in radio interferometry. It is based on Wirtinger's approach to complex differentiation. Compared to the classical case, and under reasonable approximations, the Jacobian appearing in the Levenberg-Maquardt iterative scheme presents a sparse structure, allowing for high gain in terms of algorithmic cost.
This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms.
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the a…
In this lecture, we describe a number of advanced gain calibration techniques. In particular, self-calibration is an important tool in interferometric imaging at all wavelengths. It allows the observer to determine and remove residual phase and amplitude errors that remain in the data after normal calibration while simultaneously producing a more accurate and more sensitive image of the target source. We describe the basic technique of self-calibration and attempt to dispel some common misconceptions. We proceed to give a range of useful tips, and provide continuum, spectral line, and mosaic s…
Baseline calibration of a stellar interferometer is a prerequisite to data reduction of astrometric operations. This technique of astrometry is triangulation of star positions. Since angles are deduced from the baseline and delay side of these triangles, length and pointing direction (in the celestial sphere) of the baseline vector at the time of observation are key input data. We assume that calibration follows from reverse astrometry; a set of calibrator stars with well-known positions is observed and inaccuracies in these positions are leveled by observing many of them for a common best fit…
Interferometry with phased-array feeds (PAFs) presents new calibration challenges in comparison with single-pixel feeds. In particular, temporal instability of the compound beam patterns due to element gain drifts (EGDs) can produce calibration artefacts in interferometric images. To translate imaging dynamic range requirements into PAF hardware and calibration requirements, we must learn to relate EGD levels to imaging artefact levels. We present a MeqTrees-based simulations framework that addresses this problem, and apply it to the APERTIF prototype currently in development for the WSRT.
New generation of radio interferometers are envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding under-sampled Fourier domain measurements. In practice, these measurements are contaminated by the instrumental and atmospheric effects that are well represented by Jones matrices, and are most often varying with observation direction and time. These effects, usually unknown, act as a limiting factor in achieving the required imaging performance and thus, their calibration is crucial. To address this issue, we develop a global algorithm, nam…
Bayesian polarization calibration and imaging in very long baseline interferometry
Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）；Max Planck Computing and Data Facility（马克斯·普朗克计算与数据中心）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Technische Universität München (TUM)（慕尼黑工业大学）；School of Space Research, Kyung Hee University（庆熙大学宇宙研究学院）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Department of Astrophysics, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University（拉布德大学数学、天体物理学和粒子物理研究所天体物理学系）；Institut für Experimentalphysik（实验物理研究所）
Context. The QUBIC collaboration is building a bolometric interferometer dedicated to the detection of B-mode polarization fluctuations in the Cosmic Microwave Background. Aims. We introduce a self-calibration procedure related to those used in radio-interferometry to control a large range of instrumental systematic errors in polarization-sensitive instruments. Methods. This procedure takes advantage of the fact that in the absence of systematic effects, measurements on redundant baselines should exactly match each other. For a given systematic error model, measuring each baseline independentl…
We present intensity interferometry of the luminous blue variable P Cyg in the light of its H$α$ emission performed with 1\,m-class telescopes. We compare the measured visibility points to synthesized interferometric data based on the CMFGEN physical modeling of a high-resolution spectrum of P Cyg recorded almost simultaneously with our interferometry data. Tuning the stellar parameters of P Cyg and its H$α$ linear diameter we estimate the distance of P Cyg as $1.56\pm0.25$~kpc, which is compatible within $1σ$ with $1.36\pm0.24$~kpc reported by the Gaia DR2 catalogue of parallaxes recently pub…
The celebrated CLEAN algorithm has been the cornerstone of deconvolution algorithms in radio interferometry almost since its conception in the 1970s. For all its faults, CLEAN is remarkably fast, robust to calibration artefacts and in its ability to model point sources. We demonstrate how the same assumptions that afford CLEAN its speed can be used to accelerate more sophisticated deconvolution algorithms.
Papers I and II of this series have extended the radio interferometry measurement equation (RIME) formalism to the full-sky case, and provided a RIME-based description of calibration and the problem of direction-dependent effects (DDEs). This paper aims to provide a practical demonstration of a RIME-based approach to calibration, via an example of extremely high-dynamic range calibration of WSRT observations of 3C 147 at 21 cm, with full treatment of DDEs. A version of the RIME incorporating differential gains has been implemented in MeqTrees, and applied to the 3C 147 data. This was used to p…
A Python-Based Peeling Framework for Radio Interferometry: Application to uGMRT 650MHz Imaging
Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；University of Science and Technology of China（中国科学技术大学）；Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Nanjing University（南京大学）；National Radio Astronomy Observatory, NRAO（美国国家射电天文台）；University of Cape Town（开普敦大学）；University of the Western Cape（西开普大学）
Radio interferometry most commonly involves antennas or antenna arrays of identical design. The identical antenna assumption leads to a convenient and useful mathematical simplification resulting in a scalar problem. An interesting variant to this is a "hybrid" interferometer involving two designs. We encounter this in the characterization of low-frequency antenna/array prototypes using a homogenous low-frequency array telescope such as the Murchison Widefield Array (MWA). In this work, we present an interferometry equation that applies to hybrid antennas. The resulting equation involves vecto…
In this paper we describe a new approach for mm-VLBI calibration that provides bona-fide astrometric alignment of the mm-wavelength images from a single source, for the measurement of frequency dependent effects, such as `core-shifts' near the black hole of AGN jets. We achieve our astrometric alignment by solving firstly for the ionospheric (dispersive) contributions using wide-band cm-wavelength observations. Secondly we solve for the tropospheric (non-dispersive) contributions by using fast frequency-switching at the target mm-wavelengths. These solutions can be scaled and transferred from …
For short-wavelength VLBI observations, it is difficult to measure the phase of the visibility function accurately. The closure phases are reliable measurements under this situation, though it is not sufficient to retrieve all of the phase information. We propose a new method, Phase Retrieval from Closure Phase (PRECL). PRECL estimates all the visibility phases only from the closure phases. Combining PRECL with a sparse modeling method we have already proposed, imaging process of VLBI does not rely on dirty image nor self-calibration. The proposed method is tested numerically and the results a…
Radio interferometric gain calibration can be biased by incomplete sky models and radio frequency interference, resulting in calibration artefacts that can restrict the dynamic range of the resulting images. It has been suggested that calibration algorithms employing heavy-tailed likelihood functions are less susceptible to this due to their robustness against outliers in the data. We present an algorithm based on a Student's t-distribution which leverages the framework of complex optimisation and Wirtinger calculus for efficient and robust interferometric gain calibration. We integrate this a…
Phase fluctuations introduced by the atmosphere are the main limiting factor in attaining diffraction limited performance in extended interferometric arrays at millimeter and submillimeter wavelengths. We report the results of C-PACS, the Combined Array for Research in Millimeter-Wave Astronomy Paired Antenna Calibration System. We present a systematic study of several hundred test observations taken during the 2009-2010 winter observing season where we utilize CARMA's eight 3.5-m antennas to monitor an atmospheric calibrator while simultaneously acquiring science observations with 6.1-m and 1…
We develop a new process of image plane self-calibration for interferometric imaging data. The process is based on Shape-Orientation-Size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a 3-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image ma…
In this paper we present DMC, a model and associated tool for polarimetric imaging of very long baseline interferometry datasets that simultaneously reconstructs the full-Stokes emission structure along with the station-based gain and leakage calibration terms. DMC formulates the imaging problem in terms of posterior exploration, which is achieved using Hamiltonian Monte Carlo sampling. The resulting posterior distribution provides a natural quantification of uncertainty in both the image structure and in the data calibration. We run DMC on both synthetic and real datasets, the results of whic…
Kernel-phase is a recently developed paradigm that tackles the classical problem of image deconvolution, based on an interferometric point of view of image formation. Kernel-phase inherits and borrows from the notion of closure-phase, especially as it is used in the context of non-redundant Fizeau interferometry, but extends its application to pupils of arbitrary shape, for diffraction limited images. The additional calibration brought by kernel-phase boosts the resolution of conventional images and enables the detection of otherwise hidden faint features at the resolution limit and beyond, a …
Solar radio emission, especially at metre-wavelengths, is well known to vary over small spectral ($\lesssim$100\,kHz) and temporal ($<1$\,s) spans. It is comparatively recently, with the advent of a new generation of instruments, that it has become possible to capture data with sufficient resolution (temporal, spectral and angular) that one can begin to characterize the solar morphology simultaneously along the axes of time and frequency. This ability is naturally accompanied by an enormous increase in data volumes and computational burden, a problem which will only become more acute with the …
The calibration of Very Long Baseline Interferometry (VLBI) data has long been a time consuming process. The Korean VLBI Network (KVN) is a simple array consisting of three identical antennas. Because four frequencies are observed simultaneously, phase solutions can be transferred from lower frequencies to higher frequencies in order to improve phase coherence and hence sensitivity at higher frequencies. Due to the homogeneous nature of the array, the KVN is also well suited for automatic calibration. In this paper we describe the automatic calibration of single-polarisation KVN data using the…
We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts pr…
Closure phases and closure amplitudes have proven critical to modern radio interferometry due to their insensitivity to the uncertain station gains. We present the first set of closure quantities constructed from parallel-hand and cross-hand visibilities that are insensitive to both station gains and to polarimetric leakage. These complex "closure traces" are a natural extension of closure amplitudes and closure phases, are independent of all station-based linear corruptions of the polarized visibilities, and are complete in the sense that they contain all remaining information present in the …
Paper I of the series re-derived the radio interferometry measurement equation (RIME) from first principles, and extended the Jones formalism to the full-sky case, incorporating direction-dependent effects (DDEs). This paper aims to describe both classical radio interferometric calibration (selfcal and related methods), and the recent developments in the treatment of DDEs, using the RIME-based mathematical framework developed in Paper I. It also aims to demonstrate the ease with which the various effects can be described and understood. The first section of this paper uses the RIME formalism t…
Direct imaging of protoplanetary disks promises to provide key insight into the complex sequence of processes by which planets are formed. However imaging the innermost region of such disks (a zone critical to planet formation) is challenging for traditional observational techniques (such as near-IR imaging and coronagraphy) due to the relatively long wavelengths involved and the area occulted by the coronagraphic mask. Here we introduce a new instrument -- VAMPIRES -- which combines non-redundant aperture-masking interferometry with differential polarimetry to directly image this previously i…
We describe a new method which achieves high precision Very Long Baseline Interferometry (VLBI) astrometry in observations at millimeter wavelengths. It combines fast frequency-switching observations, to correct for the dominant non-dispersive tropospheric fluctuations, with slow source-switching observations, for the remaining ionospheric dispersive terms. We call this method Source-Frequency Phase Referencing. Provided that the switching cycles match the properties of the propagation media, one can recover the source astrometry. We present an analytic description of the two-step calibration …
Distributed calibration based on consensus optimization is a computationally efficient method to calibrate large radio interferometers such as LOFAR and SKA. Calibrating along multiple directions in the sky and removing the bright foreground signal is a crucial step in many science cases in radio interferometry. The residual data contain weak signals of huge scientific interest and of particular concern is the effect of incomplete sky models used in calibration on the residual. In order to study this, we consider the mapping between the input uncalibrated data and the output residual data. We …
This paper investigates the possibility of improving radio interferometric images using an algorithm inspired by an optical method known as "lucky imaging", which would give more weight to the best-calibrated visibilities used to make a given image. A fundamental relationship between the statistics of interferometric calibration solution residuals and those of the image-plane pixels is derived in this paper. This relationship allows us to understand and describe the statistical properties of the residual image. In this framework, the noise-map can be described as the Fourier transform of the c…
In this paper, we consider random phase fluctuations imposed during wave propagation through a turbulent plasma (e.g. ionosphere) as a source of additional noise in interferometric visibilities. We derive expressions for visibility variance for the wide field of view case (FOV$\sim10$ deg) by computing the statistics of Fresnel diffraction from a stochastic plasma, and provide an intuitive understanding. For typical ionospheric conditions (diffractive scale $\sim 5-20$ km at $150$ MHz), we show that the resulting ionospheric `scintillation noise' can be a dominant source of uncertainty at low …
This manual is intended to help ALMA and other interferometer users improve images by recognising limitations and how to overcome them and deciding when and how to use self-calibration. The images provided by the ALMA Science Archive are calibrated using standard observing and data processing routines, including a quality assurance process to make sure that the observations meet the proposer's science requirements. This may not represent the full potential of the data, since any interferometry observation can be imaged with a range of resolutions and surface brightness sensitivity. The separat…
Nulling interferometry aims to detect faint objects close to bright stars. Its principle is to produce a destructive interference along the line-of-sight so that the stellar flux is rejected, while the flux of the off-axis source can be transmitted. In practice, various instrumental perturbations can degrade the nulling performance. Any imperfection in phase, amplitude, or polarization produces a spurious flux that leaks to the interferometer output and corrupts the transmitted off-axis flux. One of these instrumental pertubations is the crosstalk phenomenon, which occurs because of multiple p…
Latest-generation spectro-interferometric instruments combine a milliarcsecond angular resolution with spectral capabilities, resulting in an immensely increased information content. Here, I present methodological work and results that illustrate the fundamentally new scientific insights provided by spectro-interferometry with very high spectral dispersion or in multiple line transitions (Brackett and Pfund lines). In addition, I discuss some pitfalls in the interpretation of spectro-interferometric data. In the context of our recent studies on the classical Be stars β CMi and ζ Tau, I present…
The new operational mode of aperture masking interferometry has been added to the CONICA camera which lies downstream of the Adaptive Optics (AO) corrected focus provided by NAOS on the VLT-UT4 telescope. Masking has been shown to deliver superior PSF calibration, rejection of atmospheric noise and robust recovery of phase information through the use of closure phases. Over the resolution range from about half to several resolution elements, masking interferometry is presently unsurpassed in delivering high fidelity imaging and direct detection of faint companions. Here we present results from…
This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of …
Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture. The linear model upon which it relies theoretically leads to the formation of observable quantities robust against residual aberrations. In practice, detection limits reported thus far seem to be dominated by systematic errors induced by calibration biases not sufficiently filtered out by the kernel projection operator. This paper focuses on the impact the ini…
Context. Very Long Baseline Interferometry (VLBI) data are extremely sensitive to the phase stability of the VLBI array. This is especially important when we reach μJy r.m.s. sensitivities. Calibration using standard phase referencing techniques is often used to improve the phase stability of VLBI data but the results are often not optimal. This is evident in blank fields that do not have in-beam calibrators. Aims. We present a calibration algorithm termed Multi-Source Self-Calibration (MSSC) which can be used after standard phase referencing on wide-field VLBI observations. This is tested on …
The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems IV: NIRISS Aperture Masking Interferometry Performance and Lessons Learned
We present here three recipes for getting better images with optical interferometers. Two of them, Low- Frequencies Filling and Brute-Force Monte Carlo were used in our participation to the Interferometry Beauty Contest this year and can be applied to classical imaging using V 2 and closure phases. These two addition to image reconstruction provide a way of having more reliable images. The last recipe is similar in its principle as the self-calibration technique used in radio-interferometry. We call it also self-calibration, but it uses the wavelength-differential phase as a proxy of the objec…
Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magni…
We propose a probabilistic framework for performing simultaneous estimation of source structure and fringe-fitting parameters in Very Long Baseline Interferometry (VLBI) observations. As a first step, we demonstrate this technique through the analysis of synthetic short-duration Event Horizon Telescope (EHT) observations of various geometric source models at 230 GHz, in the presence of baseline-dependent thermal noise. We perform Bayesian parameter estimation and model selection between the different source models to obtain reliable uncertainty estimates and correlations between various source…
In this document we layout a new method to achieve "bona fide" high precision Very-Long-Baseline-Interferometry (VLBI) astrometric measurements of frequency-dependent positions of celestial sources (even) in the high (mm-wavelength) frequency range, where conventional phase referencing techniques fail. Our method, dubbed "Source/Frequency Phase Referencing" (SFPR) combines fast frequency-switching (or dual-frequency observations) with the source switching of conventional phase referencing techniques. The former is used to calibrate the dominant highly unpredictable rapid atmospheric fluctuatio…
