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.
The errors in baseline length and orientation angles drop proportional to the inverse square roots of the number of independent data taken, proportional to the errors in the individual snapshots of the delay, and proportional to the errors in the apparent positions of the calibrators. Scheduling becomes important if the baseline components are reconstructed from the sinusoidal delay of a single calibrator as a function of time.
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…
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) symmetrica…
This paper describes the concept and the beginning of an experimental investigation of whether it is possible to directly detect dark energy density on earth using atom interferometry. The concept is to null out the gravitational force using a double interferometer. This research provides a non-astronomical path for research on dark energy. The application of this method to other hypothetical weak forces and fields is also discussed. In the the final section I discuss the advantages of carrying out a dark energy density search in a satellite in earth orbit where more precise nulling of gravita…
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）
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…
Space very long baseline interferometry (VLBI) has unique applications in high-resolution imaging of fine structure of astronomical objects and high-precision astrometry due to the key long space-Earth or space-space baselines beyond the Earth's diameter. China has been actively involved in the development of space VLBI in recent years. This review briefly summarizes China's research progress in space VLBI and the future development plan.
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…
Submillimeter interferometry has the potential to image supermassive black holes on event horizon scales, providing tests of the theory of general relativity and increasing our understanding of black hole accretion processes. The Event Horizon Telescope (EHT) performs these observations from the ground, and its main imaging targets are Sagittarius A* in the Galactic Center and the black hole at the center of the M87 galaxy. However, the EHT is fundamentally limited in its performance by atmospheric effects and sparse terrestrial $(u,v)$-coverage (Fourier sampling of the image). The scientific …
Operating 1.5 million km from Earth at the Sun-Earth L2 Lagrange point, the Origins Space Telescope equipped with a slightly modified version of its HERO heterodyne instrument could function as a uniquely valuable node in a VLBI network. The unprecedented angular resolution resulting from the combination of Origins with existing ground-based millimeter/submillimeter telescope arrays would increase the number of spatially resolvable black holes by a factor of a million, permit the study of these black holes across all of cosmic history, and enable new tests of general relativity by unveiling th…
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…
Optical interferometers may not require a phase-stable optical link between the stations if instead sources of quantum-mechanically entangled pairs could be provided to them, enabling long baselines. We developed a new variation of this idea, proposing that photons from two different astronomical sources could be interfered at two decoupled stations. Interference products can then be calculated in post-processing or requiring only a slow, classical connection between stations. In this work, we investigated practical feasibility of this approach. We developed a Bayesian analysis method for the …
We address three major questions in astronomy, namely the detection of biosignatures on habitable exoplanets, the geophysics of exoplanets and cosmology. To achieve this goal, two requirements are needed. First a very large aperture to detect spectro-polarimetric and spatial features of faint objects such as exoplanets, and second a continuous monitoring to characterize the temporal behavior of exoplanets such as rotation period, meteorology and seasons. An Earth-based telescope is not suited for continuous monitoring and the atmosphere limits the ultimate angular resolution and spectro-polari…
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）
Earth-sized planets around nearby stars are being detected for the first time by ground-based radial velocity and space-based transit surveys. This milestone is opening the path towards the definition of missions able to directly detect the light from these planets, with the identification of bio-signatures as one of the main objectives. In that respect, both ESA and NASA have identified nulling interferometry as one of the most promising techniques. The ability to study distant planets will however depend on exozodiacal dust clouds surrounding the target stars. In this paper, we assess the im…
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 …
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…
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…
Recent dynamical studies indicate that the possibility of an Earth-like planet around $α\;$Cen A or B should be taken seriously. Such a planet, if it exists, would perturb the orbital astrometry by $<10 \ μ\rm as$, which is $10^{-6}$ of the separation between the two stars. We assess the feasibility of detecting such perturbations using ground-based intensity interferometry. We simulate a dedicated setup consisting of four 40-cm telescopes equipped with photon counters and correlators with time resolution $0.1\,\rm ns$, and a sort of matched filter implemented through an aperture mask. The ast…
Space interferometry is the inevitable endpoint of high angular resolution astrophysics, and a key technology that can be leveraged to analyse exoplanet formation and atmospheres with exceptional detail. However, the anticipated cost of large missions such as Darwin and TPF-I, and inadequate technology readiness levels have resulted in limited developments since the late 2000s. Here, we present a feasibility study into a small scale formation flying interferometric array in Low Earth Orbit, that will aim to prove the technical concepts involved with space interferometry while still making uniq…
The characterization of extrasolar earth-like atmospheres for biosignatures remains one of the most compelling and elusive challenges in astronomy. Coronagraphy, nulling interferometry and free-flying occulters have been advanced as potential techniques to accomplish this gaol. In this paper, a complementary approach, coherent interferometry in the far infrared is considered. For an interferometer operating close to the quantum noise limit, a collecting area of $\sim$ 1000 m$^{2}$ and baselines of 200 m are sufficient to detect an earth-like planet. The high spectral resolution achievable with…
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…
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 …
Extension of radio interferometric baselines into space is inevitable if a diffraction-limited angular resolution defined by the Earth diameter at a given observing wavelength limits a pursuit of specific scientific goals. This was understood in the early1960s, at the very dawn of the era of Earth-based Very Long Baseline Interferometry (VLBI). Since then, three VLBI missions operated in Space thus enabling baselines longer than the Earth diameter. These are the Tracking and Data Relay Satellite Orbital VLBI experiment (1986 - 1988), the VLBI Space Observatory Program (VSOP, 1997 - 2003) and R…
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…
The Earth Observation planning community has access to tools that can propagate orbits and compute coverage of Earth observing imagers with customizable shapes and orientation, model the expected Earth Reflectance at various bands, epochs and directions, generate simplified instrument performance metrics for imagers and radars, and schedule single and multiple spacecraft payload operations. We are working toward integrating existing tools to design a planner that allows commercial small spacecraft to assess the opportunities for cross-calibration of their sensors against current satellite to b…
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.
We describe the theory and first experimental work on our concept for searching on earth for the presence of dark content of the vacuum (DCV) using atom interferometry. Specifically, we have in mind any DCV that has not yet been detected on a laboratory scale, but might manifest itself as dark energy on the cosmological scale. The experimental method uses two atom interferometers to cancel the effect of earth's gravity and diverse noise sources. It depends upon two assumptions: first, that the DCV possesses some space inhomogeneity in density, and second that it exerts a sufficiently strong no…
Building on the "drPACS" contribution at ADASS XX of a simple Unix pipeline infrastructure, we implemented a pipeline toolkit using the package MIRIAD to combine Interferometric and Single Dish data (MIS). This was prompted by our observations made with the Combined Array For Research in Millimeter-wave Astronomy (CARMA) interferometer of the star-forming region NGC 1333, a large survey highlighting the new 23-element and singledish observing modes. The project consists of 20 CARMA datasets each containing interferometric as well as simultaneously obtained single dish data, for 3 molecular spe…
We present MeqSilhouette v2.0 (MeqSv2), a fully polarimetric, time-and frequency-resolved synthetic data generation software for simulating millimetre (mm) wavelength very long baseline interferometry (VLBI) observations with heterogeneous arrays. Synthetic data are a critical component in understanding real observations, testing calibration and imaging algorithms, and predicting performance metrics of existing or proposed sites. MeqSv2 applies physics-based instrumental and atmospheric signal corruptions constrained by empirically-derived site and station parameters to the data. The new versi…
Context. Closed-loop Doppler data obtained by deep space tracking networks (e.g., NASA's DSN and ESA's Estrack) are routinely used for navigation and science applications. By "shadow tracking" the spacecraft signal, Earth-based radio telescopes involved in Planetary Radio Interferometry and Doppler Experiment (PRIDE) can provide open-loop Doppler tracking data when the dedicated deep space tracking facilities are operating in closed-loop mode only. Aims. We explain in detail the data processing pipeline, discuss the capabilities of the technique and its potential applications in planetary scie…
We describe the laboratory complex for the calibration of photometers that are used in weather service to measure the water vapor content in the Earth atmosphere. The complex was built up in Pulkovo Observatory and developed within the framework of collaboration between Pulkovo Observatory and Lindenberg Meteorological Observatory (Meteorologisches Observatorium Lindenberg - Richard-Aßmann-Observatorium, Lindenberg, Germany). It is used to obtain calibration dependences for individual devices, and also to develop and compare various methods of construction of calibration dependences. These tec…
By using the satelital information of Earth observation unloaded by a station constructed in the country and reflectances measurements of the soil, we found the total radiation attenuation of the atmosphere for a small region of the Colombian territory. It was necessary to use the Fourier's theory that describes the ideal filters of signals to find the transfer functions between the spectral response of an spectroradiometer and the satelital sensor, whose radiative sign we are going to calibrate. After that, we used the reflectance spectrum of the soil taken with our spectroradiometer, the inf…
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 …
