U. Rau, S. Bhatnagar, M. A. Voronkov, T. J. Cornwell
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.
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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.
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…
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…
Laboratory Demonstration of Image-Plane Self-Calibration in Interferometry
本研究在ALBA可见光同步辐射光源上，通过孔径平面掩模验证三元干涉仪的形状-方向-尺寸守恒原理，并利用相关数据实现干涉测量的像面自校准演示。
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
本文提出基于贝叶斯方法的VLBI偏振校准与成像技术，通过联合探索后验分布提高图像质量并提供不确定性估计，适用于高分辨率偏振成像研究。
Bayesian self-calibration and imaging in Very Long Baseline Interferometry
本文提出在贝叶斯推断框架下结合变分推断，对VLBI数据进行天线增益自校准与成像，并在M87的VLBA 43GHz数据上获得比CLEAN更稳健、可复现且带不确定性估计的Stokes I图像。
GRIP: a generic data reduction package for nulling interferometry
本文推出开源工具箱 GRIP，在统一框架内用增强的统计自校准方法处理任意消零干涉仪数据，并在 GLINT 与 LBTI 数据上验证其一致性和 10$^{-4}$ 量级精度。
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…
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…
Spectrally dispersed kernel phase interferometry with SCExAO/CHARIS: proof of concept and calibration strategies
本文提出将核相位干涉测量应用于积分视场光谱仪的高光谱图像，利用SCExAO/CHARIS恢复已知双星验证了光谱色散核相位技术，并开发了光谱差分成像定标策略以抑制系统误差、提升对比度。
Very-Long Baseline Interferometry Imaging with Closure Invariants using Conditional Image Diffusion
本文提出利用条件图像扩散方法，通过生成式深度学习解决闭合不变量到图像的逆问题，实现校准无关的VLBI成像重建。
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…
On the interpolation of calibration solutions obtained in radio interferometry
针对射电干涉测量中标定解存在酉矩阵模糊度导致无法直接内插的问题，提出利用商流形理论获得不受模糊度影响的正确内插方法。
A Python-Based Peeling Framework for Radio Interferometry: Application to uGMRT 650MHz Imaging
本文提出基于Python的射电干涉去皮框架，用于解决方向依赖性校准问题，提升成像质量和弱源探测能力，适用于uGMRT 650MHz数据。
Trajectory Based RFI Subtraction and Calibration for Radio Interferometry
针对射电干涉测量中校准与RFI去除分开进行的问题，提出联合建模RFI轨迹与校准参数的tabascal算法，在模拟MeerKAT数据上测试，提升了校准精度并减少数据损失，适用于卫星等轨迹RFI场景。
VIPCALs: A fully automated calibration pipeline for very long baseline interferometry data
VIPCALs是一种全自动化的VLBI数据校准流程，能够高效处理大量观测数据，显著降低VLBI科学的进入门槛。
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 …
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…
Reinforcement Learning for Data-Driven Workflows in Radio Interferometry. I. Principal Demonstration in Calibration
本文针对射电干涉测量数据处理流程中的人工决策问题，提出一种基于客观指标量化最佳实践的自动化数据驱动决策系统，利用强化学习为处理干涉数据排序最优动作，并通过原型验证了其有效性。
Aperture Masking Interferometry used in combination with Adaptive Optics, is a powerful technique that permits the detection of faint companions at small angular separations. The precision calibration of the data achieved with this observing mode indeed leads to reliable results up to and beyond the formal diffraction limit, explaining why it has, in just a few years, been ported on most major telescopes. In this poster, we present its possible implementation on Subaru. We also discuss how the opportunity offered by the planned Extreme-AO upgrade to HiCIAO will push further the performance of …
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…
Solving Self-calibration of ALMA Data with an Optimization Method
本文将射电干涉增益校正与 PRIISM 成像统一为带正则化的优化问题，并通过迭代算法求解，在 ALMA 数据上验证了自校准与图像估计效果。
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…
Compensation of front-end and modulation delays in phase and ranging measurements for time-delay interferometry
针对 LISA 中星载模拟延迟未知且易漂移的问题，提出一种基于接收机最小功能增加的地面与在轨校准方法，通过校准测量和数据处理抑制 TDI Michelson 变量中的延迟，仿真表明地面校准可改善约一个数量级，在轨重校准可再提升一个数量级。
Exploiting Non Redundant Aperture Interferometry as a Diagnostics Tool for Synchrotron Light Characterization
研究利用受射电天文学启发的新型干涉测量方法表征电子束二维横向形状，介绍基于闭合振幅的新数据分析方法，无需自校准，展示其在波前传感中的适用性及分辨束晕的潜力。
Prospects of using closure traces directly for imaging in Very Long Baseline Interferometry
针对EHT偏振校准难题，本文探索直接拟合闭合迹进行成像的流水线，发现多目标成像技术可处理其固有简并性，并在未来更多天线的EHT继任项目中验证了该方法的可行性与竞争力。
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 closest examples of high-mass star birth occurs in deeply embedded environments at kiloparsec distances. Although much progress has been made, an observationally validated picture of the dominant processes which allows the central hydrostatic object to grow in mass has yet to be established. The observational technique of optical interferometry has demonstrated its potential in the field of high-mass star formation by delivering a milli-arcsecond infrared view on the complex accretion environment. We provide an overview of the scientific results obtained with multi-aperture telescope array…
After decades of experimental projects and fast-paced technical advances, optical / infrared (O/IR) interferometry has seen a revolution in the last years. The GRAVITY instrument at the VLTI with four 8 meter telescopes reaches thousand times fainter objects than possible with earlier interferometers, and the CHARA array routinely offers up to 330 meter baselines and aperture-synthesis with six 1 meter telescopes. The observed objects are fainter than 19 magnitude, the images have sub-milliarcsecond resolution, and the astrometry reaches micro-arcsecond precision. We give an overview of breakt…
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.
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…
Generative AI for image reconstruction in Intensity Interferometry: a first attempt
本文首次探讨应用条件生成对抗网络（cGAN）解决强度干涉测量（II）中的图像重建问题，成功从稀疏采样的空间功率谱重建快速旋转恒星特征，为未来大阵列复杂系统重建提供了新思路。
New techniques for high-resolution imaging and high-precision wavefront sensing via masked-aperture interferometry
该研究受射电干涉测量启发，开发两种掩膜孔径干涉测量方法，经ALBA同步辐射光束线验证，可实现纳米级波前传感与亚角秒级成像，应用于实验室、同步辐射及天文学领域。
Recent advances in photonics have revived the interest in intensity interferometry for astronomical applications. The success of amplitude interferometry in the early 1970s, which is now mature and producing spectacular astrophysical results (e.g. GRAVITY, MATISSE, CHARA, etc.), coupled with the limited sensitivity of intensity interferometry stalled any progress on this technique for the past 50 years. However, the precise control of the optical path difference in amplitude interferometry is constraining for very long baselines and at shorter wavelengths. Polarization measurements are also ch…
The calibration and analysis of polarization observations in Very Long Baseline Interferometry (VLBI) requires the use of specific algorithms that suffer from several limitations, closely related to assumptions in the data properties that may not hold in observations taken with new-generation VLBI equipment. Nowadays, the instantaneous bandwidth achievable with VLBI backends can be as high as several GHz, covering several radio bands simultaneously. In addition, the sensitivity of VLBI observations with state-of-the-art equipment may reach dynamic ranges of tens of thousands, both in total int…
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 …
The exquisite precision delivered by interferometric techniques is rapidly being applied to more and more branches of optical astronomy. One particularly successful strategy to obtain structures at the scale of the diffraction limit is Aperture Masking Interferometry, which is presently experience a golden age with implementations at a host of large telescopes around the world. This startlingly durable technique, which turns 144 years old this year, presently sets the standard for the recovery of faint companions within a few resolution elements from the core of a stellar point spread function…
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…
Recent advances in telescope design, photodetector efficiency, and high-speed electronic data recording and synchronization have created the observational capability to achieve unprecedented angular resolution for several thousand bright (m< 6) and hot (O/B/A) stars by means of a modern implementation of Stellar Intensity Interferometry (SII). This technology, when deployed on future arrays of large diameter optical telescopes, has the ability to image astrophysical objects with an angular resolution better than 40 μ arc-sec. This paper describes validation tests of the SII technique in the la…
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 …
The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems IV: NIRISS Aperture Masking Interferometry Performance and Lessons Learned
本研究基于ERS 1386计划的HIP 65426系统观测数据，分析JWST/NIRISS的AMI模式性能，明确校准误差来源，验证其高对比度探测能力，提出观测规划建议并推动校准策略研究，以释放该模式探测低温小质量系外行星的潜力。
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…
Recent proposals have been advanced to apply imaging air Cherenkov telescope arrays to stellar intensity interferometry (SII). Of particular interest is the possibility of model-independent image recovery afforded by the good (u, v)-plane coverage of these arrays, as well as recent developments in phase retrieval techniques. The capabilities of these instruments used as SII receivers have already been explored for simple stellar objects, and here the focus is on reconstructing stellar images with non-uniform radiance distributions. We find that hot stars (T > 6000 K) containing hot and/or cool…
TONE: A CHIME/FRB Outrigger Pathfinder for localizations of Fast Radio Bursts using Very Long Baseline Interferometry
针对CHIME无法定位多数FRB宿主星系的问题，提出TONE八天线干涉阵列作为CHIME/FRB外延站探路者，验证单脉冲VLBI技术，实现亚角秒级定位精度。
A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to first-order Born approximation and might be applicable to correct observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that not the ionospheric electron density distribution is the primary structure to model in interferometry, but its autocorrelation function or equivalent its power-spectrum. An exact …
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…
Calibration is an essential step in radio interferometric data processing that corrects the data for systematic errors and in addition, subtracts bright foreground interference to reveal weak signals hidden in the residual. These weak and unknown signals are much sought after to reach many science goals but the effect of calibration on such signals is an ever present concern. The main reason for this is the incompleteness of the model used in calibration. Distributed calibration based on consensus optimization has been shown to mitigate the effect due to model incompleteness by calibrating dat…
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…
In this paper are reviewed various designs of advanced, multi-aperture optical systems dedicated to high angular resolution imaging or to the detection of exo-planets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing to derive their basic theoretical relationships as convolution or cross correlation products suitable for fast and accurate computation. Several unusual designs, such as a super-resolving telescope utilizing a mosaicking observation procedure or a free-flying, axially recombined interfe…
New and upcoming radio interferometers will produce unprecedented amounts of data that demand extremely powerful computers for processing. This is a limiting factor due to the large computational power and energy costs involved. Such limitations restrict several key data processing steps in radio interferometry. One such step is calibration where systematic errors in the data are determined and corrected. Accurate calibration is an essential component in reaching many scientific goals in radio astronomy and the use of consensus optimization that exploits the continuity of systematic errors acr…
Mass spectrometry imaging by Fourier transform ion cyclotron resonance yields hundreds of unique peaks, many of which cannot be resolved by lower performance mass spectrometers. The high mass accuracy and high mass resolving power allow confident identification of small molecules and lipids directly from biological tissue sections. Here, calibration strategies for Fourier transform ion cyclotron resonance mass spectrometry imaging were investigated. Sub parts-per-million mass accuracy is demonstrated over an entire tissue section. Ion abundance fluctuations are corrected for by addition of tot…
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