Direction-dependent Effects Research Articles

Bayesian radio interferometric imaging with direction-dependent calibration

Context. Radio interferometers measure frequency components of the sky brightness, modulated by the gains of the individual radio antennas. Due to atmospheric turbulence and variations in the operational conditions of the antennas, these gains fluctuate. Thereby the gains do not only depend on time, but also on the spatial direction on the sky. To recover high-quality radio maps, an accurate reconstruction of the direction and time-dependent individual antenna gains is required. Aims. This paper aims to improve the reconstruction of radio images, by introducing a novel joint imaging and calibration algorithm including direction-dependent antenna gains. Methods. Building on the resolve framework, we designed a Bayesian imaging and calibration algorithm utilizing the image domain gridding method for numerically efficient application of direction-dependent antenna gains. Furthermore, by approximating the posterior probability distribution with variational inference, our algorithm can provide reliable uncertainty maps. Results. We demonstrate the ability of the algorithm to recover high resolution high dynamic range radio maps from VLA data of the radio galaxy Cygnus A. We compare the quality of the recovered images with previous work relying on classically calibrated data. Furthermore, we compare the results with a compressed sensing algorithm also incorporating direction-dependent gains. Conclusions. Including direction-dependent effects in the calibration model significantly improves the dynamic range of the reconstructed images compared to reconstructions from classically calibrated data. Compared to the compressed sensing reconstruction, the resulting sky images have a higher resolution and show fewer artifacts. For utilizing the full potential of radio interferometric data, it is essential to consider the direction dependence of the antenna gains.

Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA) – II. Code and real data proof of concept

ABSTRACT In a companion paper, a faceted wideband imaging technique for radio interferometry, dubbed Faceted HyperSARA, has been introduced and validated on synthetic data. Building on the recent HyperSARA approach, Faceted HyperSARA leverages the splitting functionality inherent to the underlying primal-dual forward-backward algorithm to decompose the image reconstruction over multiple spatio-spectral facets. The approach allows complex regularization to be injected into the imaging process while providing additional parallelization flexibility compared to HyperSARA. This paper introduces new algorithm functionalities to address real data sets, implemented as part of a fully fledged matlab imaging library made available on GitHub. A large-scale proof of concept is proposed to validate Faceted HyperSARA in a new data and parameter scale regime, compared to the state of the art. The reconstruction of a 15 GB wideband image of Cyg A from 7.4 GB of Very Large Array data is considered, utilizing 1440 CPU cores on a high-performance computing system for about 9 h. The conducted experiments illustrate the reconstruction performance of the proposed approach on real data, exploiting new functionalities to leverage known direction-dependent effects, for an accurate model of the measurement operator, and an effective noise level accounting for imperfect calibration. They also demonstrate that, when combined with a further dimensionality reduction functionality, Faceted HyperSARA enables the recovery of a 3.6 GB image of Cyg A from the same data using only 91 CPU cores for 39 h. In this setting, the proposed approach is shown to provide a superior reconstruction quality compared to the state-of-the-art wideband clean-based algorithm of the wsclean software.

Simulations of primary beam effects on the cosmic bispectrum phase observed with the Hydrogen Epoch of Reionization Array

ABSTRACT The 21 cm transition from neutral hydrogen promises to be the best observational probe of the epoch of reionization (EoR). The main difficulty in measuring the 21 cm signal is the presence of bright foregrounds that require very accurate interferometric calibration. Closure quantities may circumvent the calibration requirements but may be, however, affected by direction-dependent effects, particularly antenna primary beam responses. This work investigates the impact of antenna primary beams affected by mutual coupling on the closure phase and its power spectrum. Our simulations show that primary beams affected by mutual coupling lead to a leakage of foreground power into the EoR window, which can be up to ∼104 times higher than the case where no mutual coupling is considered. This leakage is, however, essentially confined at k < 0.3 h Mpc−1 for triads that include 29 m baselines. The leakage magnitude is more pronounced when bright foregrounds appear in the antenna sidelobes, as expected. Finally, we find that triads that include mutual coupling beams different from each other have power spectra similar to triads that include the same type of mutual coupling beam, indicating that beam-to-beam variation within triads (or visibility pairs) is not the major source of foreground leakage in the EoR window.

Outcome-dependent effects of walking speed and age on quantitative and qualitative gait measures

BackgroundWalking speed predicts many clinical outcomes in old age. However, a comprehensive assessment of how walking speed affects accelerometer based quantitative and qualitative gait measures in younger and older adults is lacking. Research questionWhat is the relationship between walking speed and quantitative and qualitative gait outcomes in younger and older adults? MethodsYounger (n = 27, age: 21.6) and older participants (n = 27, age: 69.5) completed 340 steps on a treadmill at speeds of 0.70 to a maximum of 1.75 m·s-1. We used generalized additive mixed models to determine the relationship between walking speed and quantitative (stride length, stride time, stride frequency and their variability) and qualitative (stride regularity, stability, smoothness, symmetry, synchronization, predictability) gait measures extracted from trunk accelerations. ResultsThe type of relationship between walking speed and the majority of gait measures (quantitative and qualitative) was characterized as logarithmic, with more prominent speed-effects at speeds below 1.20 m·s−1. Changes in quantitative measures included shorter strides, longer stride times, and a lower stride frequency, with more variability at lower speeds independent of age. For qualitative measures, we found a decrease in gait symmetry, stability and regularity in all directions with decreasing speeds, a decrease in gait predictability (Vertical, V, anterior-posterior, AP) and stronger gait synchronization (AP-mediolateral, ML, AP-V), and direction dependent effects of gait smoothness, which decreased in V direction, but increased in AP and ML directions with decreasing speeds. We found outcome-dependent effects of age on the quantitative and qualitative gait measures, with either no differences between age-groups, age-related differences that existed regardless of speed, and age-related differences in the type of relationship with walking speed. SignificanceThe relationship between walking speed and quantitative and qualitative gait measures, and the effects of age on this relationship, depends on the type of gait measure studied.

MIGHTEE: total intensity radio continuum imaging and the COSMOS/XMM-LSS Early Science fields

ABSTRACT MIGHTEE is a galaxy evolution survey using simultaneous radio continuum, spectropolarimetry, and spectral line observations from the South African MeerKAT telescope. When complete, the survey will image ∼20 deg2 over the COSMOS, E-CDFS, ELAIS-S1, and XMM-Newton Large Scale Structure field (XMM-LSS) extragalactic deep fields with a central frequency of 1284 MHz. These were selected based on the extensive multiwavelength data sets from numerous existing and forthcoming observational campaigns. Here, we describe and validate the data processing strategy for the total intensity continuum aspect of MIGHTEE, using a single deep pointing in COSMOS (1.6 deg2) and a three-pointing mosaic in XMM-LSS (3.5 deg2). The processing includes the correction of direction-dependent effects, and results in thermal noise levels below 2 $\mathrm{\mu }$Jy beam−1 in both fields, limited in the central regions by classical confusion at ∼8 arcsec angular resolution, and meeting the survey specifications. We also produce images at ∼5 arcsec resolution that are ∼3 times shallower. The resulting image products form the basis of the Early Science continuum data release for MIGHTEE. From these images we extract catalogues containing 9896 and 20 274 radio components in COSMOS and XMM-LSS, respectively. We also process a close-packed mosaic of 14 additional pointings in COSMOS and use these in conjunction with the Early Science pointing to investigate methods for primary beam correction of broad-band radio images, an analysis that is of relevance to all full-band MeerKAT continuum observations, and wide-field interferometric imaging in general. A public release of the MIGHTEE Early Science continuum data products accompanies this article.

Directional effects of whole-body spinning and visual flow in virtual reality on vagal neuromodulation.

Neural circuits allow whole-body yaw rotation to modulate vagal parasympathetic activity, which alters beat-to-beat variation in heart rate. The overall output of spinning direction, as well as vestibular-visual interactions on vagal activity still needs to be investigated. This study investigated direction-dependent effects of visual and natural vestibular stimulation on two autonomic responses: heart rate variability (HRV) and pupil diameter. Healthy human male subjects (n = 27) underwent constant whole-body yaw rotation with eyes open and closed in the clockwise (CW) and anticlockwise (ACW) directions, at 90°/s for two minutes. Subjects also viewed the same spinning environments on video in a VR headset. CW spinning significantly decreased parasympathetic vagal activity in all conditions (CW open p = 0.0048, CW closed p = 0.0151, CW VR p = 0.0019,), but not ACW spinning (ACW open p = 0.2068, ACW closed p = 0.7755, ACW VR p = 0.1775,) as indicated by an HRV metric, the root mean square of successive RR interval differences (RMSSD). There were no direction-dependent effects of constant spinning on sympathetic activity inferred through the HRV metrics, stress index (SI), sympathetic nervous system index (SNS index) and pupil diameter. Neuroplasticity in the CW eyes closed and CW VR conditions post stimulation was observed. Only one direction of yaw spinning, and visual flow caused vagal nerve neuromodulation and neuroplasticity, resulting in an inhibition of parasympathetic activity on the heart, to the same extent in either vestibular or visual stimulation. These results indicate that visual flow in VR can be used as a non-electrical method for vagus nerve inhibition without the need for body motion in the treatment of disorders with vagal overactivity. The findings are also important for VR and spinning chair based autonomic nervous system modulation protocols, and the effects of motion integrated VR.

Cygnus A jointly calibrated and imaged via non-convex optimization from VLA data

ABSTRACT Radio interferometric (RI) data are noisy undersampled spatial Fourier components of the unknown radio sky affected by direction-dependent antenna gains. Failure to model these antenna gains accurately results in a radio sky estimate with limited fidelity and resolution. The RI inverse problem has been recently addressed via a joint calibration and imaging approach that consists in solving a non-convex minimization task, involving suitable priors for the direction-dependent effects (DDEs), namely temporal and spatial smoothness, and sparsity for the unknown radio map via an ℓ1-norm prior, in the context of realistic RI simulations. Building on these developments, we propose to promote sparsity of the radio map via a log-sum prior, enforcing sparsity more strongly than the ℓ1 norm. The resulting minimization task is addressed via a sequence of non-convex minimization tasks composed of re-weighted ℓ1 image priors, which are solved approximately. We demonstrate the efficiency of the approach on RI observations of the celebrated radio galaxy Cygnus A obtained with the Karl G. Jansky Very Large Array at the frequency bands X, C, and S . More precisely, we showcase that the approach enhances data fidelity significantly while achieving high-resolution high-dynamic range radio maps, confirming the suitability of the priors considered for the unknown DDEs and radio image. As a clear qualitative indication of the high fidelity achieved by the data and the proposed approach, we report the detection of three background sources in the vicinity of Cyg A, at S band.

The LOFAR Two-meter Sky Survey: Deep Fields Data Release 1

The Low Frequency Array (LOFAR) is an ideal instrument to conduct deep extragalactic surveys. It has a large field of view and is sensitive to large-scale and compact emission. It is, however, very challenging to synthesize thermal noise limited maps at full resolution, mainly because of the complexity of the low-frequency sky and the direction dependent effects (phased array beams and ionosphere). In this first paper of a series, we present a new calibration and imaging pipeline that aims at producing high fidelity, high dynamic range images with LOFAR High Band Antenna data, while being computationally efficient and robust against the absorption of unmodeled radio emission. We apply this calibration and imaging strategy to synthesize deep images of the Boötes and Lockman Hole fields at ~150 MHz, totaling ~80 and ~100 h of integration, respectively, and reaching unprecedented noise levels at these low frequencies of ≲30 and ≲23μJy beam−1in the inner ~3 deg2. This approach is also being used to reduce the LOTSS-wide data for the second data release.

The LOFAR LBA Sky Survey

Context. The LOw Frequency ARray (LOFAR) is the only radio telescope that is presently capable of high-sensitivity, high-resolution (i.e. < 1 mJy beam−1 and < 15″) observations at ultra-low frequencies (< 100 MHz). To utilise these capabilities, the LOFAR Surveys Key Science Project is undertaking a large survey to cover the entire northern sky with Low Band Antenna (LBA) observations. Aims. The LOFAR LBA Sky Survey (LoLSS) aims to cover the entire northern sky with 3170 pointings in the frequency range between 42 − 66 MHz, at a resolution of 15″ and at a sensitivity of 1 mJy beam−1 (1σ). In this work, we outline the survey strategy, the observational status, and the calibration techniques. We also briefly describe several of our scientific motivations and present the preliminary public data release. Methods. The preliminary images were produced using a fully automated pipeline aimed at correcting all direction-independent effects in the data. Whilst the direction-dependent effects, such as those from the ionosphere, have not yet been corrected, the images presented in this work are still ten times more sensitive than previous available surveys at these low frequencies. Results. The preliminary data release covers 740 deg2 around the HETDEX spring field region at an angular resolution of 47″ with a median noise level of 5 mJy beam−1. The images and the catalogue of 25 247 sources have been publicly released. We demonstrate that the system is capable of reaching a root mean square (rms) noise of 1 mJy beam−1 and an angular resolution of 15″ once direction-dependent effects are accounted for. Conclusions. LoLSS will provide the ultra-low-frequency information for hundreds of thousands of radio sources, providing critical spectral information and producing a unique data set that can be used for a wide range of science topics, such as the search for high redshift galaxies and quasars, the study of the magnetosphere of exoplanets, and the detection of the oldest populations of cosmic-rays in galaxies, clusters of galaxies, as well as those produced by active galactic nuclei.

Asymmetric transcallosal conduction delay leads to finer bimanual coordination

It has been theorized that hemispheric dominance and more segregated information processing have evolved to overcome long conduction delays through the corpus callosum (transcallosal conduction delay - TCD) but that this may still impact behavioral performance, mostly in tasks requiring high timing accuracy. Nevertheless, a thorough understanding of the temporal features of interhemispheric communication is lacking.Here, we aimed to assess the relationship between TCD and behavioral performance with a noninvasive directional cortical measure of TCD obtained from transcranial magnetic stimulation (TMS)-evoked potentials (TEPs) in the motor system.Twenty-one healthy right-handed subjects were tested. TEPs were recorded during an ipsilateral silent period (iSP) paradigm and integrated with diffusion tensor imaging (DTI) and an in-phase bimanual thumb-opposition task. Linear mixed models were applied to test relationships between measures.We found TEP indexes of transcallosal communication at ∼15 ms both after primary motor cortex stimulation (M1-P15) and after dorsal premotor cortex stimulation (dPMC-P15). Both M1-and dPMC-P15 were predicted by mean diffusivity in the callosal body. Moreover, M1-P15 was positively related to iSP. Importantly, M1-P15 latency was linked to bimanual coordination with direction-dependent effects, so that asymmetric TCD was the best predictor of bimanual coordination.Our findings support the idea that transcallosal timing in signal transmission is essential for interhemispheric communication and can impact the final behavioral outcome. However, they challenge the view that a short conduction delay is always beneficial. Rather, they suggest that the effect of the conduction delay may depend on the direction of information flow.

Printing direction dependent microstructures in direct ink writing

Direct ink writing enables deposition of multiphase filaments with designed microstructures. Using acoustophoresis, we establish a narrow distribution of microparticles at the center of a direct-write nozzle. The distribution shifts and widens after deposition depending on the printing direction. We use particle image velocimetry and digital image analysis to identify flows transverse to the printing direction and characterize particle distributions in the printed filament. Sources of direction-dependent effects include square nozzles, co-deposition of support material, a rotationally asymmetric microstructure established in the nozzle, and speed inaccuracies that occur in 3-axis gantries. We propose an analytical model for predicting print direction-dependent flows and particle distributions as a function of anisotropy of the particle distribution in the nozzle, a disturbed zone near the nozzle, fluid reshaping of the print bead, uniform rotation of the print bead, calibration of the ink and support nozzle positions, and 3D printer motor error. Using the model, we propose strategies for controlling direction dependent microstructures in direct ink writing. The analytical model can be easily adapted to similar direct-write applications to diagnose sources of direction dependent microstructures.

Probabilistic direction-dependent ionospheric calibration for LOFAR-HBA

Direction-dependent calibration and imaging is a vital part of producing radio images that are deep and have a high fidelity and highly dynamic range with a wide-field low-frequency array such as LOFAR. Currently, dedicated facet-based direction-dependent calibration algorithms rely on the assumption that the size of the isoplanatic patch is much larger than the separation between bright in-field calibrators. This assumption is often violated owing to the dynamic nature of the ionosphere, and as a result, direction-dependent errors affect image quality between calibrators. In this paper we propose a probabilistic physics-informed model for inferring ionospheric phase screens, providing a calibration for all sources in the field of view. We apply our method to a randomly selected observation from the LOFAR Two-Metre Sky Survey archive, and show that almost all direction-dependent effects between bright calibrators are corrected and that the root-mean-squared residuals around bright sources are reduced by 32% on average.

Polca SARA – full polarization, direction-dependent calibration, and sparse imaging for radio interferometry

ABSTRACT New generation of radio interferometers are envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding undersampled 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, named Polca SARA, aiming to perform full polarization, direction-dependent calibration, and sparse imaging by employing a non-convex optimization technique. In contrast with the existing approaches, the proposed method offers global convergence guarantees and flexibility to incorporate sophisticated priors to regularize the imaging as well as the calibration problem. Thus, we adapt a polarimetric imaging specific method, enforcing the physical polarization constraint along with a sparsity prior for the sought images. We perform extensive simulation studies of the proposed algorithm. The results indicate the superior performance of polarization constraint based imaging when combined with the calibration of the direction-dependent effects for full Jones matrices, including their off-diagonal terms (denoting polarization leakage). The chosen priors in the proposed approach are also shown to handle the unitary ambiguity problem to a good extent.

Detailed study of the ELAIS N1 field with the uGMRT - I. Characterizing the 325 MHz foreground for redshifted 21 cm observations

In this first paper of the series, we present initial results of newly upgraded Giant Meterwave Radio Telescope (uGMRT) observation of European Large-Area ISO Survey-North 1 (ELAIS-N1) at 325 MHz with 32 MHz bandwidth. Precise measurement of fluctuations in Galactic and extragalactic foreground emission as a function of frequency as well as angular scale is necessary for detecting redshifted 21-cm signal of neutral hydrogen from Cosmic Dawn, Epoch of Reionization (EoR) and post-reionization epoch. Here, for the first time we have statistically quantified the Galactic and extragalactic foreground sources in the ELAIS-N1 field in the form of angular power spectrum using the newly developed Tapered Gridded Estimator (TGE). We have calibrated the data with and without direction-dependent calibration techniques. We have demonstrated the effectiveness of TGE against the direction dependent effects by using higher tapering of field of view (FoV). We have found that diffuse Galactic synchrotron emission (DGSE) dominates the sky, after point source subtraction, across the angular multipole range $ 1115 \leqslant \mathcal{\ell} \leqslant 5083 $ and $ 1565 \leqslant \mathcal{\ell} \leqslant 4754 $ for direction-dependent and -independent calibrated visibilities respectively. The statistical fluctuations in DGSE has been quantified as a power law of the form $\mathcal{C}_{\mathcal{\ell}}= A \mathcal{\ell}^{-\beta} $. The best fitted values of (A, $\beta$) are ($ 62 \pm 6$ $mK^{2}$, $2.55 \pm 0.3 $) and ($ 48 \pm 4$ $mK^{2}$, $2.28 \pm 0.4 $ ) for the two different calibration approaches. For both the cases, the power law index is consistent with the previous measurements of DGSE in other parts of sky.

Primary beam effects of radio astronomy antennas – I. Modelling the Karl G. Jansky Very Large Array (VLA) L-band beam using holography

Modern interferometric imaging relies on advanced calibration that incorporates direction-dependent effects. Their increasing number of antennas (e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the accuracy of their calibration. Beam accuracy drives particularly the capability for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio Interferometric Measurement Equation (RIME) proposes a refined calibration framework for wide field of views (i.e. beyond the primary lobe and first null) using beam models. We have used holography data taken on 12 antennas of the Very Large Array (VLA) with two different approaches: a `data-driven' representation derived from Principal Component Analysis (PCA) and a projection on the Zernike polynomials. We determined sparse representations of the beam to encode its spatial and spectral variations. For each approach, we compressed the spatial and spectral distribution of coefficients using low-rank approximations. The spectral behaviour was encoded with a Discrete Cosine Transform (DCT). We compared our modelling to that of the Cassbeam software which provides a parametric model of the antenna and its radiated field. We present comparisons of the beam reconstruction fidelity vs. `compressibility'. We found that the PCA method provides the most accurate model. In the case of VLA antennas, we discuss the frequency ripple over L-band which is associated with a standing wave between antenna reflectors. The results are a series of coefficients that can easily be used `on-the-fly' in calibration pipelines to generate accurate beams at low computing costs.

The twisted jets of Circinus X-1

We present the results of millimetre (33 and 35 GHz) and centimetre (2.1, 5.5 and 9.0 GHz) wavelength observations of the neutron star X-ray binary Circinus X-1, using the Australia Telescope Compact Array. We have used advanced calibration and deconvolution algorithms to overcome multiple issues due to intrinsic variability of the source and direction dependent effects. The resulting centimetre and millimetre radio maps show spatially resolved jet structures from sub-arcsecond to arcminute angular scales. They represent the most detailed investigation to date of the interaction of the relativistic jet from the X-ray binary with the young supernova remnant in which it is embedded. Comparison of projected jet axes at different wavelengths indicate significant rotation of the jet axis with increasing angular scale. This either suggests interactions of the jet material with surrounding media, creating bends in the jet flow path, or jet precession. We explore the latter hypothesis by successfully modelling the observed jet path using a kinematic jet model. If precession is the right interpretation and our modelling correct, the best fit parameters describe an accreting source with mildly relativistic ejecta ($v = 0.5 c$), inclined close to the plane of the sky ($i = 86^{\circ}$) and precessing over a 5-year period.

Image Domain Gridding: a fast method for convolutional resampling of visibilities

In radio astronomy obtaining a high dynamic range in synthesis imaging of wide fields requires a correction for time and direction-dependent effects. Applying direction-dependent correction can be done by either partitioning the image in facets and applying a direction-independent correction per facet, or by including the correction in the gridding kernel (AW-projection). An advantage of AW-projection over faceting is that the effectively applied beam is a sinc interpolation of the sampled beam, where the correction applied in the faceting approach is a discontinuous piece wise constant beam. However, AW-projection quickly becomes prohibitively expensive when the corrections vary over short time scales. This occurs, for example, when ionospheric effects are included in the correction. The cost of the frequent recomputation of the oversampled convolution kernels then dominates the total cost of gridding. Image domain gridding is a new approach that avoids the costly step of computing oversampled convolution kernels. Instead low-resolution images are made directly for small groups of visibilities which are then transformed and added to the large uv grid. The computations have a simple, highly parallel structure that maps very well onto massively parallel hardware such as graphical processing units (GPUs). Despite being more expensive in pure computation count, the throughput is comparable to classical W-projection. The accuracy is close to classical gridding with a continuous convolution kernel. Compared to gridding methods that use a sampled convolution function, the new method is more accurate. Hence, the new method is at least as fast and accurate as classical W-projection, while allowing for the correction for quickly varying direction-dependent effects.

Faceting for direction-dependent spectral deconvolution

The new generation of radio interferometers is characterized by high sensitivity, wide fields of view and large fractional bandwidth. To synthesize the deepest images enabled by the high dynamic range of these instruments requires us to take into account the direction-dependent Jones matrices, while estimating the spectral properties of the sky in the imaging and deconvolution algorithms. In this paper we discuss and implement a wideband wide-field spectral deconvolution framework (ddfacet) based on image plane faceting, that takes into account generic direction-dependent effects. Specifically, we present a wide-field co-planar faceting scheme, and discuss the various effects that need to be taken into account to solve for the deconvolution problem (image plane normalization, position-dependent Point Spread Function, etc). We discuss two wideband spectral deconvolution algorithms based on hybrid matching pursuit and sub-space optimisation respectively. A few interesting technical features incorporated in our imager are discussed, including baseline dependent averaging, which has the effect of improving computing efficiency. The version of ddfacet presented here can account for any externally defined Jones matrices and/or beam patterns.

The Pointing Self-calibration Algorithm for Aperture Synthesis Radio Telescopes

Abstract This paper is concerned with algorithms for calibration of direction-dependent effects (DDE) in aperture synthesis radio telescopes (ASRT). After correction of direction-independent effects (DIE) using self-calibration, imaging performance can be limited by the imprecise knowledge of the forward gain of the elements in the array. In general, the forward gain pattern is directionally dependent and varies with time due to a number of reasons. Some factors, such as rotation of the primary beam with Parallactic Angle for Azimuth–Elevation mount antennas are known a priori. Some, such as antenna pointing errors and structural deformation/projection effects for aperture-array elements cannot be measured a priori. Thus, in addition to algorithms to correct for DD effects known a priori, algorithms to solve for DD gains are required for high dynamic range imaging. Here, we discuss a mathematical framework for antenna-based DDE calibration algorithms and show that this framework leads to computationally efficient optimal algorithms that scale well in a parallel computing environment. As an example of an antenna-based DD calibration algorithm, we demonstrate the Pointing SelfCal (PSC) algorithm to solve for the antenna pointing errors. Our analysis show that the sensitivity of modern ASRT is sufficient to solve for antenna pointing errors and other DD effects. We also discuss the use of the PSC algorithm in real-time calibration systems and extensions for antenna Shape SelfCal algorithm for real-time tracking and corrections for pointing offsets and changes in antenna shape.

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

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 Square Kilometre Array, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. matlab code is available on GitHub.