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LOFAR, the Low-Frequency Array, is a powerful new radio telescope operating between 10 and 240 MHz. LOFAR allows detailed sensitive high-resolution studies of the low-frequency radio sky. At the same time LOFAR also provides excellent short baseline coverage to map diffuse extended emission. However, producing high-quality deep images is challenging due to the presence of direction dependent calibration errors, caused by imperfect knowledge of the station beam shapes and the ionosphere. Furthermore, the large data volume and presence of station clock errors present additional difficulties. In this paper we present a new calibration scheme, which we name facet calibration, to obtain deep high-resolution LOFAR High Band Antenna images using the Dutch part of the array. This scheme solves and corrects the direction dependent errors in a number of facets that cover the observed field of view. Facet calibration provides close to thermal noise limited images for a typical 8 hr observing run at $sim$ 5arcsec resolution, meeting the specifications of the LOFAR Tier-1 northern survey.
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A number of hardware upgrades for the Low-Frequency Array (LOFAR) are currently under development. These upgrades are collectively referred to as the LOFAR 2.0 upgrade. The first stage of LOFAR 2.0 will introduce a distributed clock signal and allow for simultaneous observation with all the low-band and high-band antennas of the array. Our aim is to provide a tool for accurate simulations of LOFAR 2.0. We present a software to simulate LOFAR and LOFAR 2.0 observations, which includes realistic models for all important systematic effects such as the first and second order ionospheric corruptions, time-variable primary-beam attenuation, station based delays and bandpass response. The ionosphere is represented as a thin layer of frozen turbulence. Furthermore, thermal noise can be added to the simulation at the expected level. We simulate a full 8-hour simultaneous low- and high-band antenna observation of a calibrator source and a target field with the LOFAR 2.0 instrument. The simulated data is calibrated using readjusted LOFAR calibration strategies. We examine novel approaches of solution-transfer and joint calibration to improve direction-dependent ionospheric calibration for LOFAR. We find that the calibration of the simulated data behaves very similarly to a real observation and reproduces characteristic properties of LOFAR data such as realistic solutions and image quality. We analyze strategies for direction-dependent calibration of LOFAR 2.0 and find that the ionospheric parameters can be determined most accurately when combining the information of the high-band and low-band in a joint calibration approach. In contrast, the transfer of total electron content solutions from the high-band to the low-band shows good convergence but is highly susceptible to the presence of non-ionospheric phase errors in the data.
We describe a method for spectral cleaning and timing calibration of short voltage time series data from individual radio interferometer receivers. It makes use of the phase differences in Fast Fourier Transform (FFT) spectra across antenna pairs. For strong, localized terrestrial sources these are stable over time, while being approximately uniform-random for a sum over many sources or for noise. Using only milliseconds-long datasets, the method finds the strongest interfering transmitters, a first-order solution for relative timing calibrations, and faulty data channels. No knowledge of gain response or quiescent noise levels of the receivers is required. With relatively small data volumes, this approach is suitable for use in an online system monitoring setup for interferometric arrays. We have applied the method to our cosmic-ray data collection, a collection of measurements of short pulses from extensive air showers, recorded by the LOFAR radio telescope. Per air shower, we have collected 2 ms of raw time series data for each receiver. The spectral cleaning has a calculated optimal sensitivity corresponding to a power signal-to-noise ratio of 0.08 (or -11 dB) in a spectral window of 25 kHz, for 2 ms of data in 48 antennas. This is well sufficient for our application. Timing calibration across individual antenna pairs has been performed at 0.4 ns precision; for calibration of signal clocks across stations of 48 antennas the precision is 0.1 ns. Monitoring differences in timing calibration per antenna pair over the course of the period 2011 to 2015 shows a precision of 0.08 ns, which is useful for monitoring and correcting drifts in signal path synchronizations. A cross-check method for timing calibration is presented, using a pulse transmitter carried by a drone flying over the array. Timing precision is similar, 0.3 ns.
Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the modes beyond the instrumental horizon (EoR/CD window). We show that this structure largely arises due to strong instrumental polarization leakage ($sim30%$) towards {Cas,A} ($sim21$ kJy at 81 MHz, brightest source in northern sky), which is far away from primary field of view. We measure an extremely small ionospheric diffractive scale ($r_{text{diff}} approx 430$ m at 60 MHz) towards {Cas,A} resembling pure Kolmogorov turbulence compared to $r_{text{diff}} sim3 - 20$ km towards zenith at 150 MHz for typical ionospheric conditions. This is one of the smallest diffractive scales ever measured at these frequencies. Our work provides insights in understanding the nature of aforementioned effects and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA) in the same frequency window.
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 Bootes and LH fields at 150 MHz, totaling $sim80$ and $sim100$ hours of integration respectively and reaching unprecedented noise levels at these low frequencies of $lesssim30$ and $lesssim23$ $mu$Jy/beam in the inner $sim3$ deg$^2$. This approach is also being used to reduce the LoTSS-wide data for the second data release.
[abridged] The International LOFAR Telescope is an interferometer with stations spread across Europe. With baselines of up to ~2,000 km, LOFAR has the unique capability of achieving sub-arcsecond resolution at frequencies below 200 MHz, although this is technically and logistically challenging. Here we present a calibration strategy that builds on previous high-resolution work with LOFAR. We give an overview of the calibration strategy and discuss the special challenges inherent to enacting high-resolution imaging with LOFAR, and describe the pipeline, which is publicly available, in detail. We demonstrate the calibration strategy by using the pipeline on P205+55, a typical LOFAR Two-metre Sky Survey (LoTSS) pointing. We perform in-field delay calibration, solution referencing to other calibrators, self-calibration, and imaging of example directions of interest in the field. For this specific field and these ionospheric conditions, dispersive delay solutions can be transferred between calibrators up to ~1.5 degrees away, while phase solution transferral works well over 1 degree. We demonstrate a check of the astrometry and flux density scale. Imaging in 17 directions, the restoring beam is typically 0.3 x 0.2 although this varies slightly over the entire 5 square degree field of view. We achieve ~80 to 300 $mu$Jy/bm image rms noise, which is dependent on the distance from the phase centre; typical values are ~90 $mu$Jy/bm for the 8 hour observation with 48 MHz of bandwidth. Seventy percent of processed sources are detected, and from this we estimate that we should be able to image ~900 sources per LoTSS pointing. This equates to ~3 million sources in the northern sky, which LoTSS will entirely cover in the next several years. Future optimisation of the calibration strategy for efficient post-processing of LoTSS at high resolution (LoTSS-HR) makes this estimate a lower limit.
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