Sub-arcsecond imaging with the International LOFAR Telescope I.
  Foundational calibration strategy and pipeline
  [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.
