  We present the deepest wide-field 115-166 MHz image at sub-arcsecond
resolution spanning an area of 2.5 by 2.5 degrees centred at the ELAIS-N1 deep
field. To achieve this, we improved the calibration for the International LOFAR
Telescope. This enhancement enabled us to efficiently process 32 hrs of data
from four different 8-hr observations using the high-band antennas (HBAs) of
all 52 stations, covering baselines up to approximately 2,000 km across Europe.
The DI calibration was improved by using an accurate sky model and refining the
series of calibration steps on the in-field calibrator, while the DD
calibration was improved by adopting a more automated approach for selecting
the DD calibrators and inspecting the self-calibration on these sources. We
also added an additional round of self-calibration for the Dutch core and
remote stations in order to refine the solutions for shorter baselines. To
complement our highest resolution at 0.3", we also made intermediate resolution
wide-field images at 0.6" and 1.2". Our resulting wide-field images achieve a
central noise level of 14 muJy/beam at 0.3", doubling the depth and uncovering
four times more objects than the Lockman Hole deep field image at comparable
resolution but with only 8 hrs of data. Compared to LOFAR imaging without the
international stations, we note that due to the increased collecting area and
the absence of confusion noise, we reached a point-source sensitivity
comparable to a 500-hr ELAIS-N1 6" image with 16 times less observing time.
Importantly, we have found that the computing costs for the same amount of data
are almost halved (to about 139,000 CPU hrs per 8 hrs of data) compared to
previous efforts, though they remain high. Our work underscores the value and
feasibility of exploiting all Dutch and international LOFAR stations to make
deep wide-field images at sub-arcsecond resolution.
