MIGHTEE: total intensity radio continuum imaging and the COSMOS /
  XMM-LSS Early Science fields
  MIGHTEE is a galaxy evolution survey using simultaneous radio continuum,
spectro-polarimetry, and spectral line observations from the South African
MeerKAT telescope. When complete, the survey will image $\sim$20 deg$^{2}$ over
the COSMOS, E-CDFS, ELAIS-S1, and XMM-LSS extragalactic deep fields with a
central frequency of 1284 MHz. These were selected based on the extensive
multiwavelength datasets 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 deg$^{2}$) and a three-pointing mosaic in XMM-LSS (3.5 deg$^{2}$).
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 $\sim$8$''$
angular resolution, and meeting the survey specifications. We also produce
images at $\sim$5$''$ resolution that are $\sim$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 9,896
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 broadband 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.
