  Motivated by the desire for wide-field images with well-defined statistical
properties for 21cm cosmology, we implement an optimal mapping pipeline that
computes a maximum likelihood estimator for the sky using the interferometric
measurement equation. We demonstrate this direct optimal mapping with data from
the Hydrogen Epoch of Reionization (HERA) Phase I observations. After
validating the pipeline with simulated data, we develop a maximum likelihood
figure-of-merit for comparing four sky models at 166MHz with a bandwidth of
100kHz. The HERA data agree with the GLEAM catalogs to <10%. After subtracting
the GLEAM point sources, the HERA data discriminate between the different
continuum sky models, providing most support for the model of Byrne et al.
2021. We report the computation cost for mapping the HERA Phase I data and
project the computation for the HERA 320-antenna data; both are feasible with a
modern server. The algorithm is broadly applicable to other interferometers and
is valid for wide-field and non-coplanar arrays.
