  In this work we study in details the influence of pure astronomical
refraction on solar metrologic measurements made from ground-based full disk
imagery and provide the tools for correcting the measurements and estimating
the associated uncertainties.For a given standard atmospheric model, we first
use both analytical and numerical methods in order to test the validity of the
commonly or historically used approximations of the differential effect of
refraction as a function of zenith distance. For a given refraction model, we
provide the exact formulae for correcting solar radius measurements at any
heliographic angle and for any zenith distance. Then, using solar images
recorded in the near infrared between 2011 and 2016, we show that these
corrections can be applied up to $70\deg$ using the usual approximate formulae
and can be extended up to $80\deg$ of zenith distance provided that a standard
atmospheric model and a full numerical integration of the refraction integral
are used. We also provide estimates of the absolute uncertainties associated
with the differential refraction corrections and show that approximate formulae
can be used up to $80\deg$ of zenith distance for computing these
uncertainties. For a given instrumental setup and the knowledge of the
uncertainties associated with local weather records, this can be used to fix
the maximum zenith distance one can observe depending on the required
astrometric accuracy.
