In this work we study in details the influence of pure astronomical refraction on solar metrological measurements made from ground-based full disc 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° using the usual approximate formulae and can be extended up to 80° 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° 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.