Pixelated liquid crystal displays have been widely used as spatial light modulators to implement programmable diffractive optical elements, particularly diffractive lenses. Many different applications of such components have been developed in information optics and optical processors that take advantage of their properties of great flexibility, easy and fast refreshment, and multiplexing capability in comparison with equivalent conventional refractive lenses. We explore the application of programmable diffractive lenses displayed on the pixelated screen of a liquid crystal on silicon spatial light modulator to ophthalmic optics. In particular, we consider the use of programmable diffractive lenses for the visual compensation of refractive errors (myopia, hypermetropia, astigmatism) and presbyopia. The principles of compensation are described and sketched using geometrical optics and paraxial ray tracing. For the proof of concept, a series of experiments with artificial eye in optical bench are conducted. We analyze the compensation precision in terms of optical power and compare the results with those obtained by means of conventional ophthalmic lenses. Practical considerations oriented to feasible applications are provided.