  We study the problem of proper discretizing and sampling issues related to
geodesic X-ray transforms on simple surfaces, and illustrate the theory on
simple geodesic disks of constant curvature. Given a notion of band limit on a
function, we provide the minimal sampling rates of its X-ray transform for a
faithful reconstruction. In Cartesian sampling, we quantify the quality of a
sampling scheme depending on geometric parameters of the surface (e.g.
curvature and boundary curvature), and the coordinate system used to represent
the space of geodesics. When aliasing happens, we explain how to predict the
location, orientation and frequency of the artifacts.
