Necessary and Sufficient Consistency Conditions for Fanbeam Projections Along a Line

In medical imaging, a fanbeam projection refers to a collection of line integrals of some two-dimensional function, for lines converging on a point known as the source point for X-ray applications. In this work, necessary and sufficient consistency conditions (also known as range conditions) are given for fanbeam projections when the source trajectory follows an infinite straight line. The conditions are specified for both angular and linear parameterizations of the projection rays. In both cases, integrals of the fanbeam projections multiplied by a certain function will be a polynomial in the trajectory variable, so these consistency conditions can be considered true analogs of the well-known Helgason-Ludwig range conditions for parallel projections.