An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source

The analytical determination of the solid angle subtended by a circular detector for a line source in a parallel plane, whose midpoint is co-axial with the detector's center, is of some relevance to the medical and nuclear power fields. No report has been found in the literature of a closed-form solution to this problem. We present a first principles solution to the problem along with a graph, which gives some indication of the behavior of the derived expression.