Generalizations of Rubyʹs formula for the geometric efficiency of a parallel-disk source and detector system

Rubyʹs formula for a parallel-disk source and detector system has been generalized to include non-coaxial disks and a source disk with an arbitrary radial distribution of surface emissivity. The results in all cases are given as one-dimensional integrals of products of Bessel functions and exponentials. For the case of coaxial disks, the solution can always be expressed in closed form as a sum of complete elliptic integrals. For the coaxial case with constant emissivity treated by Ruby, the solution is also given as a simple numerically friendly angular integral.