Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface

An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Rubyʹs formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops can be directly applied to the corresponding source/detector calculation. All formulas give G = 0.5 exactly in the limit of a very large detector.