Calculations for a disk source and a general detector using a radiation vector potential

A closed form expression for a radiation vector potential is derived for a generalized disk radiation source. By applying Stokes's theorem the surface integral for the radiation flux into a general detector is converted into a much simpler line integral of the vector potential around the edge of the detector. This line integral can be easily evaluated for general detector geometry and general location and angular orientation relative to the disk source. For a number of cases the line integral reduces to integrals of Bessel functions which give various generalizations of Ruby's formula. Explicit formulas and numerical results for the geometric efficiency are given for circular and elliptical detectors displaced and rotated relative to the disk source. Detectors with general polygonal boundaries are considered and formulas and sample numerical results are given. For uniform surface emissivity the corresponding formulas for a disk detector and a general planar source are easily obtained. Formulas are also obtained for a scalar radiation potential and some limitations for its applicability are identified.