A planar circular detector based on multiple point chemi- or bio-luminescent source within a coaxial cylindrical reactor

An analytical method was proposed for calculating radiative fluxes incident on a planar circular detector from a volume multiple point chemi- or bio-luminescent source inside a coaxial cylindrical reactor. The method was designed for a cylindrical reactor when the surface reflections were neglected and when chemi- or bio-luminescence reaches a detector embedded in the same homogeneous optical medium as the point emitters of the volume multiple point source model. The radiative fluxes from arbitrarily distributed point emitters were expressed by one generalized quadruple-integral formula. Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor. Selected results were computed and illustrated graphically. The obtained formulas are suitable for optimizing and/or calibrating the considered source-detectors systems (optical radiometers or luminometers) and determining radiative fluxes generated by chemical, biological, and physical processes leading to chemi-, bio-, radio-, and sono-luminescence for example.