In a quantitative description of bioluminescence (BL) and chemiluminescence (CL) phenomena, it is indispensable to know the total fluxes of radiation emitted by the sources studied. Such knowledge is necessary for determining the quantum yields of the examined BL and CL reactions, for comparing the data measured by different optical radiometers (luminometers), and for expressing the power of the emitted radiation in absolute units, i.e., in watts or as a number of photons per specified time period. This paper presents an integral formula for calculating radiative fluxes incident on a planar-circular detector from a volume multiple-point BL or CL source partially or completely filling an open coaxial cylindrical reactor. The formula represents the solution to the basic radiometric equation applied to the point emitters embedded within a homogeneous substrate separated from the detector by a different optical homogeneous isotropic medium. All calculations were performed for a nontransparent cylindrical reactor when the surface reflections were neglected and when optical radiation was incident on the detector through an open end of the cylindrical reactor. No additional restrictions were made with respect to the spatial distribution of the point emitters and angular distribution of the emitted radiations, so that the formula is applicable for arbitrarily distributed and arbitrarily radiating point emitters composing a BL or CL source.
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