Optical radiation flux illuminating a circular disk from an off-axis point source separated by a homogeneous plane-parallel plate.

Abstract

In a number of techniques that measure weak fluxes of optical radiation, it is frequently necessary to keep a detector in a medium different from that of the radiating source by separating it from the source with a planar transparent window. However, sources such as systems of light-emitting diodes, large-fiber illuminators, and microscopic living objects that emit biological luminescence may sometimes be regarded as multiple-point sources. To estimate the fluxes of optical radiation illuminating a surface from a nonuniformly distributed multiple-point source, a method for calculating fluxes from a single off-axis point source is needed. A formula is derived to estimate a flux of temporally incoherent optical radiation incident on a circular disk from a single off-axis point source separated by a plane-parallel plate (PPP). This formula is expressed by a series of single integrals of some superposed elementary functions. These functions depend on the variables that characterize the point-source-plane-parallel-plate-circular-disk geometry and on the optical properties of the media that separate the source from the PPP and the PPP from the disk. The solution was obtained for isotropic media. For illustrative purposes some examples of the use of the formula are presented. The selected results are illustrated by three-dimensional surface plots and compared with the values of the fluxes calculated for radiation incident on the disk from a point source not separated by a PPP.