Optical radiation flux incident on a circular disc from a coaxial circular and planar multiple-point source separated by a homogeneous plane-parallel plate

摘要

Calculation of the radiation flux incident on a circular disc from a coaxial circular and planar multiple-point source is necessary in many radiometric techniques. Such calculations are required in various problems in physics, chemistry and biology for assembling, optimizing and calibrating radiometric systems measuring optical radiation from a circular-planar multiple-point source. However, in some radiometric systems the source must be separated from the irradiated disc. In a simple case a single transparent homogeneous plane-parallel plate (PPP) can be considered to separate the source from the disc. In this paper a formula is derived to calculate the incoherent optical radiation flux incident on a circular disc from several types of multiple-point sources separated from the disc by the transparent homogeneous PPP. This formula is solved in the cylindrical coordinate system and is expressed as a series of single integrals of some superposed elementary functions. These functions are dependent on the radii of the source and the irradiated disc, on the distances between the source and the PPP and between the PPP and the disc, on the absorption coefficient of the PP and on the refractive indices of all optical media between the source and the disc. the solution is obtained for transparent homogeneous media. Some examples illustrating practical application of the formula are presented as three-dimensional surface plots.