Optical radiation flux illuminating a circular disk from an off-axis point source through two different homogeneous refractive media

Abstract

A general formula is derived for calculating the optical radiation flux that illuminates a circular disk from an off-axis point source if the disk and the source are embedded in two different homogeneous media and if the media form a refractive planar interface parallel to the disk. This formula is represented by a set of four different expressions, each valid for a different range of distances determining the position between the source and the disk symmetry axis. These expressions are given as double-definite integrals with the boundary conditions described by some transcendental equations. All expressions represent functions depending on the disk radius, on the distances between the refractive plane from the disk and from the source, on the distance between the source and the disk symmetry axis, on the refractive indices and on the absorption coefficients of both media embedding the source and the disk. In many practical situations the formula simplifies to a set of five single integrals that can be easily calculated numerically. For illustrative purposes some examples of the formula used for calculating optical radiative fluxes are presented and illustrated graphically.