The flux of radiation incident on a circular planar detector from a coaxial circular plane extended source

Abstract

A radiometric formula was derived for calculating fluxes of radiation from a coaxial planar circular source transmitted through one homogeneous isotropic medium on a planar circular detector. This formula was obtained using fundamental laws of classical radiometry. The general solution was described by quadruple definite integrals as dependent on the source radiance, on the radii of the source and the detector, and on the source–detector distance. For a wide range of source models with various angular distributions of radiances these definite integrals can be expressed in closed form and the formula simplifies considerably. To demonstrate how this formula can be used the solution was applied to the radiation emitted by the planar circular Lambertian source model. Some calculated results were illustrated graphically and analysed.