Light Gathering Properties of Optical Systems with Extended Sources

Abstract

Light gathering properties are derived which are applicable to any optical system with an extended light source when all the light rays incident at the entrance aperture are collected at or pass through the exit aperture.A fundamental property of such an optical system is given by A3/A2=n22ω¯2(1−ω¯2/4π)/n32ω¯3(1−ω¯3/4π), where A3 = area of exit aperture imbedded in a medium of refractive index n3, A2 = area of entrance aperture imbedded in a medium of refractive index n2, ω¯3=mean solid angle of light at the entrance aperture,, and ω¯3=mean solid angle of light at the entrance aperture.