The geometrical optics analysis of optical systems calls for an understanding of how an input energy intensity pattern is transformed after reflection or refraction. We present explicit formulas for the energy conservation equation, which relates input and output intensity patterns, and for the divergence factor, which describes the amplitude of an electric field after reflection or refraction. These formulas are obtained for optical systems consisting of a point source of energy, a single reflector or refractor, and a receiver surface. No symmetry requirements are imposed on either surface, nor is the receiver required to be a wave front of the system. In this general setting we derive the two expressions explicitly in terms of the polar radius of the reflector or refractor and its first and second partial derivatives. As an application we use our formulas to compute analytically the corresponding intensity expressions for conic surfaces. Finally, we present an algorithm for numerical computation of the output intensities. In addition to their use in optical systems, the derived formulas should be useful in the analysis of microwave antennas and radomes.
© 1995 Optical Society of America
Elsa Newman and Vladimir Oliker, "Determining the intensities produced by reflected and refracted wave fronts in geometrical optics," J. Opt. Soc. Am. A 12, 784-793 (1995)