Geometrical optics field of general optical systems

Abstract

Using the stationary phase approximation of the Kirchoff diffraction integral, we derive a general expression for the field in the image space of a point source for an arbitrary optical system. The concept of an “optical path matrix” (OPM), which is the Hessian of the point eiconal, is introduced. Luminosity, caustic surfaces, and evanescent fields are defined in terms of the OPM. Detailed consideration of the single-interface problem yields solutions in terms of the Gaussian, mean, and normal curvatures of the interface. A complete solution of the simple lens is given as an example of a system with two refracting surfaces.