THE HAMILTON CHARACTERISTIC FUNCTIONS IN THE DESIGN OF AN ASPHERICAL LENS

Abstract

After a brief review of Hamiltonian optics, we find the parametric equations for a correcting surface of a plane-aspherical lens. Under the variation of all the parameters involved, the general shapes adopted by this aspherical surface are shown. When the source position coincides with the plane refracting surface, the aspherical surface recovers a cartesian oval shape, as expected. As an example of this, we recover explicitly the cases of the aplanatic sphere and the Limacon of Pascal in analytical form.