Generalized Monge-Ampere Equations for Freeform Optical System Design

摘要

We present the derivation of the generalized Monge-Ampere equation for two optical systems, viz. a freeform lens with parallel incident and refracted light rays, which transforms a source emittance into a desired target illuminance, and a freeform reflector converting the intensity of a point source into a far-field distribution. The derivations are based on Hamilton's characteristic functions. We outline a least-squares solution method and apply it to a test problem from laser beam shaping.