The least action principle of Fermat, Maupertuis, Lagrange, Hamilton
and others lies at the foundation of optics and classical mechanics. Given the
initial and final positions of a system of particles (rays), the orbit of the
particles (rays) is determined by minimizing the action. I shall describe a
generalization of this principle that applies to waves. The principle will be
derived first for the Schroedinger equation, and then it will be generalized
to other wave equations and to singular solutions. I shall
also consider the application of the principle to the design of phase sensors
and illumination systems.