The Feynman path integral and its optical applications

There is a fruitful analogy between mechanics and optics. To describe the transition from quantum mechanics to classical mechanics, Feynman introduced the concept of an “integral over all paths”. The Feynman integral is used here to describe the transition from wave optics to geometrical optics. We suggest simple mathematical tools that allow use the Feynman integral and its approximation to calculate the radiation transport through an optically inhomogeneous layer and through an aperture in an infinite opaque screen.