Principle of least wave change

Fermat's principle of least time has some well-known limitations. It does not, for example, apply to diffraction gratings and holograms, because it does not include the concept of waves. The substitution of least number of waves in flight for least time of flight and the addition of a term that is a function of the grating frequency result in a generalized principle. It is easy to remember because it is based on only the number of waves minus the number of grooves, and it would be especially useful when refraction and diffraction are combined, as, for example, in some holographic optical elements.