Geometric theory of the grating

Geometric theory of the grating is developed, with special emphasis on the relation between the properties of holographic gratings and those of mechanically ruled gratings. The theory is applicable to practically all types of holographic and mechanically ruled gratings, including aspheric gratings. General expressions are given for the effective grating constant, the grating equation, the focal curves, and the light-path function. Possible applications of the theory to the design of aberration-corrected gratings are also described.