Phase effects in the diffraction of light: beyond the grating equation

Diffraction gratings affect the absolute phase of light in a way that is not obvious from the usual derivation of optical paths using the grating equation. For example, consider light which encounters first one and then the second of two parallel gratings. If one grating is moved parallel to its surface, the phase of the light diffracted from the grating pair is shifted by 2pi each time the grating is moved by one grating constant, even though the geometric path length is not altered by the motion. This additional phase shift must be included when incorporating diffraction gratings in interferometers.